Question: Cooling a cup of coffee with help of a spoon


Question: Can I compute the mass of a coin based on the sound of its fall?


Question: How does light bend around my finger tip?


Question: How does gravity escape a black hole?


Question: Did the Big Bang happen at a point?


Question: Why are mirror images flipped horizontally but not vertically?


Question: Do we know why there is a speed limit in our universe?


Question: Book recommendations


Question: What experiment would disprove string theory?


Question: Why dont metals bond when touched together?


Question: Why do ballpoint pens write better on pages that have pages below them?


Question: What is Chirped Pulse Amplification, and why is it important enough to warrant a Nobel Prize?


Question: Why does kinetic energy increase quadratically, not linearly, with speed?


Question: What really allows airplanes to fly?


Question: Why are four-legged chairs so common?


Question: If I sliced the universe in half, would the slice go through a star?


Question: Dont heavier objects actually fall faster because they exert their own gravity?


Question: How do towels stay on hooks?


Question: What exactly is a photon?


Question: Does Earth really have two high-tide bulges on opposite sides?


Question: Strange ice found in my garden


Question: Why is the detection of gravitational waves so significant?


Question: Surviving under water in air bubble


Question: Why do we bend a book to keep it straight?


Question: If photons have no mass, how can they have momentum?


Question: Why doesnt matter pass through other matter if atoms are 99.999% empty space?


Question: Why is Googles quantum supremacy experiment impressive?


Question: Are units of angle really dimensionless?


Question: Why dont electrons crash into the nuclei they orbit?


Question: Why does space expansion not expand matter?


Question: When separating an Oreo cookie, why does the cream stick to just one side only?


Question: Why does NASA use gold foil on equipment and gold-coated visors?


Question: How do moving charges produce magnetic fields?


Question: How does a knife cut things at the atomic level?


Question: Why do we not have spin greater than 2?


Question: Why do shadows from the sun join each other when near enough?


Question: Gauge symmetry is not a symmetry?


Question: Why do we actually see the sun?


Question: Whats the point of Hamiltonian mechanics?


Question: Could Legolas actually see that far?


Question: How do you make more precise instruments while only using less precise instruments?


Question: Why does holding something up cost energy while no work is being done?


Question: What makes a theory Quantum?


Question: Given Newtons third law, why are things capable of moving?


Question: Why does Stephen Hawking say black holes dont exist?


Question: Why do sunbeams diverge even though the sun is much more than a few kilometers away?


Question: How do I explain to a six year old why people on the other side of the Earth dont fall off?


Question: Simple check for the global shape of the Earth


Question: Why are the harmonics of a piano tone not multiples of the base frequency?


Question: What is a field, really?


Question: Why are the wet patches on these floor tiles circular?


Question: Why is nuclear waste more dangerous than the original nuclear fuel?


Question: Is $\pi^2 \approx g$ a coincidence?


Question: Why does a mirror split my laser beam?


Question: Why is my hand not burned by the air in an oven at 200 °C?


Question: Why would spacetime curvature cause gravity?


Question: Does someone falling into a black hole see the end of the universe?


Question: Why are the windows of bridges of ships always inclined?


Question: Does the Planck scale imply that spacetime is discrete?


Question: Is temperature a Lorentz invariant in relativity?


Question: Why do people categorically dismiss some simple quantum models?


Question: If you view the Earth from far enough away can you observe its past?


Question: Is time continuous or discrete?


Question: How can you weigh your own head in an accurate way?


Question: Why does my tea periodically alternate its rotational speed after stirring? (Link to video below)


Question: How fast does gravity propagate?


Question: How do I experimentally measure the surface area of a rock?


Question: Is the butterfly effect real?


Question: Why doesnt water boil in the oven?


Question: A list of inconveniences between quantum mechanics and (general) relativity?


Question: Why are there only derivatives to the first order in the Lagrangian?


Question: Reading the Feynman lectures in 2012


Question: Why is the vibration in my wire acting so oddly?


Question: Why can I touch aluminum foil in the oven and not get burned?


