>>10832772I mean for the OP, if he doesn't realize.
>>10832769I mean that's a philosophical question that always ends up with a question of meaning of life in general.
What is useful research? Useful to whom? Science? Civilization? Is scientific progress necessarily good for humanity? Etc.
I do R&D at work already and I like history of mathematics I guess. Also would give me a trajectory to work out personal favorites to formalizations of mathematical frameworks.
The exponential in it's forms covers a lot of different fields and has some clean and completely worked out properties that are at the same time of interest to many practical questions, so I collected some ideas on how to write a book around it.
My favorite math history book is
https://www.amazon.com/Modern-Algebra-Rise-Mathematical-Structures/dp/3764370025which captures how the notion of the field of algebra has evolved from Galois to Grothendieck. The discussions around Nothers work and contemporary of Hilbert are a bit tiresome (because nobody knows of all the math that didn't work out or found interest covered there) but I'd be willing to dig up some biographical work and tie it together. It's also a form of research, really, albeit more of a histographical one.
