Question: Real life applications of Topology


Question: Whats your favorite proof accessible to a general audience?


Question: Pullback and Pushforward Isomorphism of Sheaves


Question: Physical meaning of the null space of a matrix


Question: How do you explain to a 5th grader why division by zero is meaningless?


Question: Overview of basic facts about Cauchy functional equation


Question: Is 10 closer to infinity than 1?


Question: Examples of problems that are easier in the infinite case than in the finite case.


Question: Help find hard integrals that evaluate to $59$?


Question: Is the inverse of a symmetric matrix also symmetric?


Question: When to learn category theory?


Question: In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False?


Question: Modular exponentiation by hand ($a^b\bmod c$)


Question: How were old-school mathematics graphics created?


Question: Infiniteness of non-twin primes.


Question: probability $2/4$ vs $3/6$


Question: Continuous projections on $\ell_1$ with norm $>1$


Question: Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$?


Question: All real numbers in $[0,2]$ can be represented as $\sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \dots}}}$


Question: Olympiad Inequality $\sum\limits_{cyc} \frac{x^4}{8x^3+5y^3} \geqslant \frac{x+y+z}{13}$


Question: What is the difference between independent and mutually exclusive events?


Question: What is the Jacobian matrix?


Question: If squaring a number means multiplying that number with itself then shouldnt taking square root of a number mean to divide a number by itself?


Question: Is there a known well ordering of the reals?


Question: Intuition behind Conditional Expectation


Question: Is there an inverted dot product?


Question: Find the average of $\sin^{100} (x)$ in 5 minutes?


Question: How to find the Galois group of a polynomial?


Question: Strategies for Effective Self-Study


Question: What did Alan Turing mean when he said he didnt fully understand dy/dx?


Question: Is there a domain larger than (i.e., a supserset of) the complex number domain?


Question: Motivation for the rigour of real analysis


Question: Probability that a stick randomly broken in five places can form a tetrahedron


Question: The deep reason why $\int \frac{1}{x}\operatorname{d}x$ is a transcendental function ($\log$)


Question: Expected time to roll all 1 through 6 on a die


Question: Proofs of AM-GM inequality


Question: The math behind Warren Buffetts famous rule – never lose money


Question: Compute $\int_0^{\pi/4}\frac{(1-x^2)\ln(1+x^2)+(1+x^2)-(1-x^2)\ln(1-x^2)}{(1-x^4)(1+x^2)} x\exp(\frac{x^2-1}{x^2+1}) dx$


Question: derivative of cost function for Logistic Regression


Question: Construction of a Borel set with positive but not full measure in each interval


Question: Are the proofs by contradiction weaker than other proofs?


Question: Why are There No Triernions (3-dimensional analogue of complex numbers / quaternions)?


Question: What parts of a pure mathematics undergraduate curriculum have been discovered since $1964?$


Question: Is black hole pattern possible in Conways Game of Life that eats/clears everything?


Question: A multiplication algorithm found in a book by Paul Erdős: how does it work?


Question: Are all limits solvable without LHôpital Rule or Series Expansion


Question: $n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesnt use Chebyshevs theorem?


Question: Convergence of $\sum_{n=1}^{\infty} \frac{\sin(n!)}{n}$


Question: When is matrix multiplication commutative?


Question: What is the difference and relationship between the binomial and Bernoulli distributions?


Question: Is infinity a number?


Question: Am I just not smart enough?


Question: What is the smallest unknown natural number?


Question: Is there a positive definition for irrational numbers?


Question: Solving Special Function Equations Using Lie Symmetries


Question: Gross-Zagier formulae outside of number theory


Question: Why is the derivative of a circles area its perimeter (and similarly for spheres)?


Question: Getting better at proofs


Question: Mathematical equivalent of Feynmans Lectures on Physics?


Question: How often does it happen that the oldest person alive dies?


Question: Do mathematicians, in the end, always agree?


Question: Can an infinite sum of irrational numbers be rational?


Question: Unexpected examples of natural logarithm


Question: What are the Axiom of Choice and Axiom of Determinacy?


Question: Least prime of the form $38^n+31$


Question: Different ways to prove there are infinitely many primes?


Question: Can you give an example of a complex math problem that is easy to solve?


Question: Proof of Frullanis theorem


Question: More than 99% of groups of order less than 2000 are of order 1024?


Question: Find all functions $f$ such that if $a+b$ is a square, then $f(a)+f(b)$ is a square


Question: Does a four-variable analog of the Hall-Witt identity exist?


Question: How do I get the square root of a complex number?


Question: Prove that $||x|-|y||\le |x-y|$


Question: Prove that simultaneously diagonalizable matrices commute


Question: Could someone explain conditional independence?


Question: Good Book On Combinatorics


Question: A good way to retain mathematical understanding?


Question: Why is it important for a matrix to be square?


Question: Are there real world applications of finite group theory?


Question: Why cant calculus be done on the rational numbers?


Question: Why is there no remainder in multiplication


Question: What are the issues in modern set theory?


Question: What makes a theorem fundamental?


Question: Why is an average of an average usually incorrect?


Question: Finding a primitive root of a prime number


Question: Do factorials really grow faster than exponential functions?


Question: What exactly is the difference between a derivative and a total derivative?


Question: Nice proofs of $\zeta(4) = \frac{\pi^4}{90}$?


Question: Why, historically, do we multiply matrices as we do?


Question: Why do we still do symbolic math?


Question: Fastest way to meet, without communication, on a sphere?


Question: Grothendieck s question - any update?


Question: How to sum this series for $\pi/2$ directly?


Question: In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?


Question: Can someone clearly explain about the lim sup and lim inf?


Question: How can I understand and prove the sum and difference formulas in trigonometry?


Question: Is zero odd or even?


Question: Continuity of the roots of a polynomial in terms of its coefficients


Question: In calculus, which questions can the naive ask that the learned cannot answer?


Question: Why are mathematical proofs that rely on computers controversial?


Question: Getting Students to Not Fear Confusion


Question: Topology: The Board Game


Question: Fibonacci number that ends with 2014 zeros?


Question: What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into?


Question: Generalization of Liouvilles theorem


Question: Complete course of self-study


Question: Motivation for Ramanujans mysterious $\pi$ formula


Question: What is the most unusual proof you know that $\sqrt{2}$ is irrational?


Question: How do we know an $ \aleph_1 $ exists at all?


Question: Connected metric spaces with disjoint open balls


Question: Why is the volume of a sphere $\frac{4}{3}\pi r^3$?


Question: Incremental averageing


Question: How to show that a set of discontinuous points of an increasing function is at most countable


Question: If I flip a coin 1000 times in a row and it lands on heads all 1000 times, what is the probability that its an unfair coin?


Question: What made you choose your research field?


Question: How Do You Actually Do Your Mathematics?


Question: Is this continuous analogue to the AM–GM inequality true?


Question: Open mathematical questions for which we really, really have no idea what the answer is


Question: Is the derivative the natural logarithm of the left-shift?


Question: Has Prof. Otelbaev shown existence of strong solutions for Navier-Stokes equations?


Question: lim sup and lim inf of sequence of sets.


Question: Why is it hard to prove whether $\pi+e$ is an irrational number?


Question: How do you go about learning mathematics?


Question: Is $[0,1]$ a countable disjoint union of closed sets?


Question: Chatting about mathematics (with real-time LaTeX rendering)


Question: Calculating the integral $\int_0^\infty \frac{\cos x}{1+x^2}\, \mathrm{d}x$ without using complex analysis


Question: Finding the limit of $\frac {n}{\sqrt[n]{n!}}$


Question: What is the single most influential book every mathematician should read?


Question: Logic puzzle: Which octopus is telling the truth?


Question: Why is a geometric progression called so?


Question: Why, intuitively, is the order reversed when taking the transpose of the product?


Question: Prove the theorem on analytic geometry in the picture.


Question: Good Physical Demonstrations of Abstract Mathematics


Question: Can I think of Algebra like this?


Question: Ways to evaluate $\int \sec \theta \, \mathrm d \theta$


Question: Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$


Question: Does this property characterize a space as Hausdorff?


Question: All polynomials with no natural roots and integer coefficients such that $\phi(n)|\phi(P(n))$


Question: How to prove that eigenvectors from different eigenvalues are linearly independent


Question: Lebesgue integral basics


Question: Why rationalize the denominator?


Question: Mathematicians ahead of their time?


Question: Are all algebraic integers with absolute value 1 roots of unity?


Question: Can we remove any prime number with this strange process?


Question: Produce an explicit bijection between rationals and naturals?


Question: Is math built on assumptions?


Question: Riddles that can be solved by meta-assumptions


Question: Why are vector spaces not isomorphic to their duals?


Question: What are some examples of mathematics that had unintended useful applications much later?


Question: Division by $0$ and its restrictions


Question: Theorems with an extraordinary exception or a small number of sporadic exceptions


Question: True or false? $x^2\ne x\implies x\ne 1$


Question: $\int_{-\infty}^{+\infty} e^{-x^2} dx$ with complex analysis


Question: An integral involving Airy functions $\int_0^\infty\frac{x^p}{\operatorname{Ai}^2 x + \operatorname{Bi}^2 x}\mathrm dx$


Question: Does notation ever become easier?


Question: Mathematician vs. Computer: A Game


Question: Non-textbook Math book recommendation to read to my kids


Question: Cardioid in coffee mug?


Question: Direct proof that the wedge product preserves integral cohomology classes?


Question: How did Hermite calculate $e^{\pi\sqrt{163}}$ in 1859?


Question: What does it mean to have a determinant equal to zero?


Question: Why is the volume of a cone one third of the volume of a cylinder?


Question: Dont see the point of the Fundamental Theorem of Calculus.


Question: Comparing $\pi^e$ and $e^\pi$ without calculating them


Question: Is Bayes Theorem really that interesting?


Question: Unconventional mathematics books


Question: Does LHôpitals work the other way?


Question: Geometric interpretation of the Riemann-Roch for curves


Question: Whats the difference between theorem, lemma and corollary?


Question: Unusual mathematical terms


Question: Is infinity an odd or even number?


Question: How do you find the center of a circle with a pencil and a book?


Question: Using we have in maths papers


Question: How to learn from proofs?


Question: What are Some Tricks to Remember Fatous Lemma?


Question: Why dont analysts do category theory?


Question: Defining a manifold without reference to the reals


Question: Does a non-trivial solution exist for $f(x)=f(f(x))$?


Question: A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent


Question: A real number $x$ such that $x^n$ and $(x+1)^n$ are rational is itself rational


Question: Expectation of the maximum of gaussian random variables


Question: Simplest or nicest proof that $1+x \le e^x$


Question: What would base $1$ be?


Question: Should I put number combinations like 1111111 onto my lottery ticket?


Question: Continuous bijection from $(0,1)$ to $[0,1]$


Question: How is a system of axioms different from a system of beliefs?


Question: Why cant you add apples and oranges, but you can multiply and divide them?


