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From my classes I don't hear about a lot of italian mathematicians, but two of them, Fubini and Tonelli, are both related to multivariable calculus. Is there a reason for this? Just a coincidence? Or was Italy historically stronger in this area?

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  • $\begingroup$ Is your question referring to a specific time period? The question would be extremely broad otherwise. Are you interested in the period between XIX and XX century, i.e. when Fubini and Tonelli where around? $\endgroup$ – Easymode44 Mar 17 at 8:34
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    $\begingroup$ I suppose "your classes" means undergraduate classes. What is taught in undergraduate classes does not really reflect the contribution to mathematics of various countries. $\endgroup$ – Alexandre Eremenko Mar 17 at 13:34
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In a way, but not exactly. From about the same period (late 19th-early 20th century), the names of Peano (differential equations, mathematical logic), Betti (algebraic topology, elasticity theory), Veronese (classical geometry), Castelnuovo, Enriques (algebraic geometry), Beltrami, Bianchi, Ricci-Curbastro, Levi-Civita (Riemannian geometry, tensor calculus), Arzela, Cesaro, Dini, Vitali (mathematical analysis), Volterra (integral equations, mathematical biology) are pretty widely known. Of course, Cavalieri and Torricelli were early calculus pioneers, and both Riemannian geometry and analysis are sophisticated descendants of calculus.

According to Mathematicians in Bologna 1861–1960, p.469, "the collaboration between Betti and Brioschi was the true driving force behind the initial development of Italian mathematics". Betti befriended Riemann, and did a lot to promote his ideas in Italy. He also deserves a lot of credit for fostering top grade mathematicians, both geometers and analysts. Six of the above were his doctoral students (Arzela, Bianchi, Dini, Enriques, Ricci-Curbastro and Volterra), see his Mathematics Genealogy page. Tonelli was Arzela's student, and Fubini was both Dini's and Bianchi's. Cesàro's 1890-s textbooks also promoted both subjects. Brioschi founded Milan's Polytechnic in 1863, geometers Cremona and Beltrami were his students. Beltrami was also active in promoting Riemann's ideas, he translated his works into Italian.

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    $\begingroup$ Good answer, although I would not omit Gini in your (albeit not exhaustive) list, especially since his contribution paved the way to the foundation of what would be a flourishing Italian statistical school in the XX century. $\endgroup$ – Easymode44 Mar 17 at 8:41
  • $\begingroup$ @Easymode44 I just did not want to turn it into a laundry list. Gini is better known for his work in statistics and economics, and may be less recognizable to mathematicians than the listed names. We should also mention Pareto in the same area. $\endgroup$ – Conifold Mar 17 at 8:48

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