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Let me try to dispel the mystery about my views. I share your distaste for incomprehensible proofs that merely certify the truth of a statement...

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## About the title

**About the title**

I changed the title of the blog on March 20, 2013 (it used to have the title “Notes of an owl”). This was my immediate reaction to the news the T. Gowers was presenting to the public the works of P. Deligne on the occasion of the award of the Abel prize to Deligne in 2013 (by his own admission, T. Gowers is not qualified to do this).

The issue at hand is not just the lack of qualification; the real issue is that the award to P. Deligne is, unfortunately, the best compensation to the mathematical community for the 2012 award of Abel prize to Szemerédi. I predicted Deligne before the announcement on these grounds alone. I would prefer if the prize to P. Deligne would be awarded out of pure appreciation of his work.I believe that mathematicians urgently need to stop the growth of Gowers's influence, and, first of all, his initiatives in mathematical publishing. I wrote extensively about the first one; now there is another: to take over the arXiv overlay electronic journals. The same arguments apply.

Now it looks like this title is very good, contrary to my initial opinion. And there is no way back.

Dear Sowa,

ReplyDeleteI've been reading your blog for a while. I sympathize some of your view abour mathematics, although I don't have necessary expertise to adequately form some "metamathematical" opinions.

I wonder what do you think about theory of motives(following Grothendieck, Beilinson and Voevodsky) and how it can potentially help algebraic/arithmetic geometry and number theory.

As far as I know, there have been some theory bulding on the matter recently(Voevodsky, Cisinski, Deglise), but the theory is appears to be far from the one envisioned by Grothendieck.

Is thery of motives is still in its infancy? Or, maybe, it's not as useful as many people thought( I heard this opinion from some people).

I also heard an opinion that Grothendieck was himself dissatisfied with motives( in favor of anabelian geometry approach ) for dealing with some questions. Thought this is understandable, since it was a time before Voevodsky.

Василий Тертьяков:

ReplyDeleteSorry for the belated reply.

I really don't know answers to your questions. In fact, I am not sure that answers are possible at the moment.

Theory of motives is useful, as at the very least the work of Voevodsky shows. May be it is not as useful as people hoped, but this may change with time. As far as I know, the whole vision of Grothendieck is not realized. On the one hand side, mathematicians have no obligation to work along the lines suggested by Grothendieck. On the other side, the ideas of Grothendieck proved to be so fruitful that any of them deserves to be developed to the full extent. Even if he himself changed his opinion.