Question: How can adding an infinite number of rationals yield an irrational number?


Question: Example of a very simple math statement in old literature which is (verbatim) a pain to understand


Question: Whats the largest possible volume of a taco, and how do I make one that big?


Question: Limit of sequence in which each term is defined by the average of preceding two terms


Question: Why are all the interesting constants so small?


Question: Help me put these enormous numbers in order: googol, googol-plex-bang, googol-stack and so on


Question: $4494410$ and friends


Question: A semigroup $X$ is a group iff for every $g\in X$, $\exists! x\in X$ such that $gxg = g$


Question: Arithmetic-geometric mean of 3 numbers


Question: Geometric way to view the truncated braid groups?


Question: Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$


Question: How to find a general sum formula for the series: 5+55+555+5555+.....?


Question: What is the difference between a class and a set?


Question: Why is $\frac{987654321}{123456789} = 8.0000000729?!$


Question: The Langlands program for beginners


Question: What makes elementary functions elementary?


Question: Why would I want to multiply two polynomials?


Question: If $x$, $y$, $x+y$, and $x-y$ are prime numbers, what is their sum?


Question: Mathematicians Tensors vs. Physicists Tensors


Question: Is the determinant that shows up accidental?


Question: Given a die, what is the probability that the second roll of a die will be less than the first roll?


Question: Why is the set of all sets a paradox, in Laymans terms?


Question: Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$


Question: What seemingly innocuous results in mathematics require advanced proofs?


Question: Prove $\left(\frac{2}{5}\right)^{\frac{2}{5}}<\ln{2}$


Question: How to convince a math teacher of this simple and obvious fact?


Question: What kind of symmetry is the symmetric group about?


Question: What are good math habits that have improved your mathematical practice?$ $


Question: math fallacy problem: $-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1$?


Question: Cover of Gödel, Escher, Bach


Question: Problems that become easier in a more general form


Question: How prove this nice limit $\lim\limits_{n\to\infty}\frac{a_{n}}{n}=\frac{12}{\log{432}}$


Question: When does a sequence of rotated-and-circumscribed rectangles converge to a square?


Question: Why is the area under a curve the integral?


Question: Good 1st PDE book for self study


Question: Importance of matrix rank


Question: Much less than, what does that mean?


Question: Simple beautiful math proof


Question: Anecdotes about famous mathematicians or physicists


Question: Why do bell curves appear everywhere?


Question: What are the differences between class, set, family, and collection?


Question: What is the solution to Nashs problem presented in A Beautiful Mind?


Question: Factorial and exponential dual identities


Question: The pepperoni pizza problem


Question: How to evaluate $\int_{0}^{\infty} \frac{x^{-\mathfrak{i}a}}{x^2+bx+1} \,\mathrm{d}x$ using complex analysis?


Question: A Case Against the Math Gene


Question: Complexity class of comparison of power towers


Question: Does $\lfloor \sqrt{p} \rfloor$ generate all natural numbers?


Question: Pointwise vs. Uniform Convergence


Question: What is the algebraic intuition behind Vieta jumping in IMO1988 Problem 6?


Question: GRE Subject Test - Past Papers, Books, Advice


Question: Can the golden ratio accurately be expressed in terms of $e$ and $\pi$


Question: How do you explain the concept of logarithm to a five year old?


Question: If $f_k \to f$ a.e. and the $L^p$ norms converge, then $f_k \to f$ in $L^p$


Question: What is a real-world metaphor for irrational numbers?


Question: Intuitive explanation of Cauchys Integral Formula in Complex Analysis


Question: Why should I believe in weak solutions to PDEs?


Question: Explain homotopy to me


Question: Prove elementarily that $\sqrt[n+1] {(n+1)!} - \sqrt[n] {n!}$ is strictly decreasing


Question: Root Calculation by Hand


Question: What does the dot product of two vectors represent?


Question: Whats the difference between simple induction and strong induction?


Question: What is the most elegant proof of the Pythagorean theorem?


Question: Is the vector cross product only defined for 3D?


Question: Best Maths Books for Non-Mathematicians


Question: Self-studying real analysis — Tao or Rudin?


Question: What are differences between affine space and vector space?


Question: If $(a_n)\subset[0,\infty)$ is non-increasing and $\sum a_n<\infty$, then $\lim{n a_n} = 0$


Question: Is arrow notation for vectors not mathematically mature?


Question: I roll a die repeatedly until I get 6, and then count the number of 3s I got. Whats my expected number of 3s?


Question: What is the difference between a Hamel basis and a Schauder basis?


Question: Is there any conjecture that has been proved to be solvable/provable but whose direct solution/proof is not yet known?


Question: Results that came out of nowhere.


Question: Can the product of infinitely many elements from $\mathbb Q$ be irrational?


Question: Divisibility by 7 rule, and Congruence Arithmetic Laws


Question: Can you make a sphere out of a plane?


Question: Cutting sticks puzzle


Question: The Right Triangle Game


Question: Geometric interpretation of $\det(A^T) = \det(A)$


Question: How to prove that exponential grows faster than polynomial?


Question: Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when its an integer


Question: Good book for self study of functional analysis


Question: If $S$ is an infinite $\sigma$ algebra on $X$ then $S$ is not countable


Question: $x^y = y^x$ for integers $x$ and $y$


Question: 100 blue-eyed islanders puzzle: 3 questions


Question: Surprise exam paradox?


Question: Demystify integration of $\int \frac{1}{x} \mathrm dx$


Question: Your favourite maths puzzles


Question: Number of simple edge-disjoint paths needed to cover a planar graph


Question: Good abstract algebra books for self study


Question: Does convergence in $L^p$ imply convergence almost everywhere?


Question: Is there any difference between mapping and function?


Question: Normal subgroup of prime index


Question: Implies ($\Rightarrow$) vs. Entails ($\models$) vs. Provable ($\vdash$)


Question: Learning mathematics as if an absolute beginner?


Question: Why did no student correctly find a pair of $2\times 2$ matrices with the same determinant and trace that are not similar?


Question: Will it become impossible to learn math?


Question: Should an undergrad accept that some things dont make sense, or study the foundation of mathematics to resolve this?


Question: Is $0! = 1$ because there is only one way to do nothing?


Question: Conjecture $\int_0^1\frac{\mathrm dx}{\sqrt{1-x}\ \sqrt[4]x\ \sqrt[4]{2-x\,\sqrt3}}\stackrel?=\frac{2\,\sqrt2}{3\,\sqrt[8]3}\pi$


Question: Why are groups more important than semigroups?


Question: Can someone explain these strange properties of $10, 11, 12$ and $13$?


Question: What is the best book for studying discrete mathematics?


Question: Why cant you square both sides of an equation?


Question: For any prime $p > 3$, why is $p^2-1$ always divisible by 24?


Question: Is the notorious $n^2 + n + 41$ prime generator the last of its type?


Question: Construct a function which is continuous in $[1,5]$ but not differentiable at $2, 3, 4$


Question: Easy math proofs or visual examples to make high school students enthusiastic about math


Question: Why do we define quotient groups for normal subgroups only?


Question: Formal proof for $(-1) \times (-1) = 1$


Question: Mathematically, why was the Enigma machine so hard to crack?


Question: Is it possible to represent every huge number in abbreviated form?


Question: $1=2$ | Continued fraction fallacy


Question: How is a group made up of simple groups?


Question: Cute Determinant Question


Question: Modelling the Moving Sofa


Question: Graph theoretic proof: For six irrational numbers, there are three among them such that the sum of any two of them is irrational.


Question: Contest problem: Show $\sum_{n = 1}^\infty \frac{n^2a_n}{(a_1+\cdots+a_n)^2}0$, $\sum_{n = 1}^\infty \frac{1}{a_n}<\infty$


Question: Proof of every convex function is continuous


Question: Are calculus and real analysis the same thing?


Question: A goat tied to a corner of a rectangle


Question: Predicting Real Numbers


Question: Why is abuse of notation tolerated?


Question: Why are gauge integrals not more popular?


Question: Do numbers get worse than transcendental?


Question: Whats so special about standard deviation?


Question: What concept does an open set axiomatise?


Question: Would you ever stop rolling the die?


Question: Geometric & Intuitive Meaning of $SL(2,R)$, $SU(2)$, etc... & Representation Theory of Special Functions


Question: References for multivariable calculus


Question: When is the closure of an open ball equal to the closed ball?


Question: Can manholes be made in other shapes than circles, that prevent the cover from being able to fall down its own hole?


Question: In what sense are math axioms true?


Question: Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$


Question: Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$


Question: What are some conceptualizations that work in mathematics but are not strictly true?


Question: Why do mathematicians sometimes assume famous conjectures in their research?


Question: Where are the axioms?


Question: How to prove that $\frac{\zeta(2) }{2}+\frac{\zeta (4)}{2^3}+\frac{\zeta (6)}{2^5}+\frac{\zeta (8)}{2^7}+\cdots=1$?


Question: How do we know that Cantors diagonalization isnt creating a different decimal of the same number?


Question: In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual?


Question: Determining information in minimum trials (combinatorics problem)


Question: What is the term for a factorial type operation, but with summation instead of products?


Question: Difference between gradient and Jacobian


Question: Why does Turn! Turn! Turn! equal 241217.524881?


Question: Is there a size of rectangle that retains its ratio when its folded in half?


Question: What is ultrafinitism and why do people believe it?


Question: Decidability of the Riemann Hypothesis vs. the Goldbach Conjecture


Question: Intuition in algebra?


Question: A continuous, nowhere differentiable but invertible function?


Question: Conjecture $\int_0^1\frac{dx}{\sqrt[3]x\,\sqrt[6]{1-x}\,\sqrt{1-x\left(\sqrt{6}\sqrt{12+7\sqrt3}-3\sqrt3-6\right)^2}}=\frac\pi9(3+\sqrt2\sqrt[4]{27})$


Question: Can someone explain this integration trick for log-sine integrals?


Question: Polynomials such that roots=coefficients


Question: Does $X\times S^1\cong Y\times S^1$ imply that $X\times\mathbb R\cong Y\times\mathbb R$?


Question: Do groups, rings and fields have practical applications in CS? If so, what are some?


Question: What is special about the numbers 9801, 998001, 99980001 ..?


Question: How does Cantors diagonal argument work?


Question: Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$


Question: Why is a circle in a plane surrounded by 6 other circles?


Question: Expected number of unpecked chicks - NYT article


Question: Whats the difference between $\mathbb{R}^2$ and the complex plane?


Question: What is your favorite application of the Pigeonhole Principle?


Question: Is mathematics just a bunch of nested empty sets?


Question: Easy example why complex numbers are cool


Question: Why is the construction of the real numbers important?


Question: Any rectangular shape on a calculator numpad when divided by 11 gives an integer. Why?


