Progress report

[posic]

by Shinichi Mochizuki -- http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202013-12.pdf

Comments

[posic.livejournal.com]

Yes, in a sense. People say that the whole of Grothendieck's algebraic geometry was developed with the goal of proving Weil's conjectures in mind.

On the other hand, as the l-adic cohomology is being used far beyond this specific purpose, so one would hope that Mochizuki's theory will prove to be useful for many purposes (and generally, should I say, will expand our understanding of mathematics, or of arithmetic geometry at least). That's what Mochizuki seems to suggest in his report.

In such cases, one can say that while a theory proves validity of a theorem, the theorem in turn proves significance of the theory. This attracts people desiring to learn the theory in order to apply it to other problems.