Question: Why does paper cut through things so well?


Question: What does it mean for two objects to touch?


Question: Why do spaceships heat up when entering earth but not when exiting?


Question: Does a particle exert force on itself?


Question: Why does Newtons Third Law actually work?


Question: Why does ice cream get harder when colder?


Question: Why does the humidifier make a stoves flame orange?


Question: How does mass leave the body when you lose weight?


Question: Is anti-matter matter going backwards in time?


Question: Calculus of variations -- how does it make sense to vary the position and the velocity independently?


Question: Why dont we use weights to store energy?


Question: Why do wet objects become darker?


Question: Why am I not burned by a strong wind?


Question: The Role of Rigor


Question: On this infinite grid of resistors, whats the equivalent resistance?


Question: If all motion is relative, how does light have a finite speed?


Question: Could we send a man safely to the Moon in a rocket without knowledge of general relativity?


Question: Superfields and the Inconsistency of regularization by dimensional reduction


Question: Is it necessary to consume energy to perform computation?


Question: Toilet paper dilemma


Question: Is it possible for information to be transmitted faster than light by using a rigid pole?


Question: Why do electrons, according to my textbook, exist forever?


Question: What happens to the energy when waves perfectly cancel each other?


Question: Why does a helium filled balloon move forward in a car when the car is accelerating?


Question: What is the actual significance of the amplituhedron?


Question: Can the Heisenberg Uncertainty Principle be explained intuitively?


Question: What, in simplest terms, is gauge invariance?


Question: Can Maxwells equations be derived from Coulombs Law and Special Relativity?


Question: Is the universe fundamentally deterministic?


Question: Why are most metals gray/silver?


Question: Is it possible to start fire using moonlight?


Question: What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis?


Question: Books for general relativity


Question: Why is glass transparent?


Question: How can anything ever fall into a black hole as seen from an outside observer?


Question: Whats inside a proton?


Question: Why is oil a better lubricant than water?


Question: Why do tuning forks have two prongs?


Question: Why do fusion and fission both release energy?


Question: Why is quantum entanglement considered to be an active link between particles?


Question: Why are some people are claiming that the Big Bang never happened?


Question: How do we know that radioactive decay rates are constant over billions of years?


Question: How can I stand on the ground? EM or/and Pauli?


Question: Is Angular Momentum truly fundamental?


Question: What is $\Delta t$ in the time-energy uncertainty principle?


Question: Why the Principle of Least Action?


Question: Why does the Suns (or other stars) nuclear reaction not use up all its fuel immediately?


Question: Intuitively, why are bundles so important in Physics?


Question: Why does a sticker slowly peel off, but if it is pulled quickly it tears?


Question: What is known about the topological structure of spacetime?


Question: Does the $\frac{4}{3}$ problem of classical electromagnetism remain in quantum mechanics?


Question: How can we see an atom now? What was the scale of this equipment?


Question: Is there such thing as imaginary time dilation?


Question: Thought experiment - would you notice if you fell into a black hole?


Question: Explain it to me like Im a physics grad: Greenhouse Effect


Question: QM without complex numbers


Question: What Is Energy? Where did it come from?


Question: Why is filling a balloon from your mouth much harder initially?


Question: If gravity isnt a force, then why do we learn in school that it is?


Question: If I pull a metal bar for long enough with a constant small force, will it eventually break?


Question: Which is stronger, a rope without knots or a rope with knots?


Question: Would a pin head heated to 15 million degrees Celsius kill everyone in a 1000 mile radius?


Question: Why is there a scarcity of lithium?


Question: Why do most formulas in physics have integer and rational exponents?


Question: Is there something similar to Noethers theorem for discrete symmetries?


Question: What is a good introductory book on quantum mechanics?


Question: Best books for mathematical background?


Question: What is the physical meaning of commutators in quantum mechanics?


Question: Differentiating Propagator, Greens function, Correlation function, etc


Question: What justifies dimensional analysis?


Question: How is a quantum superposition different from a mixed state?


Question: Why dont miners get boiled to death at $4$ km deep?


