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I am recently learning about teaching the history of mathematics. Gradually, impressions about mathematicians in different countries develops in my mind. I just want to ask, whether it is helpful to think in this way:

  1. English mathematicians are very likely to be good physicists as well. We have Newton. We have the "Merton Calculators". Although many other mathematicians (such as Bernoulli) are good physicists as well, I just feel that British math are more prone to be physics. Even today, staff like quantum mechanics is important for many math students.
  2. French mathematicians are good at pure and rigorous things. For example, we have Cauchy and Lagrange who made analysis more rigorous. The name "Lagrange" also appears in abstract algebra.
  3. I don't know much about German mathematicians, but people like Hilbert and Cantor are the ones who introduces crazy modern ideas in math. (Also Poincare, Gödel, etc!) Germans seem to play a huge role in more modern math. Of course, we also have great analysist like Karl Weierstrass.

Are there any other "general trends" that we can find for mathematicians in different countries (doesn't have to be limited to the three above)? Are those trends just appearing in history books, or are they still existing in mathematicians in different countries nowadays?

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  • $\begingroup$ I think in order to fully understand the difference among different countries one should study their university and higher secondary education system in the 19th century. Don't forget the Russians as well. They did not get much fame because their language was quite different than European languages. Also it was common among mathematicians of know several languages. A reading knowledge of German, French or Russian was mandatory to obtain a PhD in mathematics in North America/Britain. $\endgroup$ – M. Farooq Jul 22 at 0:13
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    $\begingroup$ Poincare was French, not German, and also "prone to physics", as was Laplace before him. Grothendieck, MacLane and Russell (French, American and English) are also among "people like Hilbert and Cantor". Dedekind and Weierstrass (German) were also "good at pure and rigorous things". These anecdotal "generalizations" do not work any better on mathematicians than folk anecdotes about "national spirits" generally. There were mathematical schools that defined lines of research, but they often crossed national lines. $\endgroup$ – Conifold Jul 22 at 4:28
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    $\begingroup$ There is no set definition of "French / German/ English [anything]" You could refer to country of birth, country of residence, country/countries of education. This has no real meaning. $\endgroup$ – Carl Witthoft Jul 22 at 14:13
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    $\begingroup$ To discuss this one has to choose some time period. Otherwise the question is meaningless. $\endgroup$ – Alexandre Eremenko Jul 22 at 16:04

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