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.