I think it should be an ancient Greek mathematician who was interested in proving all triangle has inner angles summing to 180 degree? Was it Thales?
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2$\begingroup$ First one must define "proof." (and "important") I think this question is too vaguely worded to be answerable. $\endgroup$– Carl WitthoftDec 12, 2018 at 14:30
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$\begingroup$ who was the first to emphasize the importance of proof ? That is on my practice final for history of math. $\endgroup$– user614287Dec 12, 2018 at 14:34
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$\begingroup$ If that is on the final, then the expected answer is probably in the readings (or the lectures) for that course. $\endgroup$– Gerald EdgarDec 12, 2018 at 22:44
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According to the Greek (Hellenistic) tradition, this was Thales. He is credited with proofs of such things as that "vertical angles formed by two lines are equal". But this was written in the Hellenistic histories of mathematics centuries after Thales, and we have no idea what sort of proofs he really gave to such things.
We really do not have primary sources for pre-Euclidean mathematics earlier than Euclid himself, and Euclid does not give credits.
One has to be very cautious about Hellenistic sources. For example they claim almost unanimously that Thales and Pythagoras studied mathematics in Egypt but according to modern historians mathematics in Egypt was on very primitive level, and it is not clear what they could possibly learn in Egypt. It seems that the Greeks invented the proofs themselves, at some time between Thales and Plato, but who and when exactly, we do not know.
answered Dec 12, 2018 at 15:12