Some simple
ideas of great mathematicians
This page is dedicated to short presentations of simple ideas of
great mathematicians. Much of the work done at the highest levels of
mathematics is very sophisticated and requires a considerable amount
of background and mathematical sophistication to digest. But some of
the ideas are beautifully transparent and can be presented to a wide
mathematical audience. We are going to explore such miniatures
below. Let me note that the choice of topics is highly motivated by
my personal mathematical interests.
If you click on the name of a mathematician, it will take you to
their wikipedia page. Clicking on the title of the presentation will
take you to the .pdf with the precise statement and a proof.
If you would like to contribute a miniature to this page, please let
me know. I will gladly post it with a proper attribution, of course.
Nikolai
Chebotaryov: Minors of the Fourier matrix modulo a prime
(coming soon)
Paul
Erdos: The
square root bound for the Erdos distance problem
Paul
Erdos: The Erdos Integer Distance Principle (coming
soon)
Benjamin
Logan: minimization
and signal recovery
Klaus Roth:
Arithmetic progressions of length three (coming soon)