The medical team preparing the program of next year’s European Congress of Mathematics in Berlin has declared that algebraic number theory, along with closely related branches of mathematics, may have entered a phase of terminal decline in Europe. The team was only able to locate a single indisputably live mathematician to represent arithmetic geometry, the Langlands program, and most areas of algebraic geometry, as well as algebraic number theory.

Reported sightings of itinerant algebraic number theorists and arithmetic geometers along a swath of European territory stretching at least from Transylvania to northern England are being investigated by competent authorities. Researchers are advised to take precautions in the light of reliable warnings that undead arithmeticians and algebraic geometers, including Europeans, are making plans to congregate repeatedly and in large numbers in the months leading up to the Berlin event, notably in the Rocky Mountains and in the Upper Thames Valley.

A second medical team is presently checking vital signs and investigating symptoms and is scheduled to report its findings on July 18 [*note correction*] of next year. What the future holds in store for European algebraic number theory and similarly structured branches of mathematics — whether there is a future — will be clearer at that time.

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XerxesThe title of your post suggested a post-Snowdenesque commentary on the use of the Elliptic Curve Method (for factoring) by intelligence agencies. Sadly, the body of your post does not live up to that promise; the composition of the scientific committee for the 7ecm is a sufficient explanation for the phenomenon that you observe.

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mathematicswithoutapologiesPost authorI would hate to think things were that simple. That would imply that nothing is to be learned by studying networks.

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Pierre ColmezI had some “amusing” exchanges with the Gowers and Ghys, members of the scientific committee, in August 2014. First I wrote to Gowers:

” I just stumbled on the list of members of the scientific committee of the 7ECM, and learned that you were the head of this committee. I am a little bit puzzled by the fact that I don’t know anyone scientifically in this committee except for Ben Green who seems to represent Number Theory, but is a representative of the Number Theory that you know yourself quite well. […..]”

I sent a copy to Ghys who replied that he did not understand what I meant. So I wrote him:

“Il est possible que ca se passe bien cette fois-ci. Gowers semble relativement ouvert dans sa maniere de proceder. Ce qui me chiffonne est qu’il n’y a personne dans ce comite qui comprenne les maths qui m’interessent plus ou moins directement. Le choix de Ben Green pour s’occuper de la theorie des nombres me semble assez inquietant pour l’equilibre global du comite (c’est un specialiste de la branche analytique de la theorie des nombres, branche qui a eu quelques succes remarquables recemment (et inviter Maynard serait une bonne

idee)), mais il n’y a personne comprenant la geometrie arithmetique ou algebrique, ou les formes automorphes, alors que 3 personnes du comite semblent plus ou moins directement interessees par la theorie analytique des nombres: Green, Gowers et Seip.”

His answer forced me to point out that my interests were not restricted to algebraic number theory in a strict sense, hence the following:

“A l’ICM, voici les conferenciers dans les domaines dont je parle:

James Arthur

Janos Kollar

Manjul Bhargava

Ben Green

Takuro Mochizuki

Jonathan Pila

Francois Loeser

Matthew Emerton

Francis Brown

Harald Helfgott

Goldston-Pintz-Yildirim

Yitang Zhang

Michael Harris

Wee Teck Gan

Trevor Wooley

Peter Scholze

Seev Rudnick

Jean-Loup Waldspurger

Umberto Zannier

Tamar Ziegler

Yitang Zhang

Davesh Maulik

Mircea Mustatan

Bertrand Toen

Konstantin Ardakov

Bertrand Remy

Emmanuel Breuillard

Parmi ceux-ci, Zhang Rudnick, Wooley, Green, Ziegler, Breuillard et Goldston-Pintz-Yildirim, Helfgott travaillent en theorie analytique des nombres […] ou en theorie ergodique; deux branches bien representees dans votre comite scientifique. Les autres travaillent dans des branches non couvertes par votre comite (et j’aimerais bien qu’elles ne soient pas oubliees).”

I have to say that the result surpassed my expectations….

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volochOTOH, if you ask anybody what’s happening in algebraic number theory right now, you almost certainly will get “Scholze” as the answer. That explains what you see without any conspiracies.

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mathematicswithoutapologiesPost authorWho is talking about conspiracies?

If you look at the list, you’ll notice a number of other branches of mathematics are not particularly well represented either. Some of them are mentioned in the post; I don’t feel qualified to comment on some of the others.

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Olivier“The team was only able to locate a single indisputably live mathematician to represent arithmetic geometry, the Langlands program, and most areas of algebraic geometry, as well as algebraic number theory.”

Are you suggesting that whether Nicolas Bergeron is currently alive is in dispute? That would be sad news to me.

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mathematicswithoutapologiesPost authorThat’s a fair point. Bergeron is definitely not a zombie, but he is difficult to categorize. I see him as a geometer, and not an algebraic geometer, but that view may be outdated.

Taking a broader view, I compared the proportion of invited speakers in sections 2, 3, 4, 7 at the 2014 ICM (about 1/6) to the proportions represented by those fields in the ECM in 2012 (7/33) and 2016 (6/33, including Bergeron). There is a greater disparity among plenary speakers: at Seoul those fields accounted for 6 or 7 of 21 plenary talks, as opposed to 2/10 at the 2012 ECM and 1/10 in Berlin next year.

The main difference is that next year’s algebraists will be much less algebraic than in previous years (2 out of 6, as opposed to 5 or 6 out of 7 in 2012).

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