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.
What has been the first theorem discovered in the history of mathematics?
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3Probably something about sums and multiplications, probably from many many millennia ago... – 2012-05-02
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11It's unlikely that this question has an answer. – 2012-05-02
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0http://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus – 2012-05-02
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4Perhaps the equality "1+1 = 2". [This theorem has received some further attention last century](http://scienceblogs.com/goodmath/2006/06/extreme_math_1_1_2.php) and is not entirely trivial. – 2012-05-02
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0@WillieWong, I don't think $1+1=2$ was ever proved or even seem to need a proof before the foundation crisis. Anyway, that's an example of why I don't think this question has an answer. – 2012-05-02
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1@lhf: (a) The OP wrote "discovered", not "proved". (b) Do I really have to wave a sarcasm tag around for comments like this? – 2012-05-02
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2@Willie: Yes. You do. :-) – 2012-05-02
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1The 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. – 2012-05-02
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0@WillieWong It doesn't matter if the OP wrote "discovered" or "proved". A theorem is NOT discovered *as a theorem* until it has gotten proved. If no proof of a statement exists, then, ceteris paribus, it just qualifies as a statement. In other words, the first proof of a statement as a theorem and the discovery of such a statement as a theorem in some way coincides. – 2012-05-02
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1Casting the final vote to close. In principle I agree with @JimConant: but in light of the answers already gathered (and the current statement of the question mentioning the Sumerians, thus making it hard to interpret it in the way Jim suggests) it would be perhaps better to open a new question along Jim's suggestion than to try to edit this one into shape. – 2012-05-02
2 Answers
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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2From 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). – 2012-05-02
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.