Question: Calculating the volume of a restaurant take-away box that is circular on the bottom and square on the top


Question: Paul Erdoss Two-Line Functional Analysis Proof


Question: Numbers $n$ such that the digit sum of $n^2$ is a square


Question: How to solve these two simultaneous divisibilities : $n+1\mid m^2+1$ and $m+1\mid n^2+1$


Question: Do most numbers have exactly $3$ prime factors?


Question: Can a row of five equilateral triangles tile a big equilateral triangle?


Question: Variance of sample variance?


Question: Union of two vector subspaces not a subspace?


Question: Probability density function vs. probability mass function


Question: Determinant of a non-square matrix


Question: What is a simple example of an unprovable statement?


Question: Mathematical precise definition of a PDE being elliptic, parabolic or hyperbolic


Question: Does commutativity imply Associativity?


Question: What is the Tor functor?


Question: 100 Soldiers riddle


Question: Why does Friedberg say that the role of the determinant is less central than in former times?


Question: Is Lagranges theorem the most basic result in finite group theory?


Question: Is $\sqrt {2 \sqrt {3 \sqrt {4 \ldots}}}$ algebraic or transcendental?


Question: $6!\cdot 7!=10!$. Is there a natural bijection between $S_6\times S_7$ and $S_{10}$?


Question: Show that the set of all finite subsets of $\mathbb{N}$ is countable.


Question: $X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed


Question: Why are rotational matrices not commutative?


Question: How to use the Extended Euclidean Algorithm manually?


Question: How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?


Question: What are some interpretations of Von Neumanns quote?


Question: Why does the Mandelbrot set contain (slightly deformed) copies of itself?


Question: If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$


Question: General request for a book on mathematical history, for a VERY advanced reader.


Question: Terence Tao–type books in other fields?


Question: Alice and Bob play the determinant game


Question: Is there a definitive guide to speaking mathematics?


Question: $\frac{1}{n}$ as a difference of Egyptian fractions with all denominators $<n$


Question: What are the practical applications of the Taylor Series?


Question: Expected Number of Coin Tosses to Get Five Consecutive Heads


Question: Understanding of the theorem that all norms are equivalent in finite dimensional vector spaces


Question: Why is $e^{\pi \sqrt{163}}$ almost an integer?


Question: $\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$


Question: Does mathematics require axioms?


Question: The myth of no prime formula?


Question: What is Bra and Ket notation and how does it relate to Hilbert spaces?


Question: Intuitive meaning of Exact Sequence


Question: Whats so natural about the base of natural logarithms?


Question: What does surface area of a sphere actually mean (in terms of elementary school mathematics)?


Question: The closed form of $\int_0^{\pi/4}\frac{\log(1-x) \tan^2(x)}{1-x\tan^2(x)} \ dx$


Question: Can one deduce Liouvilles theorem (in complex analysis) from the non-emptiness of spectra in complex Banach algebras?


Question: How to get a reflection vector?


Question: Prove that $i^i$ is a real number


Question: Is there a bijective map from $(0,1)$ to $\mathbb{R}$?


Question: Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?


Question: Cardinality of set of real continuous functions


Question: A and B disjoint, A compact, and B closed implies there is positive distance between both sets


Question: Why is a full turn of the circle 360°? Why not any other number?


Question: Is there any easy way to understand the definition of Gaussian Curvature?


Question: Are all infinities equal?


Question: How to generate a random number between 1 and 10 with a six-sided die?


Question: What is $\gcd(0,0)$?


Question: In Linear Algebra, what is a vector?


Question: Why isnt reflexivity redundant in the definition of equivalence relation?


Question: Do you prove all theorems whilst studying?


Question: Are all mathematicians human calculators?


Question: Compute $ \lim\limits_{n \to \infty }\sin \sin \dots\sin n$


Question: Does mathematics become circular at the bottom? What is at the bottom of mathematics?


Question: linear algebra over a division ring vs. over a field


Question: Why is compactness in logic called compactness?


Question: 20 circles in the plane, all passing through the origin


Question: How to find this limit: $A=\lim_{n\to \infty}\sqrt{1+\sqrt{\frac{1}{2}+\sqrt{\frac{1}{3}+\cdots+\sqrt{\frac{1}{n}}}}}$


Question: Visual proof of $\sum_{n=1}^\infty \frac{1}{n^4} = \frac{\pi^4}{90}$?


Question: In $n>5$, topology = algebra


Question: Conjectured formula for the Fabius function


Question: Element-wise (or pointwise) operations notation?


Question: Where exactly are complex numbers used in the real world?


Question: Is zero positive or negative?


Question: Prove that $\lim \limits_{n \to \infty} \frac{x^n}{n!} = 0$, $x \in \Bbb R$.


Question: Finding the Transform matrix from 4 projected points (with Javascript)


Question: Reference book on measure theory


Question: How to effectively and efficiently learn mathematics


Question: Logic problem: Identifying poisoned wines out of a sample, minimizing test subjects with constraints


Question: What is a universal property?


Question: Why are differentiable complex functions infinitely differentiable?


Question: Sheaf cohomology: what is it and where can I learn it?


Question: Koch snowflake paradox: finite area, but infinite perimeter


Question: I lost my love of math; Im getting it back. How can I determine if math is actually right for me?


Question: Is there a function with a removable discontinuity at every point?


Question: Direct proof that $\pi$ is not constructible


Question: Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$


Question: Rigorous nature of combinatorics


Question: Integrals of $\sqrt{x+\sqrt{\phantom|\dots+\sqrt{x+1}}}$ in elementary functions


Question: Escaping infinitely many pursuers


Question: Relations between p norms


Question: Projection map being a closed map


Question: Math behind rotation in MS Paint


Question: The Monty Hall problem


Question: Why is the Möbius strip not orientable?


Question: Help me solve my fathers riddle and get my book back


Question: Why did my friend lose all his money?


Question: What is lost when we move from reals to complex numbers?


Question: Is linear algebra more “fully understood” than other maths disciplines?


Question: Are these solutions of $2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$ correct?


Question: How deep is the liquid in a half-full hemisphere?


Question: Why do books titled Abstract Algebra mostly deal with groups/rings/fields?


Question: What exactly are eigen-things?


Question: What is an example of a sequence which thins out and is finite?


Question: Why is $\omega$ the smallest $\infty$?


Question: Besides proving new theorems, how can a person contribute to mathematics?


Question: The Intuition behind lHopitals Rule


Question: Motivation for spectral graph theory.


Question: Mathematicians shocked(?) to find pattern in prime numbers


Question: Closed form for $\int_0^\infty\ln\frac{J_\mu(x)^2+Y_\mu(x)^2}{J_\nu(x)^2+Y_\nu(x)^2}\mathrm dx$


Question: Why cant the Polynomial Ring be a Field?


Question: A path to truly understanding probability and statistics


Question: Is there a shape with infinite area but finite perimeter?


Question: Infinite sets dont exist!?


Question: Fastest way to check if $x^y > y^x$?


Question: What is integration by parts, really?


Question: Conjectures (or intuitions) that turned out wrong in an interesting or useful way


Question: What is the intuition behind uniform continuity?


Question: Dividing 100% by 3 without any left


Question: Inscribing square in circle in just seven compass-and-straightedge steps


Question: List of interesting integrals for early calculus students


Question: The Duals of $l^\infty$ and $L^{\infty}$


Question: Finite subgroups of the multiplicative group of a field are cyclic


Question: Whats a proof that the angles of a triangle add up to 180°?


Question: Stirlings formula: proof?


Question: Is learning (theoretical) physics useful/important for a mathematician?


Question: An example of a problem which is difficult but is made easier when a diagram is drawn


Question: Multiple-choice: sum of primes below $1000$


Question: Fake induction proofs


Question: Theorem that von Neumann proved in five minutes.


Question: Why did mathematicians introduce the concept of uniform continuity?


Question: Why is $i! = 0.498015668 - 0.154949828i$?


Question: Gerrymandering on a high-genus surface/can I use my powers for evil?


Question: A strange integral: $\int_{-\infty}^{+\infty} {dx \over 1 + \left(x + \tan x\right)^2} = \pi.$


Question: Denesting radicals like $\sqrt[3]{\sqrt[3]{2} - 1}$


Question: How are mathematicians taught to write with such an expository style?


Question: Number of ways to write n as a sum of k nonnegative integers


Question: What is $\sqrt{i}$?


Question: Teenager solves Newton dynamics problem - where is the paper?


Question: Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$


Question: What is the meaning of the third derivative of a function at a point


Question: Continuous mapping on a compact metric space is uniformly continuous


Question: Prove that the set of all algebraic numbers is countable


Question: Difference between metric and norm made concrete: The case of Euclid


Question: (Theoretical) Multivariable Calculus Textbooks


Question: Quotient ring of Gaussian integers


Question: String Theory: What to do?


Question: What is the chance to get a parking ticket in half an hour if the chance to get a ticket is 80% in 1 hour?


Question: Why there is no sign of logic symbols in mathematical texts?


Question: Connections between metrics, norms and scalar products (for understanding e.g. Banach and Hilbert spaces)


Question: Interesting and unexpected applications of $\pi$


Question: How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$?


Question: Thurstons 37th way of thinking about the derivative


Question: Volumes of n-balls: what is so special about n=5?


Question: Ramanujan log-trigonometric integrals


Question: Finding out the area of a triangle if the coordinates of the three vertices are given


Question: Factorial, but with addition


Question: A simple explanation of eigenvectors and eigenvalues with big picture ideas of why on earth they matter


Question: Zero probability and impossibility


Question: Whats the difference between stochastic and random?


Question: How many connected components does $\mathrm{GL}_n(\mathbb R)$ have?


Question: Mathematical subjects you wish you learned earlier


Question: Closed form for $\sum \frac{1}{n^n}$


Question: Why cant you pick socks using coin flips?


Question: Is it bad form to write mysterious proofs without explaining what one intends to do?


Question: Does $G\cong G/H$ imply that $H$ is trivial?


Question: What does the mysterious constant marked by C on a slide rule indicate?


Question: Two curious identities on $x^x$,$e$,and $\pi$


Question: How to find perpendicular vector to another vector?


Question: How to calculate $\,(a-b)\bmod n\,$ and $ {-}b \bmod n$


Question: How was the normal distribution derived?


Question: What is the proper way to study (more advanced) math?


Question: What are the applications of functional analysis?


Question: Very *mathematical* general physics book


Question: Why not include as a requirement that all functions must be continuous to be differentiable?


Question: Bag of tricks in Advanced Calculus/ Real Analysis/Complex Analysis


Question: What would have been our number system if humans had more than 10 fingers? Try to solve this puzzle.


Question: Does associativity imply commutativity?


Question: Algebraic Intuition for Homological Algebra and Applications to More Elementary Algebra


Question: A new imaginary number? $x^c = -x$


Question: About Euclids Elements and modern video games


Question: A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum


Question: What is the math behind the game Spot It?


Question: Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)


Question: Why determinant of a 2 by 2 matrix is the area of a parallelogram?


