Re: [math-fun] about Grothendieck
On 16.11.2014 23:27, math-fun-request@mailman.xmission.com wrote:
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Today's Topics:
1. Re: Grothendieck (rcs@xmission.com) 2. Greatest 3 mathematicians of the 20th century? (Warren D Smith) 3. Re: Greatest 3 mathematicians of the 20th century? (Whitfield Diffie) 4. Re: Greatest 3 mathematicians of the 20th century? (Gustavus Simmons) 5. Re: about Grothendieck (Axel Vogt) 6. Re: about Grothendieck (Simon Plouffe)
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Message: 1 Date: Sun, 16 Nov 2014 13:25:07 -0700 From: rcs@xmission.com To: math-fun@mailman.xmission.com Cc: rcs@xmission.com Subject: Re: [math-fun] Grothendieck Message-ID: <20141116132507.9q2ab6valccwg884@webmail-backup.xmission.com> Content-Type: text/plain; charset=ISO-8859-1; DelSp="Yes"; format="flowed"
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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Message: 2 Date: Sun, 16 Nov 2014 15:38:27 -0500 From: Warren D Smith <warren.wds@gmail.com> To: math-fun@mailman.xmission.com Subject: [math-fun] Greatest 3 mathematicians of the 20th century? Message-ID: <CAAJP7Y140oz1N8X8moLwrpcokkGifDn5BBkbS_a+ADs0v6e1ew@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1
Well, since Plouffe started down that road, you know you all want to submit your votes too. Here, these ones seem pretty good to me:
Albert Einstein John von Neumann Pal Erdos
Not a fields medalist among them, though -- that's evidently the kiss of death :)
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Message: 3 Date: Sun, 16 Nov 2014 12:45:56 -0800 From: Whitfield Diffie <whitfield.diffie@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Greatest 3 mathematicians of the 20th century? Message-ID: <CAF+O-CVscUYP0N_DTzc24+3Fqad4Km6SvyP8LvnzqOdq2ZO1+Q@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1
Well, since Plouffe started down that road, you know you all want to submit your votes too.
Sure. I suggest
Emmy Noether John von Neumann Andre Weil
Whit
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Message: 4 Date: Sun, 16 Nov 2014 13:53:28 -0700 From: "Gustavus Simmons" <gsimmons30@comcast.net> To: "math-fun" <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Greatest 3 mathematicians of the 20th century? Message-ID: <D9353768BA33412CB208731553AEC92C@oldmachine> Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=original
To follow up on Warren's comment about the Field's medal, Arno Penzias -- himself a Nobel laureate for having discovered the background radiation consistent with the Big Bang theory -- was fond of saying: "The Nobel prize has ruined many an otherwise promising career in physics".
----- Original Message ----- From: "Warren D Smith" <warren.wds@gmail.com> To: <math-fun@mailman.xmission.com> Sent: Sunday, November 16, 2014 1:38 PM Subject: [math-fun] Greatest 3 mathematicians of the 20th century?
Well, since Plouffe started down that road, you know you all want to submit your votes too. Here, these ones seem pretty good to me:
Albert Einstein John von Neumann Pal Erdos
Not a fields medalist among them, though -- that's evidently the kiss of death :)
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Message: 5 Date: Sun, 16 Nov 2014 22:59:39 +0100 From: Axel Vogt <mail@axelvogt.de> To: math-fun@mailman.xmission.com Subject: Re: [math-fun] about Grothendieck Message-ID: <54691E4B.1090601@axelvogt.de> Content-Type: text/plain; charset=windows-1252; format=flowed
From: Simon Plouffe To: math-fun@mailman.xmission.com Subject: [math-fun] about Grothendieck ...
I am not aware of Bourbaki-style in reading Grothendieck.
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Message: 6 Date: Sun, 16 Nov 2014 23:26:55 +0100 From: Simon Plouffe <simon.plouffe@gmail.com> To: math-fun@mailman.xmission.com Subject: Re: [math-fun] about Grothendieck Message-ID: <546924AF.7070805@gmail.com> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
hello,
Alexander Grothendieck was a member of Bourbaki for years. From 1957 to 1962 at the least.
reference : http://en.wikipedia.org/wiki/Fondements_de_la_G%C3%A9ometrie_Alg%C3%A9brique
and here : http://www.numdam.org/numdam-bin/search?h=aur&aur=Grothendieck,+Alexander&fo...
for example this document : http://archive.numdam.org/ARCHIVE/PMIHES/PMIHES_1963__17_/PMIHES_1963__17__5...
which is from 1963, from what I can see this is the purest Bourbaki style of mathematics.
... A.G. is a great master of higher mathematics.
2 things could happen, in 200 years this will look like trivial or something else will come out in a complete different direction ? What will prevail is the principle of l'?conomie de pens?e, i.e. the shortest and simplest way to explain things. Maybe that guy was 400 years ahead of his time ? Well, this was 50 years ago and as far as I can tell, there is no simplification that came out.
I had a personal friend (Pierre Bouchard) in Montr?al, recently deceased, he was a specialist of Grothendieck's work, we (some friends and I) asked him many times, how come this is interesting ?, tell us! please!, He could hardly give any example. We all stumbled on the first books of Bourbaki (he had them all). That example of the definition of the empty set was a subject of discussion, lots of it, nothing came out of all this.
Maybe as they say in the 'le monde' article that the subconscious of mathematicians is haunted by that guy and what he did, I am not certain of this. This is my personal opinion.
Best regards, Simon Plouffe
Just about the last link: This still is not Bourbaki, it is EGA. In my own very sloppy words for that 2 chapters: The first "translates" methods of (usual) Topology to Algebra, allowing to switch if needed. And extends it to singular 'spaces'. The 2nd tells when the above behaves well. I can understand inhibitions, but suggest to have a look at Dieudonne "The historical development of Algebraic Geometry", AMS 1972, which completely avoids 'abstract nonsense'. A Bourbakist and the co-Author for EGA, just have a look.
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Axel Vogt