Story of Maths:4- To Infinity and Beyond

THE STORY OF MATHS
Part. 4(final)
TO INFINITY AND BEYOND

http://www.open2.net/storyofmaths/
http://en.wikipedia.org/wiki/The_Story_of_Maths

http://stagevu.com/video/zmrlfsazwacq
http://www.imdb.com/title/tt1926910/


EXCERPTS:

TO INFINITY AND BEYOND


GEORG CANTOR
"Before Cantor no one really knew infinity."

"Indeed, there wasn't just one infinity,
but infinitely many infinities."


"Surely the infinity of fractions is much bigger
than the infinity of whole numbers."


Continuum Hypothesis



HENRI POINCARE

"The orbits Poincare had discovered indirectly
led to what we now know as chaos theory."

"Understanding the mathematical rules of chaos explain
why a butterfly's wings could create tiny changes in the atmosphere
that ultimately might cause a tornado or a hurricane to appear
on the other side of the world.


LEONHARD EULER

7 bridges Konigsberg.
Today the city is knowns as Kalingingrad, Russia, surrounded by Poland and Lithuania.


Topology
"Some people refer to topology as Bendy Geometry
because in topology, two shapes are the same if you
can bend or morph one into another without cutting it.


Poincare Conjecture
Perelman solved it in 2002.



HILBERT


KURT GODEL
Austrian
Incompleteness Theorem
"Godel proved that within any logical system for mathematics
there will be statements about numbers which are true
but which you cannot prove.


He starts with the statements,
"This statements cannot be proved."

Now, such statements must be either true or false.
Hold on to your logical hats
as we explore the possibilities.

If the statements is false, that
means the statement could be proved,
which means it would be true, and
that's a contradiction.
So that means, the statements must be true.

In other words, here is a
mathematical statement that is true
but can't be proved.


"All around him, mathematicians and scientists
were fleeing the Nazi regime until it was only Hilbert left
to witness the destruction of one of the greatest mathematical centres of all time.


"Many of the brightest European mathematicians
were fleeing the Nazis for America.
People like Hermann Weyl: theoretical physics.
John Von Neumann: game theory, one of the poineers of computer science.


PAUL COHEN
"From a very early age,
Paul Cohen was winning mathematical competitions and prizes


WOMEN MATHEMATICIANS:
In the story of maths,
nearly all truly great mathematicians have been men.
But there have been a few exceptions.

There was the Russian SOFIA KOVALEVSKAYA.
who became the first female professor of mathematics in Stockholm in 1889.
And then
EMMY NOETHER, a talented algebraist who fled from Nazis
to America but hten died before fully realised her potential.
Then there is the woman... JULIA ROBINSON,
the frist woman ever to be elected president of the
American Mathematical Society.

Robinson Hypothesis


EVARISTE GALOIS
"Galois believed that mathematics shouldn't be the study of number and shape,
but the study of structure."


NICOLAS BOURBAKI

ALEXANDRE GROTHENDIECK
"Grothendieck produced a new powerful language to see structures in a new way."


"'There's now a million dollars for anyone who can solve teh Riemann hypothesis.
But there's more at stake than that.'
Anybody who proves this theorem will be remembered forever."

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