Question: Intuition behind using complementary CDF to compute expectation for nonnegative random variables


Question: Proof that a Combination is an integer


Question: A map is continuous if and only if for every set, the image of closure is contained in the closure of image


Question: Examples of finite nonabelian groups.


Question: Whats going on with compact implies sequentially compact?


Question: Best Algebraic Geometry text book? (other than Hartshorne)


Question: Why does the symbol for the multiplication operation change shape?


Question: Hanging a picture on the wall using two nails in such a way that removing any nail makes the picture fall down


Question: Why does the google calculator give $\tan 90^{\circ} = 1.6331779e^{+16}$?


Question: Reference request: introduction to commutative algebra


Question: When writing in math, do you use a comma or colon preceding an equation?


Question: Is linear algebra laying the foundation for something important?


Question: How come $32.5 = 31.5$? (The Missing Square puzzle.)


Question: Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?


Question: Is there an easy way to show which spheres can be Lie groups?


Question: How to solve fifth-degree equations by elliptic functions?


Question: Intuition behind conjugation in group theory


Question: How to stop forgetting proofs - for a first course in Real Analysis?


Question: Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$


Question: How to find the inverse modulo $m$?


Question: Finding a point along a line a certain distance away from another point!


Question: Graph theory: adjacency vs incident


Question: Space of bounded continuous functions is complete


Question: Why is $\Gamma\left(\frac{1}{2}\right)=\sqrt{\pi}$?


Question: Simplest proof of Taylors theorem


Question: What algorithm is used by computers to calculate logarithms?


Question: Why do we need to learn integration techniques?


Question: Solving $DEF+FEF=GHH$, $KLM+KLM=NKL$, $ABC+ABC+ABC=BBB$


Question: Why can a real number be defined as a Dedekind cut, that is, as a set of rational numbers?


Question: Mathematical research of Pokémon


Question: Why Zariski topology?


Question: Why should we prove obvious things?


Question: Drunk man with a set of keys.


Question: Will assuming the existence of a solution ever lead to a contradiction?


Question: What is $x^y$? How to understand it?


Question: Lebesgue measure theory vs differential forms?


Question: Naturally occurring non-Hausdorff spaces?


Question: What are some mathematical topics that involve adding and multiplying pictures?


Question: How to cut a cube out of a tree stump, such that a pair of opposing vertices are in the center?


Question: Why are the last two numbers of this sequence never prime?


Question: Is $ 0.112123123412345123456\dots $ algebraic or transcendental?


Question: Integral $\int_1^\infty\frac{\operatorname{arccot}\left(1+\frac{2\pi}{\operatorname{arcoth}x-\operatorname{arccsc}x}\right)}{\sqrt{x^2-1}}\mathrm dx$


Question: Representing every positive rational number in the form of $(a^n+b^n)/(c^n+d^n)$


Question: Difference between Fourier transform and Wavelets


Question: Is there a known mathematical equation to find the nth prime?


Question: Understanding Borel sets


Question: $\infty = -1 $ paradox


Question: What do $\pi$ and $e$ stand for in the normal distribution formula?


Question: Completion of rational numbers via Cauchy sequences


Question: Convergence of $\sqrt{n}x_{n}$ where $x_{n+1} = \sin(x_{n})$


Question: Combinatorial proof that $\sum \limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} (-1)^k = 2^n \binom{n}{n/2}$ when $n$ is even


Question: Why does being holomorphic imply so much about a function?


Question: Why should I care about adjoint functors


Question: How did Euler prove the Mersenne number $2^{31}-1$ is a prime so early in history?


Question: Pseudo Proofs that are intuitively reasonable


Question: Is $\sqrt1+\sqrt2+\dots+\sqrt n$ ever an integer?


Question: Is this determinant identity known?


Question: How was the Monsters existence originally suspected?


Question: How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$


Question: Conjecture $_2F_1\left(\frac14,\frac34;\,\frac23;\,\frac13\right)=\frac1{\sqrt{\sqrt{\frac4{\sqrt{2-\sqrt[3]4}}+\sqrt[3]{4}+4}-\sqrt{2-\sqrt[3]4}-2}}$


Question: What exactly is Laplace transform?


Question: $\sum k! = 1! +2! +3! + \cdots + n!$ ,is there a generic formula for this?


Question: Can a limit of an integral be moved inside the integral?


Question: If $G/Z(G)$ is cyclic, then $G$ is abelian


Question: Prove if $n^2$ is even, then $n$ is even.


Question: An Explanation of the Kalman Filter


Question: Geometric interpretation for complex eigenvectors of a 2×2 rotation matrix


Question: Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$


Question: incremental computation of standard deviation


Question: Intuitive explanation of a definition of the Fisher information


Question: Not every metric is induced from a norm


Question: Why does multiplying a number on a clock face by 10 and then halving, give the minutes? ${}{}$


Question: Equivalent Definitions of the Operator Norm


Question: Is it morally right and pedagogically right to google answers to homework?


Question: Why is the complex plane shaped like it is?


Question: What are some applications of elementary linear algebra outside of math?


Question: How can one prove that $e<\pi$?


Question: Why does this miracle method for matrix inversion work?


Question: Is there an intuitive reason for a certain operation to be associative?


Question: Laplace, Legendre, Fourier, Hankel, Mellin, Hilbert, Borel, Z...: unified treatment of transforms?


Question: Are there infinitely many super-palindromes?


Question: Let, $A\subset\mathbb{R}^2$. Show that $A$ can contain at most one point $p$ such that $A$ is isometric to $A \setminus \{p\}$.


Question: Numerical phenomenon. Who can explain?


Question: Probability of 3 people in a room of 30 having the same birthday


Question: Difference between continuity and uniform continuity


Question: Compact sets are closed?


Question: What is mathematical research like?


Question: Difference between complete and closed set


Question: When does L Hopitals rule fail?


Question: In classical logic, why is $(p\Rightarrow q)$ True if $p$ is False and $q$ is True?


Question: Whats a good place to learn Lie groups?


Question: Why do we use a Least Squares fit?


Question: Chance of meeting in a bar


Question: What is the most expensive item I could buy with £50?


Question: Can someone please explain the Riemann Hypothesis to me... in English?


Question: Prove $0! = 1$ from first principles


Question: Why cant the second fundamental theorem of calculus be proved in just two lines?


Question: What is so interesting about the zeroes of the Riemann $\zeta$ function?


Question: Does every Abelian group admit a ring structure?


Question: Are there an infinite number of prime numbers where removing any number of digits leaves a prime?


Question: Japanese Temple Problem From 1844


Question: The limit of truncated sums of harmonic series, $\lim\limits_{k\to\infty}\sum_{n=k+1}^{2k}{\frac{1}{n}}$


Question: Understandable questions which are hard for non-mathematicians but easy for mathematicians


Question: Do there exist pairs of distinct real numbers whose arithmetic, geometric and harmonic means are all integers?


Question: Fractal behavior along the boundary of convergence?


Question: Are there any valid continuous Sudoku grids?


Question: A nasty integral of a rational function


Question: Show that $\int_{0}^{\pi/2}\frac {\log^2\sin x\log^2\cos x}{\cos x\sin x}\mathrm{d}x=\frac14\left( 2\zeta (5)-\zeta(2)\zeta (3)\right)$


Question: How much does symbolic integration mean to mathematics?


Question: Evaluating sums and integrals using Taylors Theorem


Question: How to show that $\det(AB) =\det(A) \det(B)$?


Question: What is the equation for a 3D line?


Question: Density of sum of two independent uniform random variables on $[0,1]$


Question: Use of without loss of generality


Question: Why is $\pi $ equal to $3.14159...$?


Question: $\sqrt{7\sqrt{7\sqrt{7\sqrt{7\sqrt{7\cdots}}}}}$ approximation


Question: Limit $\frac{x^2y}{x^4+y^2}$ is found using polar coordinates but it is not supposed to exist.


Question: What is the largest eigenvalue of the following matrix?


Question: Good books on Math History


Question: Why is a circle 1-dimensional?


Question: Overview of basic results on cardinal arithmetic


Question: Is The empty set is a subset of any set a convention?


Question: How do people apply the Lebesgue integration theory?


Question: Why is radian so common in maths?


Question: Why do engineers use derivatives in discontinuous functions? Is it correct?


Question: Why are addition and multiplication commutative, but not exponentiation?


Question: $100$-th derivative of the function $f(x)=e^{x}\cos(x)$


Question: Is it generally accepted that if you throw a dart at a number line you will NEVER hit a rational number?


Question: Is memory unimportant in doing mathematics?


Question: Theorems names that dont credit the right people


Question: What is the oldest open problem in geometry?


Question: Why the emphasis on Projective Space in Algebraic Geometry?


Question: Is there a great mathematical example for a 12-year-old?


Question: Am I too young to learn more advanced math and get a teacher?


Question: How to straighten a parabola?


Question: Geometric intuition for the tensor product of vector spaces


Question: How likely is it not to be anyones best friend?


Question: What is a real world application of polynomial factoring?


Question: What is the proof that the total number of subsets of a set is $2^n$?


Question: How to explain for my daughter that $\frac {2}{3}$ is greater than $\frac {3}{5}$?


Question: Where is the flaw in this proof that 1=2? (Derivative of repeated addition)


Question: How to write a good mathematical paper?


Question: What are the names of numbers in the binary system?


Question: Why $9$ & $11$ are special in divisibility tests using decimal digit sums? (casting out nines & elevens)


Question: Is it technically incorrect to write proofs forward?


Question: What Is Exponentiation?


Question: Why do I get one extra wrong solution when solving $2-x=-\sqrt{x}$?


Question: Mathematicians dont quit, they fade away


Question: If I know the order of every element in a group, do I know the group?


Question: Is it possible to find an infinite set of points in the plane where the distance between any pair is rational?


Question: Have there been efforts to introduce non Greek or Latin alphabets into mathematics?


Question: Algebra: Best mental images


Question: What is the average rational number?


Question: Is this similarity to the Fourier transform of the von Mangoldt function real?


Question: Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$


Question: Topological spaces admitting an averaging function


Question: How do I tell if matrices are similar?


Question: What isnt a vector space?


Question: Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$


Question: Why is Euclids proof on the infinitude of primes considered a proof?


Question: When not to treat dy/dx as a fraction in single-variable calculus?


Question: how to read a mathematical paper?


Question: Why do people lose in chess?


Question: Is it mathematically valid to separate variables in a differential equation?


Question: How much Math do you REALLY do in your job?


Question: What is the importance of the infinitesimal generator of Brownian motion?


Question: Do Parabolic Trigonometric Functions exist?


Question: Why is the tensor product important when we already have direct and semidirect products?


Question: Nuking the Mosquito — ridiculously complicated ways to achieve very simple results


Question: Are proofs by contradiction really logical?


Question: Is it possible to formulate category theory without set theory?


Question: What is the logic/rationale behind the vector cross product?


