Descartes was himself a lawyer (by training) then there were Leibnitz, Cayley, Viete. If you include Physics you will get a bigger list.

Descartes and Fermat ran a mutual admiration society, don't read to much into it.

Both had independently come up with coordinate geometry, linking algebra and geometry

I agree Fermat probably had a wrong proof but curb your condescension towards lawyers making contributions in mathematics.