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Most histories, that I've encountered, of mathematics about the 18th century and onward focus on a chronology of publications, results, definitions, and similar "pure" interests. However, I am often interested in why these people were asking these particular questions in the first place, and why they thought to try this idea and that idea.

Of course this can be hard to discern with the slim writings that we have on the topic -- probably most of this was communicated between mathematicians in un-recorded conversation. Some of the psychology of these mathematicians may just never have been made public in any way. But I'm sure there is at least something that can be extracted from the available writing.

I'm also sure that some mathematicians had not much more motivation than curiosity. Still I know that a lot of mathematics was motivated by more specific and physical questions, and I often find those very informative when they exist.

Are there books that give a lot of attention to the motivations that mathematicians had for both their questions as well as their methods of solution? I mostly have in mind the development of analysis, but other fields would also be interesting.

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  • $\begingroup$ It was much more than just curiosity. See, for example. Riemann's Rearrangement Theorem. For example, Euler's proof of the Euler formula rearranged terms without consideration of absolute convergence. Luckily the series does converge absolutely. $\endgroup$
    – nwr
    Jan 2 at 18:10
  • $\begingroup$ And Riemann was extending an observation of Dirichlet, both of whom were trying to solve an analytical problem, arising from the vibrating string problem, about the convergence of Fourier series. See Riemann 1867, sect. 3 (p. 9). $\endgroup$
    – Michael E2
    Jan 2 at 20:01
  • $\begingroup$ @nwr On the other hand, I think Fermat's work especially in number theory was -- as far as I can tell -- motivated only out of curiosity. $\endgroup$
    – Addem
    Jan 2 at 21:06
  • $\begingroup$ Perhaps I have misunderstood your question. I read it as asking why, beginning in the 18th century, mathematicians were more focused on rigor. I don't doubt that curiosity has always been a major motivation for mathematicians. Regarding Fermat - Fermat was prior to the 18th century. $\endgroup$
    – nwr
    Jan 2 at 22:27
  • $\begingroup$ @nwr Yes, that is not what I was asking. I was asking for a detailed history of motivations, wherever it is available. So for instance, I wanted to see where a physical or statistical, or other kind of question, led to mathematics problems, which led to mathematical research and progress. $\endgroup$
    – Addem
    Jan 3 at 0:46

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"The Origins of Cauchy's Rigorous Calculus" by Judith Grabiner discusses some of the motivations of mathematicians involved in the development of calculus, starting in the eighteenth century (with Cauchy's antecedents). She also references other historians with whom she differs. I'm not sure I'd say the book gives a lot of attention to motivations, but Grabiner is interested in why the "rigorous calculus" emerged.

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