There seems to be a range of ways of approaching stuff like Greek mathematicians, and this seems to stretch over a spectrum which extends between faith that we can deduce a strong indication of when and where they lived and worked, to those who believe that most of this kind of assertion is pure guesswork.
Dating like this is a good example: About Euclid, for example, we know absolutely nothing, but the stories about him range from saying just that up to making him the founder of the mathematics department at Alexandria's Museum. Archimedes is another example: we probably know more about him with some reliability than most, perhaps all, other Greek mathematicians. His date of birth is usually given as 287 BC: which comes from the information that he died an an 'old man' during the Roman siege of Syracuse in 212 BC. Now this information comes (only?) from Tzetzes, an uncritical and prolific supplier of all manner of things. Also 'old' is usually taken to be 75, and 212 + 75 = 287. Hence .... (Also the label 'Greek' usually meant speaking or writing Greek; as far as we know, Archimedes seemed to have lived and worked in Syracuse, in Sicily. Note also that Alexandria is situated in Egypt, in North Africa.)
This basic information about Archimedes can be found in paragraph 2 of Dijksterhuis well-informed book on him (p.9 of the paperback; see below), but Dijksterhuis does not report how the conclusion was drawn, and there is no indication of the merit of Tzetzes' reputation as a source, nor of the reliability of 75 as the age of an 'old man'. (Nor is there any general information that Dijksterhuus is accurately reporting his source.)
About Eudoxus as a mathematician, we have only 3 bits of information: Aristotle, Post Anal 74a17, Proclus in his report on Elements I, and the first Scholium to Elements V. I don't want to deny thew conclusion that he was, but only want to know the strength of evidence for it.
(E J Dijksterhuis, Archimedes, tr C Dikshoorn, Princeton,1987.)