I'd like to present my point of view on the history of Greek mathematics from Thales to Euclid, which differs from Colin's.
What we know about Greek mathematics we have learnt from sources
that were written after 300 BC, and of course we do not have any
originals but copies of copies of copies. In particular, everything
we seem to know about Thales or Pythagoras is second hand knowledge
coming from histories composed at least 200 years after their death.
Just because legends about Pythagoras have been embellished a few
centuries later does not mean, however, that there is no substance
to these legends at all.
This means that there are many possible interpretations, all of which are more or less compatible with the "facts". The two extreme positions are held by
Burkert, who views Pythagoras as some kind of medicine man, and e.g.
by Zhmud (Pythagoras as a mathematician). Just because they are
extreme does not mean that they must be wrong, or that the truth lies
somewhere in between. But there is certainly not an unanimous opinion
concerning the "historical truth". For a balanced view (whatever that
means) one may consult Kahn's book "Pythagoras and the Pythagoreans".
In my opinion, honesty requires using the phrase "we do not know for certain" a lot more often than did historians in the last century. There is an "ignoramus" in history of mathematics, and unless someone comes up with a time machine, there also is an "ignorabimus".