Informal talks of the conference. (English) Zbl 0795.01016

Bott, R.; Peixoto, Mauricio Matos; Thom, René; Zeeman, E. C.

Hirsch, M. W. (ed.) et al., From topology to computation: Proceedings of the Smalefest. Papers presented at the conference “From topology to computation: Unity and diversity in the mathematical sciences” held at the University of California at Berkeley, USA, August 5-9, 1990 in honor of Stephen Smale’s 60th birthday. New York: Springer-Verlag. 65-80 (1993).

Smale is one of the leading mathematicians of his generation, whose work has been foundational in differential topology, dynamical systems, and many aspects of nonlinear analysis and geometry. Owing to his genius these subjects bear in a significant way in mechanics, economics, the theory of computation, and other branches of applied mathematics. Bott gave a very valuable talk on Smale of which consists of valuable points. Peixoto gave some recollections of the early work of Stephen Smale. His talk consists of historical remarks concerning Smale’s work. Thom generally commented on Smale’s mathematical style. It can be said that there are basically two styles of mathematical writing: The constipated style, or the easy-going or free air-style. The constipated style originated with Bourbaki and free air-style originated with Smale. He always considered mathematics as a game. Zeeman focused on three characteristics of Smale’s work. Firstly, his perception is very geometric, and this always enabled him to see through to the heart of the matter. The second characteristic is his excellent mathematical taste. The real evidence for the excellence of Smale’s mathematical judgement is the number of mathematicians worldwide who now follow his taste. The third characteristic of Smale’s work is his audacity and courage.
For the entire collection see [Zbl 0779.00016].

Reviewer: V.Singh (Allahabad)

MSC:

01A65

Development of contemporary mathematics

Keywords:

mathematical style; differential topology; dynamical systems; nonlinear analysis; geometry