The Pythagorean Theorem – a great discovery or the collapse of the Pythagorean sect?

Why today, in the age of computerization and robotics, do we turn again and again to the legacy of the ancient world including Maybe we are bored with the modern machine age and involuntarily direct our gaze to the past in search of answers to the tricky questions of existence? Or maybe humanity, turning to the heritage of antiquity, experiencing nostalgia for their childhood and adolescence, when much was unknown?

Pythagoras’ theorem initiated the rapid development of scientific thought and the further progress of civilization. It refers to right triangles and tells us that the square of the hypotenuse is equal to the sum of the squares of the cathetuses. However, the ancient Egyptians had already guessed this. But only the Greeks, when they considered a triangle with a side ratio of 3:4:5, noticed that 3² + 4² = 5² – and they found a proof of this principle.

Pythagoras’ fame as an ancient scholar will remain eternal. According to some historical sources, for example, he can be considered the founder of such disciplines as philosophy and geometry, mathematics and astronomy. In addition, Pythagoras discovered the meaning of numbers and was the author of the statement “Everything is a number.” The Pythagoreans devoted most of their lives to finding analogies between numbers. Pythagoras’ theorem primarily serves as the basis for analytic geometry and a set of trigonometry theorems. The theorem is necessary for the extraction of square roots. Some researchers consider Pythagoras’ theorem to be the quintessence of mathematics.

It should be noted here that the thought of the ancient thinkers was made up of elements that included religion and mysticism. It is already difficult for modern people to imagine this combination, because they rely on the tradition of the Enlighteners of the 18th century. Pythagoras was a mathematician and a magician at the same time – he combined the features of a rational and irrational person.

And here it is remarkable that Pythagoras’ influence was very noticeable not only on Nicolaus Copernicus (1473-1543), but also on Johannes Kepler (1571-1630). Although Kepler’s laws played a key role for the scientific revolution, the great German mathematician and astronomer himself remained a mystic.

The influence of Greek mathematics can be traced back to the 17th and 18th centuries, when there was no deductive algebra and reference to mathematical rigor was reserved for geometry. It was only with the discoveries of algebra and mathematical analysis that this was done away with.

The great paradox of scientific thought and the historical development of civilization eventually led to the collapse of the Pythagorean philosophy. It was the discovery of this theorem that marked the beginning of the end of the Pythagorean sect.

The discovery of irrational numbers derived from the Pythagorean theorem killed Pythagoras’ universe of numerical harmony. After this event, the ancient Greeks decided to treat geometry separately from arithmetic. The personality of Hippas of Metapontus is very remarkable in this respect. He was born about 500 B.C. There is a legend that he not only proved the existence of irrational numbers, but also broke the laws of the Pythagorean sect (the so-called vow of silence) by telling the world about his discovery. Again according to legend, the sectarians threw Hippas off the ship.

The date of Pythagoras’ own death is also unknown. A possible date is given as about 490 BC in the city of Metaponte, where he fled after a mutiny in Croton.

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