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March 15, 2007

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)

Posted at March 15, 2007 12:05 PM UTC

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Dolan’s wonderful tirade

a wonderful tirade Jim Dolan once launched on a view that would limit itself to truth values.

Is it online? If so could we get a link?

Posted by: isomorphismes on March 19, 2013 10:25 PM | Permalink | Reply to this

Re: Dolan’s wonderful tirade

No, it was during a workshop. But the same thought can be found through the history of higher-dimensional algebra:

Don’t rest content with equality when there’s an isomorphism giving rise to it, and so on to higher equivalences.

Mike Shulman’s making something like the same point recently in this post, beginning

Finally, in everyday mathematics…

Don’t truncate to truth values (or (1)(-1)-types), when there’s a set (or 00-type) of isomorphisms to consider, an element of which may carry further information.

Posted by: David Corfield on March 20, 2013 11:12 AM | Permalink | Reply to this

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