Sketch on history of mathematics 2013

The History of Mathematics- A BBC Documentary

http://www.youtube.com/watch?v=xioaDjF0Kao
(10 min.)

http://www.youtube.com/watch?v=gOV2kZ-3PiM
(full)

**Patterns in the Universe**

   Origin in ancient Egypt. Egyptians develop fractions for

practical needs, e.g. to divide up 9 loafs of bread equally between 10 people.
No general theories in Egyptian mathematics, only concrete numbers.

From Egypt to Babylonia. Base of 60 – from Babylonia. E.g.
in time. Invented 0.

Greek math. Invent a deductive system: axioms and proof.
Pythagoras in Samos. Schools were “a way of life”: communal living, involved in
city politics. Appeal to beautiful arguments. Relationship between a good
solution and beauty.

Plato considers math as bedrock of knowledge. Geometry is
the key to understanding the Universe. Understanding of geometry required for philosophy.

Euclid – a system of axioms and proofs. Euclidian geometry.
Alexandria. Archimedes. Designed weapons. Calculating the area of an unknown
figure using a known figure: calculating the area of a circle using triangle
approximation.

**BBC The Story of Maths - The Genius of the East**
FULL (2of4)

http://www.youtube.com/watch?feature=endscreen&v=N34bkZrQh90&NR=1

China: started building the Great Wall in 220 B.C., stimulates
mathematics about volumes (of materials), angles, etc. Use decimal place value
system, i.e. a units column, a tens columns, a hundreds, etc.

India – invent “0” in 9th century A.D.

Trigonometry – translates shapes (geometry) into numbers and
back. Math is the study of number and form. Number and form are the opposites
tied together.

Trigonometry used for understanding the distances in space,
also in engineering and sailing.

Islamic world – in Baghdad, “the house of Wisdom”. Cubic
equations. Omar Khayam – a poet and a mathematician, tries to find a general
solution to cubic (or quadratic?) equations.

Feudal Europe, Italy – Fibonacci (Leonardo of Pizza).
Introduced Hindu-Arabic numerals to Europe, against the opposition of
conservatives who saw this as too easy (as opposed to Roman numerals), and thus
giving power to the masses. Fibonacci numbers – used for calculating growth.

Tartaglia – in Bologna. Slashed across the face by a French
army. Finds a formula to solve all kinds of cubic equations.

**BBC The Story of Maths - The Frontiers of Space** (3of4)

http://www.youtube.com/watch?v=puIvz54Dx5I&feature=relmfu

   Renaissance –

combination of opposite qualities in a person, e.g. a mathematician and
an artist.

Descartes links geometry to algebra using the Cartesian
coordinates, and writing equations

Fermat – invents the modern number theory

(Development of mathematics, and science, knowledge in
general coincides with development of this or that type of culture.)

Newton – calculus

Leibniz (as Descartes) liked to lie in the bed in the
morning to think, to jot down his ideas. Leibniz invented a practical
calculating machine.

Bernoulli – from Basel, Switzerland. Merchants.

Leonard Euler – a protégé of Bernoulli

(Humboldt – a great educationist in Germany, XVIII century)

France, XVIII century – Fourier analysis.

Germany, XVIII century – Gauss. First idea that the space is
curved. Didn’t dare to publish.

Janos Bolyai – “hyperbolic geometry”, angles of a triangle
add up to less than 180 degrees

Lobachevsky discovered the same geometry 2 years prior to
Bolyai.

B. Reimann – anticipates development of relativity theory.
Mathematics in general anticipates developments in science and technology. We
have the math, but don’t know its meaning in the real world. Math is an
abstraction.

**BBC The Story of Maths - To Infinity and Beyond** (4of4)

http://www.youtube.com/watch?v=yuraReW7U8E&feature=watch-vrec

Galois
(1832) – mathematics is not a study of numbers or shapes, but of structures.

“A mathematician is a pattern searcher”

Hilbert
proves that all equations can be derived from a finite set of equations. What
the set was he couldn’t tell. Liked to flirt with young women, ride bike, drink
with students. Hilbert sets a number of math problems.

Cantor
– explores different kinds of infinities. Compares their sizes. Suffers from
manic depression (a psychiatric
diagnosis for a mood disorder in which people experience disruptive mood swings that encompass a frenzied state known as mania (or hypomania) and, usually,symptoms of
depression… у больного
наблюдаются быстрая смена симптомов мании (гипомании) и депрессии, либо
симптомы депрессии и мании одновременно (например, тоска со взвинченностью,
беспокойством либо эйфория с заторможенностью — так называемая *непродуктивная мания* — или
другие)

Henri Poincare
– French mathematician, supported Cantor. 2 hours of work in the morning, and 2
hours of work in the early evening. In between – subconscious thinking.

Chaos theory

Topology – started as
the problem of “7 bridges of Konigsberg”

Kurt Godel – an odd
guy, part of “Vienna circle” group of philosophers. Set out to solve Hilbert’s
second problem-challenge. Finds out that in any logical system (in mathematics
only?) there will be statements that are true but which one cannot prove within
the system. (25 min. in the video). Attacked by Nazi thugs. Flees to the
research center of the Institute for Advanced Study in Princeton.

Paul Cohen – an
American mathematician in 1950’s. Resolves the problem of Cantor of whether
there is an infinity between the whole numbers and fractions.

(Lesson: if there is a problem
that appears unsolvable, need to take it to a higher level, i.e. look wider
than the immediate problem.)

Julia Robertson
– first woman to be elected of the American Mathematics Society. 10th
problem of Hilbert – is there a universal method for telling whether any
equation has a whole number solution, or not?

Yuri Matusevich – at 22 solves
Hilbert’s 10th problem. Steklov Institute in St. Petersrburg.

Poincare conjecture – solved
in 2002 by G. Perelman,
St. Petersburg. Not accessible for interview. Solves the problem of Poincare by
connecting it to another problem, i.e. by combining problems. This seems like a
common trick.

**History of**
Mathematics : Mathematics Time Line

http://www.youtube.com/watch?v=UK9NTS1FZbk

Brief (2,5 min.) with subtitles, a good intro

XX century: Touring, Newmann

**History of mathematics**

From
Wikipedia, the free encyclopedia

The study of mathematics as a
subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek *μάθημα* (*mathema*), meaning "subject
of instruction"

(Development of math coincides
with development of culture in general. Математика отвечает на наиболее далекие запросы
цивилизации.)

Development of mathematics

http://library.thinkquest.org/22584/emh1000.htm