Question: Is there a simple function that generates the series; $1,1,2,1,1,2,1,1,2...$ or $-1,-1,1,-1,-1,1...$


Question: Integral $\int_0^1\frac{\ln\left(x+\sqrt2\right)}{\sqrt{2-x}\,\sqrt{1-x}\,\sqrt{\vphantom{1}x}}\mathrm dx$


Question: Can $18$ consecutive integers be separated into two groups,such that their product is equal?


Question: Integration of forms and integration on a measure space


Question: Simplicial homology of real projective space by Mayer-Vietoris


Question: Evaluating the log gamma integral $\int_{0}^{z} \log \Gamma (x) \, \mathrm dx$ in terms of the Hurwitz zeta function


Question: Does the string of prime numbers contain all natural numbers?


Question: Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even


Question: Differential forms on fuzzy manifolds


Question: Difference between NFA and DFA


Question: Given this transformation matrix, how do I decompose it into translation, rotation and scale matrices?


Question: How can a probability density be greater than one and integrate to one


Question: Good books on mathematical logic?


Question: There are 4 cups of liquid. Three are water and one is poison. If you were to drink 3 of the 4 cups, what is the probability of being poisoned?


Question: How to convince a layperson that the $\pi = 4$ proof is wrong?


Question: Every subsequence of $x_n$ has a further subsequence which converges to $x$. Then the sequence $x_n$ converges to $x$.


Question: Intuitive explanation of a positive semidefinite matrix


Question: Proving that the tensor product is right exact


Question: Integrals of the form ${\large\int}_0^\infty\operatorname{arccot}(x)\cdot\operatorname{arccot}(a\,x)\cdot\operatorname{arccot}(b\,x)\ dx$


Question: Express 99 2/3% as a fraction? No calculator


Question: What exactly is calculus?


Question: Does it ever make sense NOT to go to the most prestigious graduate school you can get into?


Question: Set of continuity points of a real function


Question: Does every prime divide some Fibonacci number?


Question: Does $\sum _{n=1}^{\infty } \frac{\sin(\text{ln}(n))}{n}$ converge?


Question: Understanding the Laplace operator conceptually


Question: What is Cauchy Schwarz in 8th grade terms?


Question: Proving the existence of a proof without actually giving a proof


Question: How and why does Grothendiecks work provide tools to attack problems in number theory?


Question: Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$


Question: Does multiplying all a numbers roots together give a product of infinity?


Question: What are some good ways to get children excited about math?


Question: Why does $\cos(x) + \cos(y) - \cos(x + y) = 0$ look like an ellipse?


Question: When is an infinite product of natural numbers regularizable?


Question: Why is it not true that $\int_0^{\pi} \sin(x)\; dx = 0$?


Question: Evaluating $\int_{0}^{1}\cdots\int_{0}^{1}\bigl\{\frac{1}{x_{1}\cdots x_{n}}\bigr\}^{2}\:\mathrm{d}x_{1}\cdots\mathrm{d}x_{n}$


Question: Are the sums $\sum_{n=1}^{\infty} \frac{1}{(n!)^k}$ transcendental?


Question: Does $\Bbb{CP}^{2n} \mathbin{\#} \Bbb{CP}^{2n}$ ever support an almost complex structure?


Question: Closed form solution for $\sum_{n=1}^\infty\frac{1}{1+\frac{n^2}{1+\frac{1}{\stackrel{\ddots}{1+\frac{1}{1+n^2}}}}}$.


Question: What is a good book for learning math, from middle school level?


Question: difference between dot product and inner product


Question: Check if a point is within an ellipse


Question: What does proving the Riemann Hypothesis accomplish?


Question: Is Serge Langs Algebra still worth reading?


Question: Highest power of a prime $p$ dividing $N!$


Question: Proof that Pi is constant (the same for all circles), without using limits


Question: Interesting real life applications of serious theorems


Question: How do I motivate myself to do math again?


Question: Under what conditions the quotient space of a manifold is a manifold?


Question: How to effectively study math?


Question: Is there any branch of Mathematics which has no applications in any other field or in real world?


Question: Nice expression for minimum of three variables?


Question: What exactly is a number?


Question: Dominoes and induction, or how does induction work?


Question: Riemann hypothesis: is Bender-Brody-Müller Hamiltonian a new line of attack?


Question: Why do we not have to prove definitions?


Question: Optimal strategy for cutting a sausage?


Question: Symbol for probably equal to (barring pathology)?


Question: Is it not effective to learn math top-down?


Question: If we randomly select 25 integers between 1 and 100, how many consecutive integers should we expect?


Question: A new general formula for the quadratic equation?


Question: Conways Murder Weapon


Question: How to explain to the layperson what mathematics is, why its important, and why its interesting


Question: Is the box topology good for anything?


Question: Does the series $ \sum\limits_{n=1}^{\infty} \frac{1}{n^{1 + |\sin(n)|}} $ converge or diverge?


Question: Does Fermats Last Theorem hold for cyclotomic integers in $\mathbb{Q(\zeta_{37})}$?


Question: In combinatorics, how can one verify that one has counted correctly?


Question: Algebraic Topology Challenge: Homology of an Infinite Wedge of Spheres


Question: Fourier Transform of Derivative


Question: What is the relation between rank of a matrix, its eigenvalues and eigenvectors


Question: What is the standard basis for fields of complex numbers?


Question: Good books for a high schooler self-studying Abstract Algebra?


Question: Why do the French count so strangely?


Question: A comprehensive list of binomial identities?


Question: What is a covector and what is it used for?


Question: First-Order Logic vs. Second-Order Logic


Question: Why is the determinant the volume of a parallelepiped in any dimensions?


Question: Introductory texts on manifolds


Question: Functions that are their own inverse.


Question: How do I convince my students that the choice of variable of integration is irrelevant?


Question: If a coin toss is observed to come up as heads many times, does that affect the probability of the next toss?


Question: A way to find this shaded area without calculus?


Question: Learning Roadmap for Algebraic Topology


Question: What is the limit of $n \sin (2 \pi \cdot e \cdot n!)$ as $n$ goes to infinity?


Question: How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical communitys standards?


Question: When to give up on a hard math problem?


Question: Simplicial Complex vs Delta Complex vs CW Complex


Question: Why are primes considered to be the building blocks of the integers?


Question: What are some mathematically interesting computations involving matrices?


Question: Arranging numbers from $1$ to $n$ such that the sum of every two adjacent numbers is a perfect power


Question: Given real numbers: define integers?


Question: Arc length contest! Minimize the arc length of $f(x)$ when given three conditions.


Question: Is $ \sum\limits_{n=1}^\infty \frac{|\sin n|^n}n$ convergent？


Question: What does strength refer to in mathematics?


Question: Is there a reason it is so rare we can solve differential equations?


Question: Why it is important to write a function as sum of even and odd functions?


Question: What is a proof?


Question: Area covered by a constant length segment rotating around the center of a square.


Question: Is it normal to treat Math Theorems as Black Boxes


Question: Good history of mathematical ideas book?


Question: Abstract nonsense proof of snake lemma


Question: How to find a total order with constrained comparisons


Question: Integers $n$ such that $i(i+1)(i+2) \cdots (i+n)$ is real or pure imaginary


Question: Which Algebraic Properties Distinguish Lie Groups from Abstract Groups?


Question: I have learned that 1/0 is infinity, why isnt it minus infinity?


Question: Difference between axioms, theorems, postulates, corollaries, and hypotheses


Question: Is the sum and difference of two irrationals always irrational?


Question: What is the difference between the Frobenius norm and the 2-norm of a matrix?


Question: How does a calculator calculate the sine, cosine, tangent using just a number?


Question: How do you compute negative numbers to fractional powers?


Question: Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction


Question: Probability that random moves in the game 2048 will win


Question: Why does $\tan^{-1}(1)+\tan^{-1}(2)+\tan^{-1}(3)=\pi$?


Question: Proof of the Hockey-Stick Identity: $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$


Question: How can you prove that the square root of two is irrational?


Question: Is the Law of Large Numbers empirically proven?


Question: Cardinality of Borel sigma algebra


Question: Motivation and methods for self-study


Question: Intuition on group homomorphisms


Question: Can someone explain the Yoneda Lemma to an applied mathematician?


Question: Polynomial division: an obvious trick? [reducing mod $\textit{simpler}$ multiples]


Question: How can I introduce complex numbers to precalculus students?


Question: $n$th derivative of $e^{1/x}$


Question: What should an amateur do with a proof of an open problem?


Question: Why does an exponential function eventually get bigger than a quadratic


Question: Big List of Erdős elementary proofs


Question: Continuity and the Axiom of Choice


Question: Graphs for which a calculus student can reasonably compute the arclength


Question: Conjugate subgroup strictly contained in the initial subgroup?


Question: Rigour in mathematics


Question: Where does the word torsion in algebra come from?


Question: Computation with a memory wiped computer


Question: Let $k$ be a natural number . Then $3k+1$ , $4k+1$ and $6k+1$ cannot all be square numbers.


Question: Unexpected approximations which have led to important mathematical discoveries


Question: On Ramanujans curious equality for $\sqrt{2\,(1-3^{-2})(1-7^{-2})(1-11^{-2})\cdots} $


Question: Is $\lfloor n!/e\rfloor$ always even for $n\in\mathbb N$?


Question: How do I prove that a function is well defined?


Question: Is the rank of a matrix the same of its transpose? If yes, how can I prove it?


Question: Evaluating the indefinite integral $ \int \sqrt{\tan x} ~ \mathrm{d}{x}. $


Question: Proof that the irrational numbers are uncountable


Question: Can a complex number ever be considered bigger or smaller than a real number, or vice versa?


Question: Prove every odd integer is the difference of two squares


Question: how to be good at proving?


Question: Are there any examples of non-computable real numbers?


Question: What is a good book to study linear algebra?


Question: Why is empty set an open set?


Question: How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?


Question: Probability for the length of the longest run in $n$ Bernoulli trials


Question: Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$


Question: What do prime ideals in $k[x,y]$ look like?


Question: Characterizing units in polynomial rings


Question: Entire one-to-one functions are linear


Question: Let $X$ be an infinite dimensional Banach space. Prove that every Hamel basis of X is uncountable.


Question: How do you show monotonicity of the $\ell^p$ norms?


Question: Strategies to denest nested radicals $\sqrt{a+b\sqrt{c}}$


Question: How would you explain to a 9th grader the negative exponent rule?


Question: Why learn to solve differential equations when computers can do it?


Question: Big List of Fun Math Books


Question: What is the definition of a set?


Question: Is there such a thing as proof by example (not counter example)


Question: Can there be two distinct, continuous functions that are equal at all rationals?


Question: Whats the goal of mathematics?


Question: How to debug math?


Question: What does communicated by mean in math papers?


Question: Using Gröbner bases for solving polynomial equations


Question: Which is larger? $20!$ or $2^{40}$?


