• Archimedes (around 240 B. C.)
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As I have already said, what we really know about mathematicians of this time - about their lives, as opposed to their mathematics - is ... nothing. Archimedes is a strong exception to this because - very, very unusually for a mathematician - he took part in a datable historical event of some importance in the world at large, the Roman siege of the Greek colony of Syracuse on eastern coast of the island of Sicily, in the year 212 B.C. This was part of the contnuous war between Rome and Carthage, in which Syracuse made a bad choice. (Well, maybe no choice was good.)

This and the date of the foundation of Alexandria (330 B.C.) are the only precise and verifiable dates in the history of early Greek mathematics! (But this just raises another topic: Greek calendars.)