You will see it written that Hadamard was the last of the universal mathematicians--- the last, that is, to encompass the whole of the subject, before it became so large that this was impossible. However, you will also see this said of Hilbert, Poincare, Klein, and perhaps of one or two other mathematicians of the period. I don't know to whom the title most properly belongs, though I suspect the answer is actually Gauss.
- I have never heard Hadamard or Klein mentioned as such, though this does not mean it has not been said.
- I would add Kolmogorov to the list of candidates.
- My wife would add Aristotle and Archimedes to the list.
- Gauss seems like a good choice to me.
- Do any current mathematicians qualify? One stumbling block--- I do not know of anyone lately who has made serious contributions to logic and some non-logic branch of mathematics.
- It is, of course, an ill defined question. Is there a way to better define it and answer it?