Question: Trace of a commutator is zero - but what about the commutator of $x$ and $p$?


Question: About the complex nature of the wave function?


Question: Why was carbon-12 chosen for the atomic mass unit?


Question: Why does the shower curtain move towards me when I am taking a hot shower?


Question: Where is the flaw in this machine that decreases the entropy of a closed system?


Question: Why does the atmosphere rotate along with the earth?


Question: Why does hot water clean better than cold water?


Question: What is the speed of sound in space?


Question: How can a black hole produce sound?


Question: What is the proper way to explain the twin paradox?


Question: Why are radiators always placed under windows?


Question: Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip?


Question: If Earth had rings?


Question: How can time dilation be symmetric?


Question: Quantum Entanglement - Whats the big deal?


Question: If we had a perfectly efficient computer and all the energy in the Milky-way available, what number could it count to?


Question: Why does the LIGO observation disprove higher dimensions?


Question: Why does nature favour the Laplacian?


Question: What software programs are used to draw physics diagrams, and what are their relative merits?


Question: Why do same/opposite electric charges repel/attract each other, respectively?


Question: What conservation law corresponds to Lorentz boosts?


Question: Why quantum mechanics?


Question: Does a gun exert enough gravity on the bullet it fired to stop it?


Question: Why does my wooden door disperse light into a rainbow color spectrum?


Question: What is the relation between electromagnetic wave and photon?


Question: Why is the $S_{z} =0$ state forbidden for photons?


Question: Seeing something from only one angle means you have only seen (what?)% of its surface area at most?


Question: Are Newtons laws of motion laws or definitions of force and mass?


Question: Does juggling balls reduce the total weight of the juggler and balls?


Question: Why does a remote car key work when held to your head/body?


Question: Why does matter exist in 3 states (liquids, solid, gas)?


Question: How did Einstein know the speed of light was constant?


Question: Why does a billiard ball stop when it hits another billiard ball head on?


Question: Am I attracting Pluto?


Question: Why does a yellow object turn white under a yellow light? Shouldnt it turn yellow instead?


Question: Why is a laserpointer able to erase a glow-in-the-dark sticker?


Question: Can tin foil hats block anything?


Question: Why is a $5-60 mph$ time slower than a $0-60 mph$ time for some automobiles?


Question: Why do scientists think that all the laws of physics that apply in our galaxy apply in other galaxies?


Question: Why do phones land face down?


Question: What is a manifold?


Question: Why cant $ i\hbar\frac{\partial}{\partial t}$ be considered the Hamiltonian operator?


Question: How does this baby rattle work?


Question: Superluminal neutrinos


Question: Why do metals only glow red, yellow and white and not through the full range of the spectrum?


Question: What is time, does it flow, and if so what defines its direction?


Question: How exactly do you avoid fooling yourself?


Question: Why are differential equations for fields in physics of order two?


Question: Quantum Field Theory from a mathematical point of view


Question: Why is light bent but not accelerated?


Question: Why can Hiroshima be inhabited when Chernobyl cannot?


Question: What makes running so much less energy-efficient than bicycling?


Question: Why is it bad taste to have a dimensional quantity in the argument of a logarithm or exponential function?


Question: What is spontaneous symmetry breaking in quantum systems?


Question: Why does a full moon seem uniformly bright from earth, shouldnt it be dimmer at the border?


Question: Why is information indestructible?


Question: Why dont fluorescent lights produce shadows?


Question: If you are vacuuming your carpet and you wrap the cord around your body do you become a magnet?


Question: When I walk down the stairs where does my potential energy go?


Question: What is more fundamental, fields or particles?


Question: Why does rainwater form moving waves on the ground? Is there a name for this effect?


Question: List of freely available physics books


Question: In the earths crust, why is there far more uranium than gold?


Question: Could a living planet alter its own trajectory only by changing its shape?


Question: Classical and quantum anomalies


Question: What causes the water in this fountain to reverse direction?


Question: What is spin as it relates to subatomic particles?


