Serre: Finite groups, Yesterday and Today

[@ovenlovesyou]

audio and visual out of sync for me

[@haggaisimon7748]

Just today I was thinking of Serre as the greatest mathematician of the second half of 20 century. But then I was thinking of Grothendiek and Deligne. Add to this Wiles. Mazur is a genius, but still these guys did a lot. I'd also think of Conway and Archbacher from simple groups.

[@08padam]

For me Serre and Grothendieck are in another galaxy. Wiles demonstrated Fermat, which makes him one of the greats, but Serre and Grothendieck created so much, so many theories. I can't even imagine what would have happened if Grothendieck didn't stop.

[@sergiorgio2000]

JP Serre is a FIeld Medal, Alexander Grothendieck was Grothendieck.

[@orwppi9278]

​@@sergiorgio2000jp is also an abel prize

[@vector8310]

Serre's writings are among the clearest expositions around. But this lecture, compounded by muddled sound and dim video, was like wandering through fog.

[@rodovre]

Sound is shifted.

[@christianlapointe3033]

is that Lurie in the front row?

[@pookz3067]

+Christian LaPointe Yep! and next to him you see the legendary Dick Gross, Barry Mazur, and (I believe) John Tate! And Pete Kronheimer gives the introduction. Quite a group!

Jesus, you probably think he is the outstanding mathematician there when actually the only genius in that room is Serre.

[@MathNerdGamer]

Barry Mazur is absolutely a genius, so Serre is not the only genius in that room.

[@Just_a_user3]

Audio and visual are out of sync

[@edernollivier]

Yep, and with the simplex it is sovled as an evident proof.

[@Barbapippo]

Out of Sync Group Theory

[@takashikashiwase3461]

thx thx

[@pinklady7184]

Chalks are not white enough.

[@Hiiii739]

In this talk, Jean-Pierre Serre says that the research papers, that were published - in the 60s, 70s, 80s -- leading towards the Classification of the Finite Simple Groups, were too long. Then what does he make of the 1000s of pages that Bourbaki published, and later EGA and SGA? Note that the entire first thirty years of Bourbaki were theories after theories without any conclusive resolution of any long standing problem. Only much later were the Weil Conjectures settled by Pierre Deligne. [This was also the reason Jean Leray left Bourbaki right at its inception]. There is more to this talk than it seems - plain politics. Sunlight is the best disinfectant. Please show this comment to Barry Mazur so that he can respond appropriately. Some background seems necessary: during the period 2008 - 10, in personal correspondence with Barry Mazur (CC’d to all then-living Fields medallists), I had promised to use tools and techniques from economics, literature, law and psychology to circumscribe modern mathematics, as practiced in academia. Being that my PhD work was in representations of finite groups, as a rejoinder, I had raised the question to Mazur, why do I think that if I studied the classics of the Western Civilization, rather than the Classification Theorem of Finite Simple Groups, I would know the classification theorem itself much deeper! Following this correspondence, Serre and Mazur have taken it as an excuse to criticize the lengthy, prolonged work carried out by mathematicians (mostly based in America), on the classification of finite simple groups. I’m with Serre and Mazur when they criticize the finite group theorists. But I don’t want this as an excuse to pass the blame - that is, to make it look as if it is only the finite group theorists that have bad culture of mathematics, while Serre, Mazur, etc. personify the highest culture of mathematics. It is regrettable that John Tate who was in the audience is no more. But the rest of the worthies are still there - Mazur, Gross, Serre, Kronheimer, … The verdict of history is inescapable!

[@nathheast5829]

The goal of Bourbaki has never been to establish new theories, but to organize existing solid results as they say in that video (in French) kzbin.info/www/bejne/h6K1ZWhvgN13jLc. Comparing the length of dozens of textbooks with that of an article makes little sense to me.

[@Hiiii739]

@@nathheast5829 Thank you for your message. But the Classification Theorem of Finite Simple Groups is not a single article. It is a huge collection of research articles (along with one survey book by Gorenstein), in all totaling about 10,000 pages published over the 50s, 60s, 70s and 80s. From the other side, the books that Bourbaki published, for sure, were not undergraduate level textbooks, that "organized existing solid results", as you say, but were comprehensive tomes that could be used as sourcebooks at the research level. They were meant to provide foundations for entire areas of mathematics, with the fundamental perspective that there is a unity in all of mathematics. There are mathematicians who believe that it was this altogether new perspective of unity in all of mathematics, that was pursued by Bourbaki and his associates, that made it possible in the 20th/21st century to solve many long standing problems in mathematics like Fermat's last theorem, Mordell Conjecture, Weil Conjectures, etc. If this activity of Bourbaki is not considered as developing new theories, then what is? Don't know whether you are a professional mathematician, in which case you would definitely know about Bourbaki. There were two streams of work for Bourbaki. One was the 10 or 12 members of Bourbaki meeting two or three times annually to write comprehensive volumes on all major areas of mathematics. These are what Andre Weil refers to as Bourbaki conferences in his autobiography. The other was to invite other leading experts in the world to give Bourbaki seminars. At any given time in the second half of the 20th century, the members of Bourbaki were themselves leading experts in the world. They were not high school or college teachers concerned with writing expository undergraduate textbooks. In any case, it is not my obligation or responsibility to defend Bourbaki from being misinterpreted as authors of undergraduate textbooks. Regarding the other video you are referring to, where Alain Connes interviews three older Bourbakis, I have copious notes in the comments section there already, with more coming. Verdict of history is inescapable.

[@jeancerrien3016]

@@Hiiii739 You're comparing apples and oranges.

[@Hiiii739]

@@jeancerrien3016 No, definitely not. It’s apples for Bourbaki and apples for the finite group theorists. The fact is that starting from the second half of the 20th century, research effort in any area of mathematics required the collective engagement of a global team of academics. Because the complexity and quantity of mathematics that needed to be written down had grown many-fold. So 1000s of pages were written and discussed informally. In this video, Serre/Mazur are promoting a view of mathematics wherein nobody should publish a proof until its validity was entirely established. This is a very dishonest view. They might have followed this principle when they published their research papers in journals. But it is undeniable that they benefitted from informal discussions and publications among small groups of researchers (like Bourbaki), which led the world community of mathematics in the wrong direction for more than 70 years. So academics sitting in Western universities were unfairly gaining fame as serious mathematicians when in fact they were pursuing low quality of mathematics with low scholarly culture.

[@jeancerrien3016]

​ @Cello and other stuff Bourbaki covers a very broad range of mathematics. The CFSG is very narrow. Comparing them is comparing apples to oranges. Grothendieck's contributions were foundational and very broad in contribution. Deligne's proof of the Weil conjectures using them is relatively concise and has been summarized in a handful of textbooks (cf. Hartshorne, Milne, and Kiehl-Weissauer). Try as Aschbacher et al might, CSFG will never be stated so concisely or address such a broad range of topics.

[@aprendefutbol244]

Translate, I do not understand

[@NothingMaster]

A brilliant mathematician, his almost transparent chalk, and his insufferable English accent. Oh well; genius doesn’t mean perfect.

[@rhubiks8430]

in all fairness he was like 88 or something when doing this

[@radical_drift1019]

“English accent”

[@JamesBlevins0]

Wait until you are a parent and want to get a small child to fall asleep. Then, you shall appreciate Serre's accent, and you shall wish that the audio had more white noise.