listening to mathematicians isn't an easy task, but while reading smale's paper about finding the horseshoe on the beaches of rio again i finally got appetite to do the same having a beach nearby. maybe in the hope to understand better or at least to clear my head, try to get in 'some' shape and avoid sonar.

the two cultures of mathematics

The "two cultures" I wish to discuss will be familiar to all professional mathematicians. Loosely speaking, I mean the distinction between mathematicians who regard their central aim as being to solve problems, and those who are more concerned with building and understanding theories ...

My main purpose here is to defend some of the less fashionable subjects against criticisms commonly made of them.

...Some branches of mathematics are dominated by a small number of problems of universally acknowledged importance. One can justify many results by saying that, in however small a way, they shed light on the Riemann hypothesis, the Birch-Swinnerton-Dyer conjecture, Thurston's geometrization conjecture, the Novikov conjecture or something of the kind. Other branches of mathematics derive their appeal from an abundance of mysterious phenomena that demand explanation. (two cultures of mathematics)

there is this " tradition" in math to adress problems once in a while in the form of a list. hilbert did so 1900, listening 23 which are called "paris problems", well he anounced them in paris. steve smale did the same (or go to wolfram's overview) 1998, also in paris (somewhere i read the organizers were eager to find the same room hilbert was in); listening 18 problems which gonna be solved. the riemann hypothesis is first.