Question: Unsolved Problems due to Lack of Computational Power


Question: Whats wrong with this reasoning that $\frac{\infty}{\infty}=0$?


Question: Are there theoretical applications of trigonometry?


Question: The last digit of $2^{2006}$


Question: Intuition for the Importance of Modular Forms


Question: Linear Algebra Versus Functional Analysis


Question: Whats the point of studying topological (as opposed to smooth, PL, or PDiff) manifolds?


Question: Find three non-constant, pairwise unequal functions $f,g,h:\mathbb R\to \mathbb R$...


Question: Surprisingly elementary and direct proofs


Question: Closed Form for $~\int_0^1\frac{\text{arctanh }x}{\tan\left(\frac\pi2~x\right)}~dx$


Question: Is $n \sin n$ dense on the real line?


Question: When are nonintersecting finite degree field extensions linearly disjoint?


Question: The relation between trace and determinant of a matrix


Question: How to prove every closed interval in R is compact?


Question: Is there a step by step checklist to check if a multivariable limit exists and find its value?


Question: Is an automorphism of the field of real numbers the identity map?


Question: What do eigenvalues have to do with pictures?


Question: Why cant you flatten a sphere?


Question: List of problem books in undergraduate and graduate mathematics


Question: What is the importance of Calculus in todays Mathematics?


Question: Why does $\frac{1}{x} < 4$ have two answers?


Question: Explain this mathematical meme (Geometers bird interrupting Topologists bird)


Question: Coin flipping probability game ; 7 flips vs 8 flips


Question: Finite Groups with exactly $n$ conjugacy classes $(n=2,3,...)$


Question: Help understanding Algebraic Geometry


Question: 7 fishermen caught exactly 100 fish and no two had caught the same number of fish. Then there are three who have together captured at least 50 fish.


Question: Can a number have infinitely many digits before the decimal point?


Question: How can I show that $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt\ldots}}}$ exists?


Question: Whats the intuition with partitions of unity?


Question: Center-commutator duality


Question: In how many different ways can a 9-panel comic grid be used?


Question: I need mathematical proof that the distance from zero to 1 is the equal to the distance from 1 to 2


Question: I almost quit self-studying mathematics, but should I continue?


Question: What is Trinity Hall Prime number?


Question: Examples of morphisms of schemes to keep in mind?


Question: Review of my T-shirt design


Question: Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix


Question: Is A New Kind of Science a new kind of science?


Question: What am I doing when I separate the variables of a differential equation?


Question: Does every set have a group structure?


Question: Why do we use trig functions in Fourier transforms, and not other periodic functions?


Question: How to evaluate $I=\int_0^{\pi/2}x^2\ln(\sin x)\ln(\cos x)\ \mathrm dx$


Question: Is it possible to simplify $\frac{\Gamma\left(\frac{1}{10}\right)}{\Gamma\left(\frac{2}{15}\right)\ \Gamma\left(\frac{7}{15}\right)}$?


Question: Can squares of infinite area always cover a unit square?


Question: Whats the probability that a sequence of coin flips never has twice as many heads as tails?


Question: $5^n+n$ is never prime?


Question: What does it take to divide by $2$?


Question: If a two variable smooth function has two global minima, will it necessarily have a third critical point?


Question: Subgroups as isotropy subgroups and regular orbits on tuples


Question: A question about Sylow subgroups and $C_G(x)$


Question: How to know if a point is inside a circle?


Question: Poisson Distribution of sum of two random independent variables $X$, $Y$


Question: Explanation on arg min


Question: Product of two Gaussian PDFs is a Gaussian PDF, but Product of two Gaussian Variables is not Gaussian


Question: Is the product of symmetric positive semidefinite matrices positive definite?


Question: Matrices commute if and only if they share a common basis of eigenvectors?


Question: What are the formal names of operands and results for basic operations?


Question: Differentiating an Inner Product


Question: How to show that the commutator subgroup is a normal subgroup


Question: Nobody told me that self teaching could be so damaging...


Question: (undergraduate) Algebraic Geometry Textbook Recommendations


Question: Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD?


Question: Dot Product Intuition


Question: Divisor -- line bundle correspondence in algebraic geometry


Question: How to tell if Im good enough for graduate school?


Question: How is the derivative truly, literally the best linear approximation near a point?


Question: Why is the Continuum Hypothesis (not) true?


Question: Good examples of double induction


Question: A very general method for proving inequalities. Too good to be true?


Question: Is it possible to have three real numbers that have both their sum and product equal to $1$?


Question: What was the book that opened your mind to the beauty of mathematics?


Question: Research done by high-school students


Question: Why does the discriminant in the Quadratic Formula reveal the number of real solutions?


Question: Understanding the intuition behind math


Question: A circle rolls along a parabola


Question: Why is $\varphi$ called the most irrational number?


Question: How can I intuitively understand complex exponents?


Question: It looks straightforward, but actually it isnt


Question: Refuting the Anti-Cantor Cranks


Question: Could I be using proof by contradiction too much?


Question: Is there any geometric intuition for the factorials in Taylor expansions?


Question: Why do differential forms have a much richer structure than vector fields?


Question: A Challenging Logarithmic Integral $\int_0^1 \frac{\log(x)\log(1-x)\log^2(1+x)}{x}dx$


Question: Quadratic reciprocity via generalized Fibonacci numbers?


Question: Penroses remark on impossible figures


Question: Why are asymptotically one half of the integer compositions gap-free?


Question: Mirror algorithm for computing $\pi$ and $e$ - does it hint on some connection between them?


Question: Difference between ≈, ≃, and ≅


Question: What is the difference between only if and iff?


Question: Gradient of squared $2$-norm


Question: Distance/Similarity between two matrices


Question: Are all eigenvectors, of any matrix, always orthogonal?


Question: Area of a square inside a square created by connecting point-opposite midpoint


Question: How to generate random points on a sphere?


Question: Number of monic irreducible polynomials of prime degree $p$ over finite fields


Question: Should I be worried that I am doing well in analysis and not well in algebra?


Question: Negative versus Minus


Question: Discontinuous linear functional


Question: Geometric interpretation for sum of fourth powers


Question: The two-daughter-problem


Question: Has there ever been an application of dividing by $0$?


Question: Why do we miss 8 in the decimal expansion of 1/81, and 98 in the decimal expansion of 1/9801?


Question: Why does the Cauchy-Schwarz Inequality even have a name?


Question: What use is the Yoneda lemma?


Question: Is there a function whose antiderivative can be found but whose derivative cannot?


Question: Similar matrices and field extensions


Question: Are there mathematical concepts that exist in dimension $4$, but not in dimension $3$?


Question: Is there a definition of determinants that does not rely on how they are calculated?


Question: Unexpected use of topology in proofs


Question: Does this Fractal Have a Name?


Question: How is the Gödels Completeness Theorem not a tautology?


Question: How many 7-note musical scales are possible within the 12-note system?


Question: Approximating a $\sigma$-algebra by a generating algebra


Question: How do different definitions of degree coincide?


Question: What is the size of each side of the square?


Question: A non-losing strategy for tic-tac-toe $\times$ tic-tac-toe


Question: Can there be an injective function whose derivative is equivalent to its inverse function?


Question: Evaluating $\int_0^\infty \frac{dx}{\sqrt{x}[x^2+(1+2\sqrt{2})x+1][1-x+x^2-x^3+...+x^{50}]}$


Question: Trigonometric sums related to the Verlinde formula


Question: A bestiary about adjunctions


Question: Is OEIS A248049 an integer sequence?


Question: Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $


Question: Golden Number Theory


Question: Explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$


Question: An illusionist and their assistant are about to perform the following magic trick


Question: The most effective windshield-wiper setup. (Packing a square with sectors)


Question: How prove this inequality $\sin{\sin{\sin{\sin{x}}}}\le\frac{4}{5}\cos{\cos{\cos{\cos{x}}}}$


Question: Period of the sum/product of two functions


Question: Example of Partial Order thats not a Total Order and why?


Question: What does curly (curved) less than sign $\succcurlyeq$ mean?


Question: Why we consider log likelihood instead of Likelihood in Gaussian Distribution


Question: Is there an equation to describe regular polygons?


Question: Eigenvalues of the rank one matrix $uv^T$


Question: Under what condition we can interchange order of a limit and a summation?


Question: Calculating pi manually


Question: Difference between basis and subbasis in a topology?


Question: Visualizing the 4th dimension.


Question: Why does the derivative of sine only work for radians?


Question: Origin of the dot and cross product?


Question: What is the arithmetic mean of no numbers?


Question: The $\sigma$-algebra of subsets of $X$ generated by a set $\mathcal{A}$ is the smallest sigma algebra including $\mathcal{A}$


Question: Would a proof to the Riemann Hypothesis affect security?


Question: What lies beyond the Sedenions


Question: Is it possible to determine if you were on a Möbius strip?


Question: Big O Notation is element of or is equal


Question: Is there a slowest rate of divergence of a series?


Question: Any smart ideas on finding the area of this shaded region?


Question: Can we calculate $ i\sqrt { i\sqrt { i\sqrt { \cdots } } }$?


Question: Is it possible that A counter-example exists but it cannot be found


Question: Applications of complex numbers to solve non-complex problems


Question: Is it an abuse of language to say *the* integers, *the* rational numbers, or *the* real numbers, etc.?


Question: Paradox: increasing sequence that goes to $0$?


Question: Is it possible to prove a mathematical statement by proving that a proof exists?


Question: Is $6.12345678910111213141516171819202122\ldots$ transcendental?


Question: Big list of guided discovery books


Question: Are there any Turing-undecidable problems whose undecidability is independent of the Halting problem?


Question: Funny double infinite sum


Question: Geometry problem involving infinite number of circles


Question: What proportion of positive integers have two factors that differ by 1?


Question: What are Different Approaches to Introduce the Elementary Functions?


Question: Finding triplets $(a,b,c)$ such that $\sqrt{abc}\in\mathbb N$ divides $(a-1)(b-1)(c-1)$


Question: How to think of the group ring as a Hopf algebra?


Question: Whats the value of this Viète-style product involving the golden ratio?


Question: Is $1+x+\frac{x^2}2+\dots+\frac{x^n}{n!}$ irreducible?


Question: How many values of $2^{2^{2^{.^{.^{.^{2}}}}}}$ depending on parenthesis?


Question: Looking for a definitive source about Dirichlet finally proving the Unit Theorem in the Sistine Chapel


Question: Whats the sign of $\det\left(\sqrt{i^2+j^2}\right)_{1\le i,j\le n}$?


Question: Is there a good reason why $\left\lfloor \frac{n!}{11e}\right\rfloor$ is always even?


Question: What does E mean in 9.0122222900391E-5?


Question: What’s the difference between analytical and numerical approaches to problems?


Question: How to find the multiplicity of eigenvalues?


Question: Is the power set of the natural numbers countable?


Question: Finding $\int x^xdx$


Question: Calculate on which side of a straight line is a given point located?


