As a mathematician, I dominated the mathematical world during the second half of the fifth century B.C....but I had nothing to do with medicine.
Aristotle (that cad) once wrote about me: It is well known that persons stupid in one respect are by no means so in all others; thus ****, though a competent geometer, seems in other regards to be stupid and lacking in sense."
Perhaps Archimedes was referring to the fact that I was robbed of all my money and property, had to go to Athens to prosecute the offenders, learned mathematics there from the Pythagoreans, and then started charging people a fee if they wanted to learn geometry from me.
I made significant progress in the resolving of the "squaring of the circle" problem...by showing that some lunes (i.e. region formed by the intersection of two circles) could be squared (i.e. using only a compass and a straight edge, I could construct a square with the same area as certain lunes).
Unfortunately, I died thinking I had solved the "squaring the circle" problem...but all of my mathematical writings on lunes have been preserved to the modern day, thanks to the sixth-century commentator Simplicius.
Hippocrates (470 - 410 B.C.)