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