Question: If dark matter only interacts with gravity, why doesnt it all clump together in a single point?


Question: Why doesnt water actually perfectly wet glass?


Question: Can photons be detected without being absorbed?


Question: Is there a symmetry associated to the conservation of information?


Question: What does one second after big bang mean?


Question: What happened to David John Candlin?


Question: Why do travelling waves continue after amplitude sum = 0?


Question: Will a hole cut into a metal disk expand or shrink when the disc is heated?


Question: Why does public mains power use 50-60 Hz and 100-240 V?


Question: How can magnets be used to pick up pieces of metal when the force from a magnetic field does no work?


Question: How do laser tape measures work?


Question: Why must a physical theory be mathematically self-consistent?


Question: Why does a rubber band become a lighter color when stretched?


Question: Does centrifugal force exist?


Question: Why does water stop boiling immediately after turning off the heat?


Question: Why does fire make very little sound?


Question: Where does the extra kinetic energy come from in a gravitational slingshot?


Question: What was the major discovery on gravitational waves made March 17th, 2014, in the BICEP2 experiment?


Question: Why doesnt the Moon fall onto the Earth?


Question: How and why do accelerating charges radiate electromagnetic radiation?


Question: Visually stunning math concepts which are easy to explain


Question: Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?


Question: How long will it take Marie to saw another board into 3 pieces?


Question: Can I use my powers for good?


Question: The staircase paradox, or why $\pi\ne4$


Question: How to study math to really understand it and have a healthy lifestyle with free time?


Question: Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem)


Question: Whats an intuitive way to think about the determinant?


Question: Does $\pi$ contain all possible number combinations?


Question: Splitting a sandwich and not feeling deceived


Question: What was the first bit of mathematics that made you realize that math is beautiful? (For childrens book)


Question: Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real?


Question: Why can you turn clothing right-side-out?


Question: Examples of patterns that eventually fail


Question: Mathematical difference between white and black notes in a piano


Question: Do complex numbers really exist?


Question: What are imaginary numbers?


Question: How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?


Question: Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$


Question: The Egg: Bizarre behavior of the roots of a family of polynomials.


Question: Is this Batman equation for real?


Question: Best Sets of Lecture Notes and Articles


Question: My sons Sum of Some is beautiful! But what is the proof or explanation?


Question: Proofs that every mathematician should know.


Question: Why does $1+2+3+\cdots = -\frac{1}{12}$?


Question: What is the intuitive relationship between SVD and PCA?


Question: How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?


Question: On familiarity (or How to avoid going down the Math Rabbit Hole?)


Question: Fourier transform for dummies


Question: The Ring Game on $K[x,y,z]$


Question: Pedagogy: How to cure students of the law of universal linearity?


Question: Find five positive integers whose reciprocals sum to $1$


Question: Can every proof by contradiction also be shown without contradiction?


Question: Obvious theorems that are actually false


Question: Zero to the zero power – is $0^0=1$?


Question: If $AB = I$ then $BA = I$


Question: Calculating the length of the paper on a toilet paper roll


Question: How can you prove that a function has no closed form integral?


Question: A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language


Question: Surprising identities / equations


Question: Is it true that $0.999999999\ldots=1$?


Question: Why dont we define imaginary numbers for every impossibility?


Question: What is the importance of eigenvalues/eigenvectors?


Question: Nice examples of groups which are not obviously groups


Question: Multiple-choice question about the probability of a random answer to itself being correct


Question: In Russian roulette, is it best to go first?


Question: One question to know if the number is 1, 2 or 3


Question: Why does this innovative method of subtraction from a third grader always work?


Question: Intuition for the definition of the Gamma function?


Question: Why can ALL quadratic equations be solved by the quadratic formula?


Question: Math without pencil and paper


Question: V.I. Arnold says Russian students cant solve this problem, but American students can -- why?


Question: Really advanced techniques of integration (definite or indefinite)


Question: Is mathematics one big tautology?


Question: Help with a prime number spiral which turns 90 degrees at each prime


Question: Is $10$ a magical number or I am missing something?