Question: Generating correlated random numbers: Why does Cholesky decomposition work?


Question: product distribution of two uniform distribution, what about 3 or more


Question: Dantzigs unsolved homework problems


Question: Interesting math-facts that are visually attractive


Question: How does TREE(3) grow to get so big? (Laymen explanation)


Question: Order of general- and special linear groups over finite fields.


Question: Why are two permutations conjugate iff they have the same cycle structure?


Question: What is an operator in mathematics?


Question: Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral?


Question: Are there any differences between tensors and multidimensional arrays?


Question: Is it possible to write a sum as an integral to solve it?


Question: Why divide by $2m$


Question: Can math be subjective?


Question: Is there an easy way to see associativity or non-associativity from an operations table?


Question: Matrix is conjugate to its own transpose


Question: Is there a third dimension of numbers?


Question: Proving that $m+n\sqrt{2}$ is dense in $\mathbb R$


Question: What is the antiderivative of $e^{-x^2}$


Question: Is there a math expression equivalent to the conditional ternary operator?


Question: Understanding Gödels Incompleteness Theorem


Question: Do harmonic numbers have a “closed-form” expression?


Question: Is $\{0\}$ a field?


Question: How hard is the proof of $\pi$ or $e$ being transcendental?


Question: Interesting results easily achieved using complex numbers


Question: All natural numbers are equal.


Question: Geometrical interpretation of Ricci curvature


Question: Why are real numbers useful?


Question: $x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?


Question: What kind of work do modern day algebraists do?


Question: Choice of $q$ in Baby Rudins Example 1.1


Question: Why is there never a proof that extending the reals to the complex numbers will not cause contradictions?


Question: Is there any conjecture that we know is provable/disprovable but we havent found a proof of yet?


Question: Gaps or holes in rational number system


Question: What is $-i$ exactly?


Question: What knot is this?


Question: Doesnt the unprovability of the continuum hypothesis prove the continuum hypothesis?


Question: What is the fastest/most efficient algorithm for estimating Eulers Constant $\gamma$?


Question: What is the crime of lèse-Bourbaki?


Question: Natural example of cosets


Question: Is Complex Analysis equivalent Real Analysis with $f:\mathbb R^2 \to \mathbb R^2$?


Question: If $e^A$ and $e^B$ commute, do $A$ and $B$ commute?


Question: A discrete math riddle


Question: How does one give a mathematical talk?


Question: Probability that a quadratic equation has real roots


Question: How to identify surfaces of revolution


Question: Is there an abstract definition of a matrix being upper triangular?


Question: Self-learning mathematics - help needed!


Question: What is this pattern called?


Question: The $100$th derivative of $(x^2 + 1)/(x^3 - x)$


Question: Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$


Question: Infinite Series $\sum\limits_{n=1}^\infty\frac{(H_n)^2}{n^3}$


Question: In which ordered fields does absolute convergence imply convergence?


Question: Crazy pattern in the simple continued fraction for $\sum_{k=1}^\infty \frac{1}{(2^k)!}$


Question: A sequence that avoids both arithmetic and geometric progressions


Question: Proof of triangle inequality


Question: How to find the factorial of a fraction?


Question: What is the general equation of the ellipse that is not in the origin and rotated by an angle?


Question: Prove that the union of countably many countable sets is countable.


Question: Symbol for elementwise multiplication of vectors


Question: Difference between supremum and maximum


Question: What is difference between a ring and a field?


Question: Picking random points in the volume of sphere with uniform probability


Question: Necessity/Advantage of LU Decomposition over Gaussian Elimination


Question: Introductory Group theory textbook


Question: Does non-symmetric positive definite matrix have positive eigenvalues?


Question: Difference between Analytic and Holomorphic function


Question: Evaluating the nested radical $ \sqrt{1 + 2 \sqrt{1 + 3 \sqrt{1 + \cdots}}} $.


Question: Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?


Question: What does it take to get a job at a top 50 math program in the U.S.?


Question: Is an irrational number odd or even?


Question: Definitions of Hessian in Riemannian Geometry


Question: How to calculate the pullback of a $k$-form explicitly


Question: How to prove that $\log(x)1$?


Question: Exam with $12$ yes/no questions (half yes, half no) and $8$ correct needed to pass, is it better to answer randomly or answer exactly 6 times yes?


Question: Distinguishing probability measure, function and distribution


Question: False proof: $\pi = 4$, but why?


Question: Books about the Riemann Hypothesis


Question: Why is $\text{Hom}(V,W)$ the same thing as $V^* \otimes W$?


Question: What is exactly the difference between a definition and an axiom?


Question: Non-associative operations


Question: Is $\sqrt{64}$ considered $8$? or is it $8,-8$?


Question: What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$?


Question: Mathematical explanation behind a picture posted (lifted from facebook)


Question: Path-connected and locally connected space that is not locally path-connected


Question: Can I search for factors of $\ (11!)!+11!+1\ $ efficiently?


Question: Solutions to the matrix equation $\mathbf{AB-BA=I}$ over general fields


Question: Square root confusion: Why am I getting an answer if it doesnt work?


Question: Geometric understanding of differential forms.


Question: Why are the only division algebras over the real numbers the real numbers, the complex numbers, and the quaternions?


Question: What is the formula for pi used in the Python decimal library?


Question: Intuition for why the difference between $\frac{2x^2-x}{x^2-x+1}$ and $\frac{x-2}{x^2-x+1}$ is a constant?


Question: Axiom of choice and automorphisms of vector spaces


Question: Show that floating point $\sqrt{x \cdot x} \geq x$ for all long $x$.


Question: How to entertain a crowd with mathematics?


Question: Colliding Bullets


Question: False beliefs about Lebesgue measure on $\mathbb{R}$


Question: Evaluating $\int P(\sin x, \cos x) \text{d}x$


Question: Is there a geometric idea behind Sylows theorems?


Question: Is $29$ the only prime of the form $p^p+2$?


Question: Is Stokes Theorem natural in the sense of category theory?


Question: Trying to define $\mathbb{R}^{0.5}$ topologically


Question: Conjectured value of a harmonic sum $\sum_{n=1}^\infty\left(H_n-\,2H_{2n}+H_{4n}\right)^2$


Question: Elementary proof that the derivative of a real function is continuous somewhere


Question: Can $\sqrt{p}^{\sqrt{p}^{\sqrt{p}}}$ be an integer, if $p$ is a non-square positive integer?


Question: How to tell if a set of vectors spans a space?


Question: Easy way of memorizing values of sine, cosine, and tangent


Question: What does ∈ mean?


Question: Recognizable vs Decidable


Question: Why have we chosen our number system to be decimal (base 10)?


Question: How the product of two integrals is iterated integral? $\int\cdot \int = \iint$


Question: How to take the gradient of the quadratic form?


Question: Why cant a set have two elements of the same value?


Question: Order of finite fields is $p^n$


Question: Why is $A^TA$ invertible if $A$ has independent columns?


Question: Proof that the largest eigenvalue of a stochastic matrix is $1$


Question: how does expectation maximization work?


Question: Are functions of independent variables also independent?


Question: What is an intuitive explanation for $\operatorname{div} \operatorname{curl} F = 0$?


Question: What is the difference between projected gradient descent and ordinary gradient descent?


Question: Functions which are Continuous, but not Bicontinuous


Question: Choose a random number between $0$ and $1$ and record its value. Keep doing it until the sum of the numbers exceeds $1$. How many tries do we need?


Question: How I can prove that the sequence $\sqrt{2} , \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}$ converges to 2?


Question: Difference between bijection and isomorphism?


Question: $\lim\limits_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite


Question: An easy example of a non-constructive proof without an obvious fix?


Question: Why doesnt induction extend to infinity? (re: Fourier series)


Question: A really complicated calculus book


Question: Why isnt several complex variables as fundamental as multivariable calculus?


Question: Parabola is an ellipse, but with one focal point at infinity


Question: Formal definition of conditional probability


Question: Why is it worth spending time on type theory?


Question: Why is cross product defined in the way that it is?


Question: What are the rules for equals signs with big-O and little-o?


Question: What book can bridge high school math and the more advanced topics?


Question: Foundation for analysis without axiom of choice?


Question: Intuition behind ideal


Question: How far is the list of known primes known to be complete?


Question: Why the real and imaginary parts of a complex analytic function are not independent?


Question: Do circles divide the plane into more regions than lines?


Question: On the functional square root of $x^2+1$


Question: $n!+1$ being a perfect square


Question: Does $\zeta(3)$ have a connection with $\pi$?


Question: Why do we need so many trigonometric definitions?


Question: Prove that the sum of pythagorean triples is always even


Question: What is the explanation for this visual proof of the sum of squares?


Question: Why are topological spaces interesting to study?


Question: Good math books to discover stuff by yourself


Question: Integral $\int_{-1}^{1} \frac{1}{x}\sqrt{\frac{1+x}{1-x}} \log \left( \frac{(r-1)x^{2} + sx + 1}{(r-1)x^{2} - sx + 1} \right) \, \mathrm dx$


Question: Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space?


Question: Why is the Laplacian important in Riemannian geometry?


Question: MIT 2015 Integration Question


Question: Is there a name for this type of polygon?


Question: Intuition behind Snake Lemma


Question: Is it possible for a function to be smooth everywhere, analytic nowhere, yet Taylor series at any point converges in a nonzero radius?


Question: Proof that a trigonometric function of a rational angle must be non-transcendental


Question: Does $|n^2 \cos n|$ diverge to $+\infty$?


Question: What are exact sequences, metaphysically speaking?


Question: What structure does the alternating group preserve?


Question: About the integral $\int_{0}^{+\infty}\sin(x\,\log x)\,dx$


Question: Effective Research Notes


Question: A new continued fraction for Apérys constant, $\zeta(3)$?


Question: Two questions about weakly convergent series related to $\sin(n^2)$ and Weyls inequality


Question: What is the integral of 1/x?


Question: How does one denote the set of all positive real numbers?


Question: Prove: If a sequence converges, then every subsequence converges to the same limit.


Question: How many prime numbers are known?


Question: What books are prerequisites for Spivaks Calculus?


Question: Create unique number from 2 numbers


Question: What is the main difference between a vector space and a field?


Question: If eigenvalues are positive, is the matrix positive definite?


Question: $\epsilon$-$\delta$ proof that $\lim\limits_{x \to 1} \frac{1}{x} = 1$.


Question: Finding Value of the Infinite Product $\prod \Bigl(1-\frac{1}{n^{2}}\Bigr)$


Question: Pen, pencils and paper to write math


Question: Video lectures on Real Analysis?


Question: If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative.


Question: Which of the numbers $1, 2^{1/2}, 3^{1/3}, 4^{1/4}, 5^{1/5}, 6^{1/6} , 7^{1/7}$ is largest, and how to find out without calculator?


Question: Zero divided by zero must be equal to zero


Question: Proof that every number ≥ $8$ can be represented by a sum of fives and threes.


