Manin on Mathematics
Posted by David Corfield
On the ArXiv today, Yuri Manin has one of those wide-ranging overviews of the life of mathematics: Mathematical knowledge: internal, social and cultural aspects. One comment -
When Poincaré said that there are no solved problems, there are only problems which are more or less solved, he was implying that any question formulated in a yes/no fashion is an expression of narrow-mindedness.
- put me in mind of a wonderful tirade Jim Dolan once launched on a view that would limit itself to truth values.
Manin’s article meanders over an enormous area. Café visitors may prefer his earlier Georg Cantor and his heritage where we hear (page 8) about n-categories as the new emerging ‘foundations’, in his sense of the term:
the historically variable conglomerate of rules and principles used to organize the already existing and always being created anew body of mathematical knowledge of the relevant epoch. (p. 6)