Question: Funny identities


Question: Cant argue with success? Looking for bad math that gets away with it


Question: Is $7$ the only prime followed by a cube?


Question: In the history of mathematics, has there ever been a mistake?


Question: The Mathematics of Tetris


Question: Given an infinite number of monkeys and an infinite amount of time, would one of them write Hamlet?


Question: Why do mathematicians use single-letter variables?


Question: How does one prove the determinant inequality $\det\left(6(A^3+B^3+C^3)+I_{n}\right)\ge 5^n\det(A^2+B^2+C^2)$?


Question: Is a matrix multiplied with its transpose something special?


Question: How discontinuous can a derivative be?


Question: Too old to start math


Question: Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$


Question: What is the maximum volume that can be contained by a sheet of paper?


Question: Please explain the intuition behind the dual problem in optimization.


Question: Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?


Question: Norms Induced by Inner Products and the Parallelogram Law


Question: Fun but serious mathematics books to gift advanced undergraduates.


Question: Which answer in this list is the correct answer to this question?


Question: What is the practical difference between a differential and a derivative?


Question: Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$


Question: Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers


Question: Can you answer my sons fourth-grade homework question: Which numbers are prime, have digits adding to ten and have a three in the tens place?


Question: The Integral that Stumped Feynman?


Question: In (relatively) simple words: What is an inverse limit?


Question: What is the importance of the Collatz conjecture?


Question: What are some examples of when Mathematics accidentally discovered something about the world?


Question: Derivative of sigmoid function $\sigma (x) = \frac{1}{1+e^{-x}}$


Question: Conjectures that have been disproved with extremely large counterexamples?


Question: Best Fake Proofs? (A M.SE April Fools Day collection)


Question: Any open subset of $\Bbb R$ is a countable union of disjoint open intervals


Question: Why study Algebraic Geometry?


Question: Why are rings called rings?


Question: What is the result of $\infty - \infty$?


Question: Integral Milking


Question: A 1,400 years old approximation to the sine function by Mahabhaskariya of Bhaskara I


Question: How to read a book in mathematics?


Question: Why do we care about dual spaces?


Question: What are some counter-intuitive results in mathematics that involve only finite objects?


Question: How many fours are needed to represent numbers up to $N$?


Question: Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer?


Question: Your favourite application of the Baire Category Theorem


Question: What books must every math undergraduate read?


Question: Proving you *cant* make $2011$ out of $1,2,3,4$: nice twist on the usual


Question: Does the open mapping theorem imply the Baire category theorem?


Question: Optimizing response times of an ambulance corp: short-term versus average


Question: Is there a 0-1 law for the theory of groups?


Question: How can a piece of A4 paper be folded in exactly three equal parts?


Question: Eigenvectors of real symmetric matrices are orthogonal


Question: Do men or women have more brothers?


Question: In simple English, what does it mean to be transcendental?


Question: How to check if a point is inside a rectangle?


Question: Good books and lecture notes about category theory.


Question: Why does this matrix give the derivative of a function?


Question: Is it faster to count to the infinite going one by one or two by two?


Question: What are the Differences Between a Matrix and a Tensor?


Question: How do I convince someone that $1+1=2$ may not necessarily be true?


Question: How do I sell out with abstract algebra?


Question: Why can a Venn diagram for $4+$ sets not be constructed using circles?


Question: Identification of a quadrilateral as a trapezoid, rectangle, or square


Question: Meaning of Rays in Polar Plot of Prime Numbers


Question: What does $2^x$ really mean when $x$ is not an integer?


Question: What do modern-day analysts actually do?


Question: Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$


Question: Is computer science a branch of mathematics?


Question: What is the difference between linear and affine function


Question: Which one result in mathematics has surprised you the most?


Question: Books on Number Theory for Layman


Question: Teaching myself differential topology and differential geometry


Question: List of interesting math videos / documentaries


Question: Exterior Derivative vs. Covariant Derivative vs. Lie Derivative


Question: How to show $e^{e^{e^{79}}}$ is not an integer


Question: Are $14$ and $21$ the only interesting numbers?


