Jacob LurieWhy? And who would he have been more deserving than?
I don’t understand his work (I work in a completely different field), but my colleagues who do consider him as the second coming of Grothendieck, making him probably more deserving of the Fields medal than almost all other medalists (Scholze and Tao probably being the only exceptions).
As far as I know, only 4 set theory papers were published in the Annals in the 21st century (and only one in recursion theory).These fields are relatively very small.
How many annals papers you expect from them?
I’d expect a number that is more or less proportional to the percentage of set theorists among all mathematicians.
Jacob LurieWhy? And who would he have been more deserving than?
I don’t understand his work (I work in a completely different field), but my colleagues who do consider him as the second coming of Grothendieck, making him probably more deserving of the Fields medal than almost all other medalists (Scholze and Tao probably being the only exceptions).
If Lurie wanted the fields, he could have nontrivially increased his chances just by publishing in a normal (or more normal) manner. He’s had now several of the very best possible positions in academic math. He’s done fine.
What do you mean by normal publishin?
Jacob Lurie
Why? And who would he have been more deserving than?
I don’t understand his work (I work in a completely different field), but my colleagues who do consider him as the second coming of Grothendieck, making him probably more deserving of the Fields medal than almost all other medalists (Scholze and Tao probably being the only exceptions).
If Lurie wanted the fields, he could have nontrivially increased his chances just by publishing in a normal (or more normal) manner. He’s had now several of the very best possible positions in academic math. He’s done fine.
Jacob LurieWhy? And who would he have been more deserving than?
I don’t understand his work (I work in a completely different field), but my colleagues who do consider him as the second coming of Grothendieck, making him probably more deserving of the Fields medal than almost all other medalists (Scholze and Tao probably being the only exceptions).
That doesn't explain why he would be more deserving than people like Okounkov, Villani, Mirzakhani, Avila, Hairer or other winners (who qualified for the medal at the same time as him). It'd be interesting to see one good reason.
As far as I know, only 4 set theory papers were published in the Annals in the 21st century (and only one in recursion theory).These fields are relatively very small.
How many annals papers you expect from them?I’d expect a number that is more or less proportional to the percentage of set theorists among all mathematicians.
But these fields are at this point quite isolated from most mathematicians. Any small field which isn’t proving things most people care about is gonna have problems getting glory.
It’s not like the publication prospects of these fields are better in IHES and Invent
As far as I know, only 4 set theory papers were published in the Annals in the 21st century (and only one in recursion theory).
These fields are relatively very small.
How many annals papers you expect from them?I’d expect a number that is more or less proportional to the percentage of set theorists among all mathematicians.
But these fields are at this point quite isolated from most mathematicians. Any small field which isn’t proving things most people care about is gonna have problems getting glory.
It’s not like the publication prospects of these fields are better in IHES and Invent
I agree with your second statement. However, the concept of “general interest to mathematicians” that you’re hinting at is an absurd. The vast majority of mathematicians who don’t work in AG (or any AG-adjacent area) can’t even parse the abstracts of most AG papers that get published in top journals. In 90% of the cases, a paper that is “of general interest” is mostly a paper of Princtonian interest (where Princtonian here is mostly an umbrella term for the establishment).
Jacob Lurie
Why? And who would he have been more deserving than?
I don’t understand his work (I work in a completely different field), but my colleagues who do consider him as the second coming of Grothendieck, making him probably more deserving of the Fields medal than almost all other medalists (Scholze and Tao probably being the only exceptions).
That doesn't explain why he would be more deserving than people like Okounkov, Villani, Mirzakhani, Avila, Hairer or other winners (who qualified for the medal at the same time as him). It'd be interesting to see one good reason.
Infinity categories are indepensible for the schemes of the 21st century. Personally I like Lie algebras more than schemes, but I have to say it’s entirely nonobvious that AO should be recognized when Lurie is not. Others I cannot comment on mathematically (but AA is a bro). Also, complaints about publication style is silly. Lurie’s huge user manuals are not acceptable but Perelman’s very economically-written preprints are? Obviously it was content that mattered in that case and it should have been what mattered when they considered Lurie, which they surely must have at some level. Maybe a committee member thought that he was to close to VV or some nonsense.
There is no precedent for a fields medal just building foundational theory. Lurie is not comparable to Grothendieck at all, the way they worked was completely different. Grothendieck proved GRR by age 28 (!), Lurie still hasn’t proven a big result of that impact; the stuff about elliptic cohomology and cobordism hypothesis has not been taken up outside algebraic topology and higher categories theory.
There is no precedent for a fields medal just building foundational theory. Lurie is not comparable to Grothendieck at all, the way they worked was completely different. Grothendieck proved GRR by age 28 (!), Lurie still hasn’t proven a big result of that impact; the stuff about elliptic cohomology and cobordism hypothesis has not been taken up outside algebraic topology and higher categories theory.