Question: What is the difference between a Ring and an Algebra?


Question: Intuitive understanding of the derivatives of $\sin x$ and $\cos x$


Question: A linear operator commuting with all such operators is a scalar multiple of the identity.


Question: Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian


Question: Is $\pi$ equal to $180^\circ$?


Question: Is every Lebesgue measurable function on $\mathbb{R}$ the pointwise limit of continuous functions?


Question: Seeking a laymans guide to Measure Theory


Question: What are the Laws of Rational Exponents?


Question: An intuitive approach to the Jordan Normal form


Question: Intuitive Understanding of the constant $e$


Question: How far can one see over the ocean?


Question: Every power series is the Taylor series of some $C^{\infty}$ function


Question: Is the axiom of choice really all that important?


Question: On average, how many friends would I need to have to have at least one friends birthday every day?


Question: Is there a purely algebraic proof of the Fundamental Theorem of Algebra?


Question: What books should I get to self study beyond Calculus for someone about to start undergrad mathematics?


Question: Are there any objects which arent sets?


Question: What is the theme of analysis?


Question: Is there any geometric way to characterize $e$?


Question: Why and How do certain manipulations in indefinite integrations just work?


Question: History of the Concept of a Ring


Question: Simplest way to get the lower bound $\pi > 3.14$


Question: What to answer when people ask what I do in mathematics


Question: How many super imaginary numbers are there?


Question: Fibonacci infinite sum resulting in $\pi$


Question: Is $i = \sqrt{e^{\pi\sqrt{e^{\pi\sqrt\ldots}}}}$?


Question: Example of a compact set that isnt the spectrum of an operator


Question: Why is one $\infty$ number enough for complex numbers?


Question: How do the Catalan numbers turn up here?


Question: What is so special about $\alpha=-1$ in the integral of $x^\alpha$?


Question: To evaluate $\int_0^{+\infty} \frac{\;\mathrm dx}{\sqrt[3]{x^3+a^3}\sqrt[3]{x^3+b^3}\sqrt[3]{x^3+c^3}}$


Question: On a long proof


Question: Why do all the Platonic Solids exist?


Question: Bijection $f\colon\mathbb{N}\to\mathbb{N}$ with $f(0)=0$ and $|f(n)-f(n-1)|=n$


Question: How to solve an nth degree polynomial equation


Question: Number of onto functions


Question: What does := mean?


Question: Adding two polar vectors


Question: Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $


Question: Average Distance Between Random Points on a Line Segment


Question: Understanding Dot and Cross Product


Question: What are good books/other readings for elementary set theory?


Question: Best Algebraic Topology book/Alternative to Allen Hatcher free book?


Question: What is the implicit function theorem?


Question: What does it mean to integrate with respect to the distribution function?


Question: Very good linear algebra book.


Question: Can a piece of A4 paper be folded so that its thick enough to reach the moon?


Question: Every nonzero element in a finite ring is either a unit or a zero divisor


Question: Projection is an open map


Question: Can someone explain Cayleys Theorem step by step?


Question: Lemma/Proposition/Theorem, which one should we pick?


Question: Game theory - self study


Question: What are the required backgrounds of Robin Hartshornes Algebraic Geometry book?


Question: Semi-direct v.s. Direct products


Question: Why is it that if I count years from 2011 to 2014 as intervals I get 3 years, but if I count each year separately I get 4 years?


Question: What exactly is infinity?


Question: How do we know the ratio between circumference and diameter is the same for all circles?


Question: Good introductory book on geometric algebra


Question: Jacobi identity - intuitive explanation


Question: Why does the volume of the unit sphere go to zero?


Question: Is it possible to place 26 points inside a rectangle that is 20 cm by 15 cm so that the distance between every pair of points is greater than 5 cm?


Question: What does it mean to solve an equation?


Question: Isomorphic quotients by isomorphic normal subgroups


Question: How can this function have two different antiderivatives?


Question: Why arent integration and differentiation inverses of each other?


Question: Is 128 the only multi-digit power of 2 such that each of its digits is also a power of 2?


Question: Do we really need reals?


Question: How can someone reject a math result if everything has to be proved?


Question: What are some things we can prove they must exist, but have no idea what they are?


Question: I dont understand Gödels incompleteness theorem anymore


Question: Where to begin with foundations of mathematics


Question: Development of the Idea of the Determinant


Question: Do we need to formally teach the Greek Alphabet?


Question: The Meaning of the Fundamental Theorem of Calculus


Question: A conjecture involving prime numbers and circles


Question: Is the percentage symbol a constant?


Question: Is a proof still valid if only the writer understands it?


Question: Set Theoretic Definition of Numbers


Question: Why cant Antoines necklace fall apart?


Question: Areas versus volumes of revolution: why does the area require approximation by a cone?


Question: Designing an Irrational Numbers Wall Clock


Question: Must eigenvalues be numbers?


Question: How does the divisibility graphs work?


Question: Axiom of Choice: Where does my argument for proving the axiom of choice fail? Help me understand why this is an axiom, and not a theorem.


Question: The identity cannot be a commutator in a Banach algebra?


Question: If the field of a vector space werent characteristic zero, then what would change in the theory?


Question: What are some math books written in dialogue or story form, e.g., a teacher explaining to a student?


Question: A zero sum subset of a sum-full set


Question: Why cant we define more elementary functions?


Question: A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$


Question: Sheldon Cooper Primes


Question: Notations that are mnemonic outside of English


Question: Hidden patterns in $\sin(a x^2)$


Question: AM-GM-HM Triplets


Question: Why is the Galois Correspondence intuitively plausible?


Question: Generalizing the sum of consecutive cubes $\sum_{k=1}^n k^3 = \Big(\sum_{k=1}^n k\Big)^2$ to other odd powers


Question: A curious equality of integrals involving the prime counting function?


Question: Xmas Maths 2015


Question: How to evaluate $\int_0^\infty\operatorname{erfc}^n x\ \mathrm dx$?


Question: Time to reach a final state in a random dynamical system (answer known, proof unknown)


Question: What numbers can be created by $1-x^2$ and $x/2$?


Question: Is there a way to get trig functions without a calculator?


Question: Sample Standard Deviation vs. Population Standard Deviation


Question: Why does an integral change signs when flipping the boundaries?


Question: Why is the absolute value function not differentiable at $x=0$?


Question: Effect of elementary row operations on determinant?


Question: Do all square matrices have eigenvectors?


Question: Is zero a prime number?


Question: How to find a basis for the intersection of two vector spaces in $\mathbb{R}^n$?


Question: Subgroup of index $2$ is Normal


Question: The generating function for the Fibonacci numbers


Question: Examples of infinite groups such that all their respective elements are of finite order.


Question: Why are $3D$ transformation matrices $4 \times 4$ instead of $3 \times 3$?


Question: Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$


Question: Every linear mapping on a finite dimensional space is continuous


Question: difference between maximal element and greatest element


Question: How can a set contain itself?


Question: Sum of two closed sets in $\mathbb R$ is closed?


Question: How unique are $U$ and $V$ in the Singular Value Decomposition?


Question: Are normal subgroups transitive?


Question: Why is the ring of matrices over a field simple?


Question: In set theory, how are real numbers represented as sets?


Question: Is it possible to plot a graph of any shape?


Question: Proving $\frac{\sin x}{x} =\left(1-\frac{x^2}{\pi^2}\right)\left(1-\frac{x^2}{2^2\pi^2}\right) \left(1-\frac{x^2}{3^2\pi^2}\right)\cdots$


Question: Subgroups of finitely generated groups are not necessarily finitely generated


Question: $|G|>2$ implies $G$ has non trivial automorphism


Question: There exists a power of 2 such that the last five digits are all 3s or 6s. Find the last 5 digits of this number


Question: Does a Fourier transformation on a (pseudo-)Riemannian manifold make sense?


Question: $\sin 1^\circ$ is irrational but how do I prove it in a slick way? And $\tan(1^\circ)$ is .....


Question: How many fair dice exist?


Question: How to start a math blog?


Question: Modus moron rule of inference?


Question: precise official definition of a cell complex and CW-complex


Question: Alternative proofs that $A_5$ is simple


Question: Can you give me some concrete examples of magmas?


Question: Does Monty Hall logic apply to this real world situation?


Question: Are there dictionaries in math?


Question: How did early mathematicians make it without Set theory?


Question: Sharing a pepperoni pizza with your worst enemy


Question: Is it wrong to tell children that $1/0 =$ NaN is incorrect, and should be $∞$?


Question: Why is the Daniell integral not so popular?


Question: Say $a=b$. Is Do the same thing to both sides of an equation, and it still holds an axiom?


Question: Why is there antagonism towards extended real numbers?


Question: What is a topological space good for?


Question: Are rational points dense on every circle in the coordinate plane?


Question: What do mathematicians mean by equipped?


Question: Category-theoretic limit related to topological limit?


Question: Notation for an interval when you dont know which bound is greater


Question: Why can we use induction when studying metamathematics?


Question: Finding the value of $\sqrt{1+2\sqrt{2+3\sqrt{3+4\sqrt{4+5\sqrt{5+\dots}}}}}$


Question: What if $\pi$ was an algebraic number? (significance of algebraic numbers)


Question: Solution to the equation of a polynomial raised to the power of a polynomial.


Question: Are commutative C*-algebras really dual to locally compact Hausdorff spaces?


Question: Is $dx\,dy$ really a multiplication of $dx$ and $dy$?


Question: Proving $\sum_{n=-\infty}^\infty e^{-\pi n^2} = \frac{\sqrt[4] \pi}{\Gamma\left(\frac 3 4\right)}$


Question: How do you prove Gautschis inequality for the gamma function?


Question: Function that is the sum of all of its derivatives


Question: Identity for simple 1D random walk


Question: Prove $\int\limits_{0}^{\pi/2}\frac{dx}{1+\sin^2{(\tan{x})}}=\frac{\pi}{2\sqrt{2}}\bigl(\frac{e^2+3-2\sqrt{2}}{e^2-3+2\sqrt{2}}\bigr)$


Question: How to maintain enthusiasm and joy in teaching when the material grows stale


Question: An exotic sequence


Question: Making trigonometric substitutions rigorous


Question: A new kind of fractal?


Question: How do you go about doing mathematics on a day to day basis?


Question: $C^{k}$-manifolds: how and why?


Question: Why do I only breathe out of one nostril?


Question: Why are so few foods blue?


Question: Does DNA have the equivalent of IF-statements, WHILE loops, or function calls? How about GOTO?


Question: How many times did terrestrial life emerge from the ocean?


Question: Do bacteria die of old age?


Question: Is there a reason why human eyesight and plants make use of the same wavelength of light?


Question: Why is thymine rather than uracil used in DNA?


Question: Are male and female brains physically different from birth?


Question: What is the effect of non-vaccinated people on vaccinated people?


Question: Why do plants have green leaves and not red?


Question: Can HIV be transmitted via mosquitos?