Question: How could we define the factorial of a matrix?


Question: When can you switch the order of limits?


Question: List of Interesting Math Blogs


Question: Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$


Question: How do we prove that something is unprovable?


Question: How many sides does a circle have?


Question: Whats the intuition behind Pythagoras theorem?


Question: Why is compactness so important?


Question: Can a coin with an unknown bias be treated as fair?


Question: A Topology such that the continuous functions are exactly the polynomials


Question: What is the geometric interpretation of the transpose?


Question: Counterintuitive examples in probability


Question: What is a good complex analysis textbook, barring Ahlforss?


Question: What were some major mathematical breakthroughs in 2016?


Question: How to intuitively understand eigenvalue and eigenvector?


Question: Importance of Representation Theory


Question: Advice to young mathematicians


Question: Why cant differentiability be generalized as nicely as continuity?


Question: How to define a bijection between $(0,1)$ and $(0,1]$?


Question: Derivative of Softmax loss function


Question: Some users are mind bogglingly skilled at integration. How did they get there?


Question: How do people perform mental arithmetic for complicated expressions?


Question: Can we ascertain that there exists an epimorphism $G\rightarrow H$?


Question: What Does it Really Mean to Have Different Kinds of Infinities?


Question: How do you revise material that you already half-know, without getting bored and demotivated?


Question: Are there any series whose convergence is unknown?


Question: When can a sum and integral be interchanged?


Question: A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$


Question: Symmetry of function defined by integral


Question: Why $\sqrt{-1 \cdot {-1}} \neq \sqrt{-1}^2$?


Question: Self-Contained Proof that $\sum\limits_{n=1}^{\infty} \frac1{n^p}$ Converges for $p > 1$


Question: There are apparently $3072$ ways to draw this flower. But why?


Question: Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction


Question: Proof that the trace of a matrix is the sum of its eigenvalues


Question: Limit of $L^p$ norm


Question: Is there a categorical definition of submetry?


Question: Deleting any digit yields a prime... is there a name for this?


Question: Inverse of the sum of matrices


Question: What is $dx$ in integration?


Question: Is $2048$ the highest power of $2$ with all even digits (base ten)?


Question: Why is Eulers Gamma function the best extension of the factorial function to the reals?


Question: $L^p$ and $L^q$ space inclusion


Question: Do we have negative prime numbers?


Question: Why do people use it is easy to prove?


Question: Taking Seats on a Plane


Question: Why is $1^{\infty}$ considered to be an indeterminate form


Question: Mathematical ideas that took long to define rigorously


Question: Open problems in General Relativity


Question: How far can one get in analysis without leaving $\mathbb{Q}$?


Question: How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?


Question: Rational roots of polynomials


Question: Lesser-known integration tricks


Question: A variation of Fermats little theorem in the form $a^{n-d}\equiv a$ (mod $p$).


Question: Is there a homology theory that counts connected components of a space?


Question: Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$


Question: An Introduction to Tensors


Question: Transpose of inverse vs inverse of transpose


Question: How to prove Eulers formula: $e^{i\varphi}=\cos(\varphi) +i\sin(\varphi)$?


Question: Intuition behind Matrix Multiplication


Question: Striking applications of integration by parts


Question: Why is the Penrose triangle impossible?


Question: Software for drawing geometry diagrams


Question: How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?


Question: Examples of mathematical discoveries which were kept as a secret


Question: What properties of busy beaver numbers are computable?


Question: What happens when we (incorrectly) make improper fractions proper again?


Question: Can you provide me historical examples of pure mathematics becoming useful?


Question: What are the most overpowered theorems in mathematics?


Question: Do we know if there exist true mathematical statements that can not be proven?


Question: Is there any integral for the Golden Ratio?


Question: Using proof by contradiction vs proof of the contrapositive


Question: Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$


Question: Induction on Real Numbers


Question: Proof that ${\left(\pi^\pi\right)}^{\pi^\pi}$ (and now $\pi^{\left(\pi^{\pi^\pi}\right)}$) is a noninteger.


