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:
- 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.
- 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.
- 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?