a great challenge. Didn't quite get there...

This one beat me. A good grid. Thanks!

I know Plato was fundamentally a philosopher, but he was also a mathematician - Platonic solids etc.

Some nice red herrings here with all the crossovers.

Since when is Aristotle a mathematician?

Yes, plato can be regarded as a mathematician. Aristotle is not noted as a mathematician. Curie was more of a chemist. Newton probably regarded himself as a mathematician.

I adore the subject matter, but unfortunately, many of these polymaths can fit into more than one category, so the solution is not unique.

It's so nearly perfect, i'd love to see you have another go at this one.

I think swapping Aristotle and Newton would produce a better solution. Aristotle was a logician but not really a mathematician, so he'd fit better in the physicists group by virtue of having written his work called "Physics." Newton can readily backfill him in the mathematicians group by virtue of having developed calculus.