Question: The Hole in One Pizza


Question: Proof of $\frac{1}{e^{\pi}+1}+\frac{3}{e^{3\pi}+1}+\frac{5}{e^{5\pi}+1}+\ldots=\frac{1}{24}$


Question: What functions can be made continuous by mixing up their domain?


Question: Is there a general formula for solving 4th degree equations (quartic)?


Question: Discontinuous derivative.


Question: Monty hall problem extended.


Question: The sum of an uncountable number of positive numbers


Question: Is Apple ipad / tablet good for mathematics students?


Question: Stopping the Will I need this for the test question


Question: Are there any open mathematical puzzles?


Question: Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?


Question: How to distinguish between walking on a sphere and walking on a torus?


Question: Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?


Question: Is there another simpler method to solve this elementary school math problem?


Question: Most ambiguous and inconsistent phrases and notations in maths


Question: Why does factoring eliminate a hole in the limit?


Question: Whats the point in being a skeptical learner


Question: Good book for self study of a First Course in Real Analysis


Question: Overview of basic results about images and preimages


Question: How to determine with certainty that a function has no elementary antiderivative?


Question: What actually is a polynomial?


Question: Sum of random decreasing numbers between 0 and 1: does it converge??


Question: Are there real-life relations which are symmetric and reflexive but not transitive?


Question: Calculate Rotation Matrix to align Vector A to Vector B in 3d?


Question: Whats new in higher dimensions?


Question: How do you describe your mathematical research in laymans terms?


Question: Pythagorean triples that survive Eulers totient function


Question: Whats the significance of Tates thesis?


Question: What is the difference between singular value and eigenvalue?


Question: Intuition of the meaning of homology groups


Question: Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?


Question: Why does an argument similiar to 0.999...=1 show 999...=-1?


Question: Does a cubic matrix exist?


Question: Is the following matrix invertible?


Question: Do most mathematicians know most topics in mathematics?


Question: Slice of pizza with no crust


Question: Has lack of mathematical rigour killed anybody before?


Question: Alternative notation for exponents, logs and roots?


Question: Math and mental fatigue


Question: What is the Riemann-Zeta function?


Question: Why do both sine and cosine exist?


Question: What is the best book to learn probability?


Question: The square roots of different primes are linearly independent over the field of rationals


Question: Can someone explain the math behind tessellation?


Question: Where to start learning Linear Algebra?


Question: Intuitively, what is the difference between Eigendecomposition and Singular Value Decomposition?


Question: Looking for an intuitive explanation why the row rank is equal to the column rank for a matrix


Question: Example of infinite field of characteristic $p\neq 0$


Question: Is non-standard analysis worth learning?


Question: Connection between Fourier transform and Taylor series


Question: Are we allowed to compare infinities?


Question: Online tool for making graphs (vertices and edges)?


Question: Whats 4 times more likely than 80%?


Question: Simple theorems that are instances of deep mathematics


Question: Do Arithmetic Mean and Geometric Mean of Prime Numbers converge?


Question: Partial derivative in gradient descent for two variables


Question: Apparently sometimes $1/2 < 1/4$?


Question: Is the product of two Gaussian random variables also a Gaussian?


Question: Intuitive explanation of entropy


Question: The Best of Dover Books (a.k.a the best cheap mathematical texts)


Question: Are mathematical articles on Wikipedia reliable?


Question: What are the differences between rings, groups, and fields?


Question: Why do units (from physics) behave like numbers?


Question: Studying Euclidean geometry using hyperbolic criteria


Question: Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$


Question: Identification of a curious function


Question: What is the difference between regression and classification?


Question: How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen?


Question: How do you respond to I was always bad at math?


Question: What are the numbers before and after the decimal point referred to in mathematics?


Question: Can you explain the Axiom of choice in simple terms?


Question: Why do we use the word scalar and not number in Linear Algebra?


Question: What is the difference between Fourier series and Fourier transformation?


Question: What is the difference between a point and a vector?


Question: The direct sum $\oplus$ versus the cartesian product $\times$


Question: Is the blue area greater than the red area?


