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In an interview made for the 25th anniversary of the Institut de Mathématiques de Jussieu-Paris Rive Gauche, its head Professor Loïc Merel says at 1:25:

Les doctorants que nous formons aurons une lourde tâche: celle de reprendre le flambeau de l'école mathématique française, qui est rentrée dans un creux démographique.

[Personnal translation: The graduate students that we educate will have a daunting task: that of taking up the mantle of the French school of mathematics, which has entered a demographical dip.]

What are references backing this claim, and how pronounced is the effect ? For instance, will there be an actual shortage of talent and even some areas taking a toll, or just slightlty less competition for a while ?

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    In developed countries, IQ scores are dropping 1 point per generation — if not more. Make talented people spend their fertile years in universities and offices, then complain about lack of talent. Talent is conceived and birthed by talented people. Modern society obviously hates biology. – Rodrigo de Azevedo Nov 2 '19 at 15:03
  • Not sure I understand what is the "French school of mathematics". Or is he just speaking of a drop in numbers and a difficulty, therefore, of collaboration within France? – Buffy Nov 2 '19 at 15:26
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    I could be mistaken, but it seems that he means "mathematicians educated in France". But I cannot understand if he means that there are fewer graduate students coming out of that system, or not enough compared to the number of people retiring. And I think he's refering not just about collaborations within France, but really a potential drop of highly regarded researchers from France (say, like invited speakers at ICMs). – Thomas Sauvaget Nov 2 '19 at 16:31
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    @Buffy As far as I know, France is known to have a good tradition for what concerns certain topics of mathematics and physics, which is reflected not only in the publication record, but also in the way in which these subjects are taught. For instance, I have several many French books about mathematics and physics and they have certain characteristics that cannot be found in other literature and which I appreciate very much. That is what I call a "school", and which is probably the intended meaning in the quote. – Massimo Ortolano Nov 2 '19 at 17:52
  • Actually, you could ask him directly: webusers.imj-prg.fr/loic.merel – Buffy Nov 2 '19 at 18:36
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Here is some additional info compared to the other answer (which does not have a lot of detail).

Loïc's comment is mainly about fundamental (AKA pure) mathematics. The IMJ-PRG is a pure math research institute. There is a trend in French academia that funding is going more and more towards research that has immediate applications, with some level of disregard for fundamental research. This is the case in pretty much all fields of science (maybe with the exception of computer science). It goes without saying that the situation is dire in social science and the arts, apart from economics, management, and law. (I did not choose these at random, they are legally treated separately from the rest.)

The French ministry periodically releases some demographic information. Here is the latest one for faculty in Section 25, i.e. pure math. Even if you can't read French, the graphics speak for themselves. On the first page, the first graphic is about professors, the second about lecturers (maîtres de conférences), the third about the total. The brown line is pure math, the light blue line is "Group 5" (pure math + applied math + CS), the dark blue line is Science, the black line is the whole of French academia. The graphics are normalized at 100 in 1998. You can get graphics for other years and fields on this page.

To summarize: the number of faculty in pure math has decreased by 15% in France between 1998 and 2018. This is enormous. The number of students increases every year. Administrative tasks are always increasing. This puts an enormous amount of stress on the remaining faculty. (As a comparison, the number of faculty in applied math increased by 11.4%.)

The situation is also dire for new doctors: finding a permanent position is an ordeal, even more so than in similar countries. In the PDF I linked, Figure 3.2 on page 4 is especially telling: in 2018, there were 420 candidates for 22 lecturer positions, and 136 candidates for 14 professor positions. This does not include candidates who were rejected from the "qualification" (94.7% of candidates for professorships and 88.7% of candidates for lectureships are "qualified").

Note that this graphic also shows that there is not much shortage of talent. The number of candidates per position (column "Ratio B/A") decreased between 2014 and 2015, but it's increasing since 2015. The decrease in 2014–2015 was due to the fact that there was an exceptionally low number of available positions in 2014.

A remark, for intellectual honesty: not all French math researchers are faculty. Some are full-time researchers employed by the CNRS. Update: According to the CNRS's official statistics, the total number of researchers in Section 41 (pure maths + applied math, no, it's not the same section as the CNU) is 373: 210 junior and 163 senior. To compare, in 2018 there were 1321 faculty in pure math and 1776 in applied math. That's 3097 total, so CNRS researchers represent about 12%. I cannot say what the distribution between pure and applied is. "Common knowledge" tells me that it's around 10% for pure math.

PS: The ministry's website has a wealth of information. There are statistics about pretty much everything, as well as explanatory notes about the conjonctures. I highly recommend it to anyone who wants to learn about the evolution of French academia. However, be careful about aggregates: data about a "Group" (e.g. pure+applied math + CS) may not tell you everything about a "Section" (e.g. pure math).

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    France was and is a pioneering nation for pure mathematics -- The nation that produced Serre, Grothendieck, and Cartan in the 20th century could be no less. It is sad to hear that they are succumbing to the Anglo-Saxon disease of chasing areas with "immediate applications". – user_of_math Nov 5 '19 at 14:10
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As suggested by Buffy in the comments, I've now written to Professor Merel and have obtained his answer. Since he didn't mention that I could give it here I'll keep it private. I'll just say that a relevant reference is this publicly available page on the Opération Postes website. Edit (given the comments): the plots on that page show a very subtantial decrease in the number of offered positions in the space of 10 years. On the other hand, it is known that the number of new PhDs per year has not decreased.

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    Self-answers are fine, but this answer doesn't have enough information to be useful to the rest of the community without following the link, and links can die over time. It would be better to put at least a summary of what you are referencing in your answer itself. – Bryan Krause Nov 4 '19 at 22:11
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    It is also like saying: I found the answer on my own, and am not going to tell you what it is. – Kimball Nov 4 '19 at 22:28
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    So how is an extreme shortage of jobs a "demographic dip"? – Elizabeth Henning Nov 5 '19 at 18:14

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