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Pythagoras spent some time away from his home city of Samos for political reasons. During this time he studied mathematics. Historical scholarship has come to understand that the Pythagorean Theorem predated Pythagoras by a millennia, it is generally accepted that he was the first to prove it.
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While today we are accustomed to thinking about numbers abstractly, such a concept does not necessarily come naturally to the human mind. Knowing that 1 apple + 1 apple = 2 apples is not the same thing as 1 + 1 = 2. His School also contributed to the concept of "Proofs", as in demonstrating mathematical principles through abstract principles. The establishment of Pythagoras' school marks the beginning of such abstract mathematical thought within scientific philosophy.
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Ancient philosophers spent a great deal of time thinking about what the primary element of nature was. Some thought the universe was formed from water, some earth, and others air. Each had their own arguments based on the knowledge of their time. Pythagoras thought the Universe was derived from numbers. While Pythagoras' imaginings saw numbers in a more religious context, one can see the establishment of the philosophical concept that would lead to today's search for the "Universal Equation".
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Pythagoras liked nice neat whole numbers. His esoteric beliefs about them included qualities that went beyond pure mathematics, such as personality traits and masculine and feminine energies. Despite what contributions he made to the philosophy of science, he was still a cultic fanatic. Thus, when Hippasus discovered and proved the existence of irrational numbers, using the Pythagorean Theorem no less, Pythagoras promptly drowned him for his transgression.
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Laertius, Diogenes, and Charles Duke Yonge. The Lives and Opinions of Eminent Philosophers. Vol. 8, Andesite Press, 2015. Three Minute Philosophy: Pythagoras
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