Question: Does $R[x] \cong S[x]$ imply $R \cong S$?


Question: Why does mathematical convention deal so ineptly with multisets?


Question: List of interesting math podcasts?


Question: Can you raise a number to an irrational exponent?


Question: Examples of mathematical results discovered late


Question: $\pi$ in arbitrary metric spaces


Question: Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$


Question: Is there any mathematical reason for this digit-repetition-show?


Question: Visually deceptive proofs which are mathematically wrong


Question: Best book of topology for beginner?


Question: Can someone explain Gödels incompleteness theorems in layman terms?


Question: Why is $1$ not a prime number?


Question: Studying for the Putnam Exam


Question: Intuitive interpretation of the Laplacian


Question: what is expected from a PhD student?


Question: Why is the eigenvector of a covariance matrix equal to a principal component?


Question: Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$


Question: Is it possible for a function to be in $L^p$ for only one $p$?


Question: What are some examples of notation that really improved mathematics?


Question: Classification of prime ideals of $\mathbb{Z}[X]$


Question: Division by $0$


Question: Application of Hilberts basis theorem in representation theory


Question: Is $0$ a natural number?


Question: Why is negative times negative = positive?


Question: On Ph.D. Qualifying Exams


Question: Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$


Question: What are some examples of a mathematical result being counterintuitive?


Question: Can you be 1/12th Cherokee?


Question: Why did mathematicians take Russells paradox seriously?


Question: Values of $\sum_{n=0}^\infty x^n$ and $\sum_{n=0}^N x^n$


Question: How to find ${\large\int}_0^1\frac{\ln^3(1+x)\ln x}x\mathrm dx$


Question: What is the probability that a point chosen randomly from inside an equilateral triangle is closer to the center than to any of the edges?


Question: Why is learning modern algebraic geometry so complicated?


Question: What should be the intuition when working with compactness?


Question: Motivation of irrationality measure


Question: Show that the determinant of $A$ is equal to the product of its eigenvalues


Question: The median minimizes the sum of absolute deviations (the $ {\ell}_{1} $ norm)


Question: Why is gradient the direction of steepest ascent?


Question: Learning Lambda Calculus


Question: Is there a function that grows faster than exponentially but slower than a factorial?


Question: How to find solutions of linear Diophantine ax + by = c?


Question: What is category theory useful for?


Question: Are half of all numbers odd?


Question: Can $x^{x^{x^x}}$ be a rational number?


Question: Prove that $C\exp(x)$ is the only set of functions for which $f(x) = f(x)$


Question: Are if and iff interchangeable in definitions?


Question: Is there an integral that proves $\pi > 333/106$?


Question: Past open problems with sudden and easy-to-understand solutions


Question: How to prove $\int_0^1\tan^{-1}\left[\frac{\tanh^{-1}x-\tan^{-1}x}{\pi+\tanh^{-1}x-\tan^{-1}x}\right]\frac{dx}{x}=\frac{\pi}{8}\ln\frac{\pi^2}{8}?$


Question: What remains in a students mind


Question: Proof $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$


Question: Why is $\infty \cdot 0$ not clearly equal to $0$?


Question: What are good books to learn graph theory?


Question: Can an irrational number raised to an irrational power be rational?


Question: Advantages of Mathematics competition/olympiad students in Mathematical Research


Question: Whats the difference between predicate and propositional logic?


Question: How can I find the surface area of a normal chicken egg?


Question: Why does LHopitals rule fail in calculating $\lim_{x \to \infty} \frac{x}{x+\sin(x)}$?


Question: Why study linear algebra?


Question: Why is integration so much harder than differentiation?


Question: Why is $\cos (90)=-0.4$ in WebGL?


Question: Why “characteristic zero” and not “infinite characteristic”?


Question: Why are the solutions of polynomial equations so unconstrained over the quaternions?


Question: Making Friends around a Circular Table


Question: Is There An Injective Cubic Polynomial $\mathbb Z^2 \rightarrow \mathbb Z$?


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