### Tao on Structure and Randomness

Terence Tao is posting the text
of his lectures on "Structure and Randomness"
(part
I on number theory and Fourier
analysis; part
II on combinatorial number theory, graph theory, ergodic theory and "ergodic
graphs";
and part
III on partial differential equations). It's a fascinating glimpse into
the mind of a truly accomplished pure mathematician. Most striking to me is
how Tao completely avoids rounding up any of the usual
suspects --- Paul
Erdös and Mark Kac's work on statistical independence in number
theory*, statistical mechanics, Kolmogorov complexity, etc. --- while still
finding fascinating things to say about,
e.g., Wick
rotation. All three posts, I guess I should say, are for mathematically
mature audiences only.

Tao's earlier post
on Why
global regularity for Navier-Stokes is hard is also very worth reading.

*: Kac's beautiful little book on Statistical Independence in
Probability, Analysis and Number Theory is still in print (ISBN
978-0-88385-025-1, \$21.95), but the publisher,
the Mathematical Association of America,
makes it impossible to actually link to its catalogue page. The best I can do
is refer to the page for
the series in
which it is published.

**Update**, 14 February 2009: there's
more.

Mathematics;
Enigmas of Chance

Posted at April 08, 2007 19:25 | permanent link