Jacob Lurie proved the Baez-Dolan Cobordism hypothesis. Along with Denis Gaitsgory, he proved Seigel-Mass formula for function fields. Saying that Jacob Lurie didn’t prove any “big” theorem is like saying Grothendeick never proved any “big” theorem.
There is no precedent for a fields medal just building foundational theory. Lurie is not comparable to Grothendieck at all, the way they worked was completely different. Grothendieck proved GRR by age 28 (!), Lurie still hasn’t proven a big result of that impact; the stuff about elliptic cohomology and cobordism hypothesis has not been taken up outside algebraic topology and higher categories theory.Jacob Lurie proved the Baez-Dolan Cobordism hypothesis. Along with Denis Gaitsgory, he proved Seigel-Mass formula for function fields. Saying that Jacob Lurie didn’t prove any “big” theorem is like saying Grothendeick never proved any “big” theorem.
Also his geometric construction of tmf
I agree with your second statement. However, the concept of “general interest to mathematicians” that you’re hinting at is an absurd. The vast majority of mathematicians who don’t work in AG (or any AG-adjacent area) can’t even parse the abstracts of most AG papers that get published in top journals. In 90% of the cases, a paper that is “of general interest” is mostly a paper of Princtonian interest (where Princtonian here is mostly an umbrella term for the establishment).
At least 10x as many people know schemes as know forcing. Is this just Princeton influence?
I agree with your second statement. However, the concept of “general interest to mathematicians” that you’re hinting at is an absurd. The vast majority of mathematicians who don’t work in AG (or any AG-adjacent area) can’t even parse the abstracts of most AG papers that get published in top journals. In 90% of the cases, a paper that is “of general interest” is mostly a paper of Princtonian interest (where Princtonian here is mostly an umbrella term for the establishment).At least 10x as many people know schemes as know forcing. Is this just Princeton influence?
That's not the point. If the Annals was committed to publishing the best 1% (say) of papers in each field, then the result will be 10x more Annals papers on schemes than on forcing and I wouldn't complain about that. The point is that currently it's more like the Annals publishing the top 2% of papers in AG and the top 0.1% of papers in set theory (I'm too lazy to count and compute the actual numbers, which are probably even worse), and this is done with the excuse that the AG papers or of interest to the general mathematical community and the set theory papers are not. Even if the number of people who know schemes is 10 times the number of people who know forcing, their percentage among all pure mathematicians is still far too small in order for AG papers to qualify as being of "general mathematical interest" (furthermore, in order to understand Annals AG papers, it's usually not enough to just know schemes).
There is no precedent for a fields medal just building foundational theory. Lurie is not comparable to Grothendieck at all, the way they worked was completely different. Grothendieck proved GRR by age 28 (!), Lurie still hasn’t proven a big result of that impact; the stuff about elliptic cohomology and cobordism hypothesis has not been taken up outside algebraic topology and higher categories theory.Jacob Lurie proved the Baez-Dolan Cobordism hypothesis. Along with Denis Gaitsgory, he proved Seigel-Mass formula for function fields. Saying that Jacob Lurie didn’t prove any “big” theorem is like saying Grothendeick never proved any “big” theorem.
Also his geometric construction of tmf
I already mentioned the cobordism hypothesis and tmf (that comes under elliptic cohomology), and like I said, no one really cares outside homotopy theory and related areas. Ok, there is some application in mathematical physics, but his controbution in MP can’t be compared with other FMs like Okounkov, Kontsevich, Donaldson, Witten, etc
Tamagawa number stuff with Gaitsgory was too late for fields I’m pretty sure, and anyway it’s not a conjecture anyone really posed beforehand. Has it been applied for anything? Don’t think so.
Grothendieck had GRR at age 28. I’m not even going into everything he did later. Where is Lurie’s GRR? You may not realize the impact GRR has had in AG and related areas (even that has been applied more in math physics, through stringy stuff, than cobordism hypothesis actually).
Grothendieck's first theorem in AG was Grothendieck-Riemann-Roch. Similarly, his 1958 ICM address motivated scheme theory as a route to get to Serre's suggestion to find a cohomology theory for the Weil conjectures.
I'm sure few at the time understood what Grothendieck was saying, but people at the time definitely knew about the importance of Riemann-Roch and the Weil conjectures, so when his whole abstract framework started to flesh out it was hard to ignore.
Had Lurie been able to ground his work in that way he would have had one of the easiest Fields in history. But I think he just wasn't interested ("theories about theories").
As far as I know, only 4 set theory papers were published in the Annals in the 21st century (and only one in recursion theory).
What do you count as set theory? 03E as primary MSC? In true obsessive EJMR spirit I did a quick search on Mathscinet, and since 2000 I found 6 in Annals, 4 in Acta, 1 in Publ. IHES and 3 in Inventiones. Also, while it's obviously very small number statistics, it seemed to me that publications in 03E (and 03 in general) seemed to be concentrated more towards the recent years.
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