Timeline for Gossip about Grothendieck and distributive lattices
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 28, 2021 at 19:33 | comment | added | Tri | @Pete L. Clark, there is a version by Baker and Pixley, "Polynomial Interpretation and the Chinese Remainder Theorem for Algebraic Systems," that relates to Mal'cev conditions. Of course, I'm not sure if that's what Professor Rota had in mind. | |
| Apr 21, 2020 at 21:53 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Sep 20, 2010 at 22:21 | comment | added | Todd Trimble | @Timothy: thanks. I appreciate that you were at MIT and may have spoken Rotaese well, and I'm glad to hear you defend him. But Rota expresses himself a lot more aggressively than you are making out! "Those mathematicians who knew some lattice theory watched with amazement as the algebraic geometers of the Grothendieck school clumsily reinvented the rudiments of lattice theory in their own language." Nice! @Yemon: that's a good observation. My appetite for gnomic, cryptic utterances is less than it used to be. Sometimes they're profound, but often times not. I'm still undecided in this case. | |
| Sep 20, 2010 at 19:04 | comment | added | Yemon Choi | Having found my copy of Indiscrete Thoughts, and skimmed over the section "A Mathematician's Gossip", it reminds me vaguely in style of aphoristic philosophy texts, with tendentiousness being somehow part of the aim rather than an unwitting flaw ;) [This comes from someone rather fond of such texts, by the way.] I suspect Justin Hillburn's answer below might be close to the mark, especially given the bits which Mariano didn't quote. | |
| Sep 20, 2010 at 18:31 | comment | added | Timothy Chow | @Todd: I think the problem is that you're not a native speaker of Rotaese. Translated into plain English, Rota said, "I think that if algebraic geometers were to study more lattice theory, they would find fruitful connections between the two subjects." The following is a mistranslation into English: "I know of some extremely fruitful connections between lattice theory and algebraic geometry but I'm not going to tell you." Perhaps one day Babelfish will have "Rota" among its language options, and confusions like this will be avoided. | |
| Sep 20, 2010 at 3:25 | comment | added | Todd Trimble | @Mark: perhaps the "emperor's clothes" went a bit too far (although I have to say that IMO quite a lot of Indiscrete Thoughts, which I have read and reread a number of times, is similarly both exasperatingly vague and polemical at the same time). To put this in balance: I am a huge admirer of Rota when he is behaving like a professional mathematician; he writes mathematics beautifully and most thought-provokingly. But in this particular case, nobody here seems to know what he's talking about exactly, and I'd honestly like to know if there's anything there. Can one of his students explain? | |
| Sep 20, 2010 at 0:56 | comment | added | user6976 | PS By "applications" in my previous comment I meant applications to algebraic geometry/commutative algebra, of course. Lattice theory has lots of applications elsewhere (for applications to combinatorics, one can consult, I guess, Richard Stanley who is frequently seen here). | |
| Sep 20, 2010 at 0:52 | comment | added | user6976 | @Todd: Your comment are unnecessarily aggressive, especially since Rota can't answer you. Truth, so far the only real application of lattice theory mentioned here is CRT which is not worth the efforts, in my opinion. But Rota mentioned several applications. Perhaps somebody can present any other. | |
| Sep 19, 2010 at 23:33 | comment | added | Todd Trimble | @Yemon: that's true, but if really he had something important to say, then maybe he (or one of his students) should have published it or made a note of it somewhere, in a responsible way. Instead, he whines (and coyly hints at secret knowledge possessed by lattice theorists). It looks kind of passive-aggressive to me, and I eagerly await for someone to prove that the emperor wore some beautiful clothes in this case. | |
| Sep 19, 2010 at 23:28 | comment | added | Pete L. Clark | I wonder what version of CRT Rota had in mind? The one I think is most standard -- see e.g. p. 34 of math.uga.edu/~pete/integral.pdf -- holds in any commutative ring. | |
| Sep 19, 2010 at 20:39 | comment | added | Yemon Choi | @Todd: from my (re)readings of Indiscrete Thoughts, just "spitting it out" in that way wouldn't have been Rota's style - he seemed to like the epigrammatic approach. I'll have to check my copy to see the context in which he asked "what if Grothendieck had known..?" | |
| Sep 19, 2010 at 15:17 | comment | added | Harry Gindi | It's also strange that in the article, Rota notes that Dieudonné expressed interest in the subject, but somehow that Grothendieck was completely unaware of it. Wasn't Dieudonné not only a close collaborator of Grothendieck in the late fifties and early sixties, but also his mentor and doctoral advisor (jointly with L. Schwartz)? | |
| Sep 19, 2010 at 15:03 | comment | added | Todd Trimble | What annoys me is: if Rota knowingly asserts that lattice theory will contribute new insights if only algebraic geometers would pay more attention, then why doesn't he just spit it out? Given his stature, algebraic geometers would have paid attention. Why cloak it all in mystery and coyness? | |
| Sep 19, 2010 at 13:25 | comment | added | Harry Gindi | What I'd be really interested in hearing is the response of an algebraic geometer to the above statement. | |
| Sep 19, 2010 at 10:54 | comment | added | Victor Protsak | What a nice answer! I am glad the question had not been closed prematurely. | |
| Sep 19, 2010 at 10:44 | history | answered | Marko Amnell | CC BY-SA 2.5 |