I don’t buy your factors (1) or (2). Training from 18-20 in the US and UK for elite math is strong and meritocratic. And brilliant mathematicians have career stability in the US and UK.
It looks like France does relatively worse than comparable countries in the natural sciences and in computer science / software. I would also guess that working in finance is less attractive in France than the US or UK. So one possible factor is opportunity cost.
The UK/US system typically gives tenure around ~40, typically after ~two postdocs and a assistant → associate → full prof.
In the French system a typical case might land an effectively tenured job at 30. Since 30-40 is a decade of peak creativity for scientists in general, mathematicians in particular I would say this is highly
Laurent Lafforgue is a good example. Iirc he published almost nothing for seven years after his PhD until the work that he did for the Fields medal. He wouldnt have gotten a job in the American system.
He is an extreme example but generically having many more effectively tenured positions at a younger age means that mathematicians feel the freedom to doggedly pursue important, but perhaps obscure-at-present, research bets.
My point is primarily that the selection is at 20, instead of at 18. It s not about training per se, although here too the French system has an advantage. Paris has ~ 14 universities, a number of grand ecolees, research labs, etc a large fraction which do serious research mathematics. Paris consequently has the largest and most diverse assortiment of advanced coursework in the world. I don’t believe there is any place in the US that compares [I’ve researched this in detail in the past].
The UK does not have the same tenure system as the US. I believe top mathematicians have historically (i.e. last 70 years) often become permanent lecturers fairly young (e.g. by age 32).
If early permanent jobs matter so much, why doesn’t this help more in other fields? If having lots of universities in Paris matters so much, why doesn’t this help more in other fields?
I wouldn’t claim to be an expert on the UK system but from talking with colleagues at UCL it seems to be the case that French positions are more secure and given out earlier [and this was possibly a bigger difference in the past]. I am not entirely sure about the number 32. Anecdotally, I would say many of the best people I know did not obtain tenure this early. This is something that may also vary by field—some fields are more popular, better funded because of [perceived] practical applications.
Mathematiscs is very different from other fields. For instance: it is more long-tailed, benefits from ′ deep research, deep ideas’ far more than other fields, is difficult to paralellize, has ultimate ground truth [proofs], and in large fraction of subfields [e.g. algebraic geometry, homotopy theory …] the amount of prerequisite knowledge is very large,[1] has many specialized subdisciplines , there are no empirical
All these factors suggest that the main relevant factor of production is how many positions that allow intellectuall freedom, are secure, at a young age plus how they are occupied by talented people is.
e.g. it often surprises outsiders that in certian subdisciplines of mathematics even very good PhD students will often struggle reading papers at the research frontier—even after four years of specialized study.
I’d defend a version of claim (1): My understanding is that to a greater extent than anywhere else, top French students wanting to concentrate in STEM subjects must take rigorous math coursework from 18-20. In my one year experience in the French system, I also felt that there was a greater cultural weight and institutionalized preference (via course requirements and choice of content) for theoretical topics in ML compared to US universities.
I know little about ENS, but somewhat doubt that it’s as significantly different of an experience from US/UK counterparts.
I don’t buy your factors (1) or (2). Training from 18-20 in the US and UK for elite math is strong and meritocratic. And brilliant mathematicians have career stability in the US and UK.
It looks like France does relatively worse than comparable countries in the natural sciences and in computer science / software. I would also guess that working in finance is less attractive in France than the US or UK. So one possible factor is opportunity cost.
https://royalsocietypublishing.org/doi/10.1098/rsos.180167
Those are some good points certainly.
The UK/US system typically gives tenure around ~40, typically after ~two postdocs and a assistant → associate → full prof.
In the French system a typical case might land an effectively tenured job at 30. Since 30-40 is a decade of peak creativity for scientists in general, mathematicians in particular I would say this is highly
Laurent Lafforgue is a good example. Iirc he published almost nothing for seven years after his PhD until the work that he did for the Fields medal. He wouldnt have gotten a job in the American system.
He is an extreme example but generically having many more effectively tenured positions at a younger age means that mathematicians feel the freedom to doggedly pursue important, but perhaps obscure-at-present, research bets.
My point is primarily that the selection is at 20, instead of at 18. It s not about training per se, although here too the French system has an advantage. Paris has ~ 14 universities, a number of grand ecolees, research labs, etc a large fraction which do serious research mathematics. Paris consequently has the largest and most diverse assortiment of advanced coursework in the world. I don’t believe there is any place in the US that compares [I’ve researched this in detail in the past].
The UK does not have the same tenure system as the US. I believe top mathematicians have historically (i.e. last 70 years) often become permanent lecturers fairly young (e.g. by age 32).
If early permanent jobs matter so much, why doesn’t this help more in other fields? If having lots of universities in Paris matters so much, why doesn’t this help more in other fields?
I wouldn’t claim to be an expert on the UK system but from talking with colleagues at UCL it seems to be the case that French positions are more secure and given out earlier [and this was possibly a bigger difference in the past]. I am not entirely sure about the number 32. Anecdotally, I would say many of the best people I know did not obtain tenure this early. This is something that may also vary by field—some fields are more popular, better funded because of [perceived] practical applications.
Mathematiscs is very different from other fields. For instance: it is more long-tailed, benefits from ′ deep research, deep ideas’ far more than other fields, is difficult to paralellize, has ultimate ground truth [proofs], and in large fraction of subfields [e.g. algebraic geometry, homotopy theory …] the amount of prerequisite knowledge is very large,[1] has many specialized subdisciplines , there are no empirical
All these factors suggest that the main relevant factor of production is how many positions that allow intellectuall freedom, are secure, at a young age plus how they are occupied by talented people is.
e.g. it often surprises outsiders that in certian subdisciplines of mathematics even very good PhD students will often struggle reading papers at the research frontier—even after four years of specialized study.
I’d defend a version of claim (1): My understanding is that to a greater extent than anywhere else, top French students wanting to concentrate in STEM subjects must take rigorous math coursework from 18-20. In my one year experience in the French system, I also felt that there was a greater cultural weight and institutionalized preference (via course requirements and choice of content) for theoretical topics in ML compared to US universities.
I know little about ENS, but somewhat doubt that it’s as significantly different of an experience from US/UK counterparts.
Certainly for many/most other subjects the French system is not so good. E.g. for ML all that theory is mostly a waste.