re Applications of Grothendieck, some possible links. There's a not-yet-comprehended K-page proof of the ABC conjecture by Mochizuki. He might understand Grothendieck's work better than anyone else. Based only on superficial verbal similarity (I don't understand this stuff at all), M's Inter-Universal_Teichmuller_Theory appears to be descended from G. Mochizuki has announced a seminar for next Spring. Chen has a decent summary. Jeff Lagarias told me a long story about trying to find reviewers for the proof, and failing. http://projectwordsworth.com/the-paradox-of-the-proof/ Caroline Chen http://en.wikipedia.org/wiki/Abc_conjecture http://en.wikipedia.org/wiki/Shinichi_Mochizuki http://www.kurims.kyoto-u.ac.jp/~motizuki/top-english.html M's web page http://en.wikipedia.org/wiki/Inter-universal_Teichm%C3%BCller_theory One obvious approach is to try to force the proof through a computer proof checking program. This seems too hard. A recent success (August 2014) is Hales' computer check of the 1998 Ferguson-Hales proof of the Kepler Conjecture -- there's no denser way to pack spheres than the usual "one". https://code.google.com/p/flyspeck/wiki/AnnouncingCompletion The Flyspeck project team is a couple of dozen people, working for a few years. The final product includes a special version of the proof checker. One contrast with the ABC work is that the Kepler proof has no particular conceptual mountain to climb-- it's a boatload of linear & non-linear programming problems. The final computer check needs only 5K compute-hours. The real cost here is the effort of the project team. Rich ---------- Quoting Warren D Smith <warren.wds@gmail.com>:
http://en.wikipedia.org/wiki/Weil_conjectures
is something that Grothendieck contributed to, which seems amazing and whose statement can actually be comprehended. Does it have any applications, or does it just seem amazing? Well, I actually am aware of a few applications of the Weil conjectures, but I think most or all of those applications were later also accomplished in far simpler ways without needing to go anywhere near said conjectures.
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