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I know there are many ancient theorems like the Euclid's theoems concerning geomentry. The Pithagorean theorem is also very old, maybe known by Sumerians. Does someone knows what has been the first theorem ever discovered? Many thanks.

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Probably something about sums and multiplications, probably from many many millennia ago... –  Asaf Karagila May 2 '12 at 11:19
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It's unlikely that this question has an answer. –  lhf May 2 '12 at 11:22
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Perhaps the equality "1+1 = 2". This theorem has received some further attention last century and is not entirely trivial. –  Willie Wong May 2 '12 at 11:26
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@Willie: Yes. You do. :-) –  Asaf Karagila May 2 '12 at 11:56
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The question is not answerable as is. A better question might be: "What is the first known example of a published theorem?" or something along those lines. There are several votes to close, but I think the question has merit if interpreted this way. –  Grumpy Parsnip May 2 '12 at 12:03
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closed as not constructive by lhf, Benjamin Lim, Eric Naslund, Alex B., Willie Wong May 2 '12 at 12:34

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The first mathematicians considered was Thales but the first theorem proved was a a little bit self evident but the important was that he wrote down a proof.

That was the theorem of the opposite angles [http://www.icoachmath.com/math_dictionary/Opposite_Angles.html][1].

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From my reading of the Wikipedia entry it's not entirely clear that Thales wrote anything down. He might have communicated his proof verbally (or even possibly a myth arose that he had communicated a proof at some point, when he had none). –  Doug Spoonwood May 2 '12 at 12:35
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Though there undoubtedly existed many mathematical truths in even prehistoric times that people knew about, it's not exactly clear that any theorems existed for prehistoric people. For any given mathematical truth, you don't end up having a theorem until there exists a proof of that theorem. From what I understand of the history of ancient civilizations, you don't find the notion of proof in mathematics becoming prominent until the Greeks. William Dunham in Journey Through Genius attributes the first theorem, or equivalently a mathematical "truth with a proof", to Thales of Miletus, and it gets called Thales Theorem. It says that if points A, B, and C lie on the circumference of a circle, and if line AC cuts across the diameter of a circle, then angle ABC is a right angle. It does not seem that Thales proof currently exists, and it's not clear that it ever got written down in text.

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