When Pythagoras and his school say that "everything is a number", what they call "number" is an integer, or the ratio (fraction) of integers. In their eyes, numbers are beautiful, harmonious and accurate. The universe is built on numbers. Hippasus found that the hypotenuse length of an equilateral right triangle with a side length of 1 is a mysterious infinite non-integer.
According to Aristotle, Pythagoras himself was aware of this problem, but because this number would shake the foundation of the whole school, it became the top secret and the biggest taboo.
The emergence of irrational numbers not only dealt a fatal blow to the Pythagorean school, but also seriously hurt the beliefs of all Greeks at that time. A number is infinite and acyclic, and it can never be presented absolutely accurately. How can such decimals destroy people's beliefs, people's sense of security and lead to a serious crisis of understanding. What a terrible number.
There are different stories about hippasus's death. Some people say that he got wind of the fatwa from school, fled in a hurry and was shipwrecked. Others said that he was caught by the school and thrown directly into the sea. Anyway, he died in the sea because he found irrational numbers. Judging from the available data, hippasus is not the only one who died of irrational numbers, because the ancient Greek mathematician ProColas wrote in his annotation to Elements of Geometry: "It is said that the person who first revealed the secret of irrational numbers lost his life, because all things that cannot be expressed and amorphous should be kept secret, and those who exposed and asked questions will be destroyed and swallowed up by eternal waves forever."
However, people who find irrational numbers can be eliminated, but irrational numbers themselves cannot be killed. The discovery of irrational numbers, together with Zhi Nuo's "four paradoxes" about sports, finally triggered the "first mathematical crisis" in the history of human science. However, mathematicians are constantly trying to solve this crisis. According to Article 5 of Euclid's Elements of Geometry, in 370 BC, Odysseus proposed a tortuous or self-deceiving solution: irrational numbers are allowed in geometry, but illogical and illegal in algebra. In other words, irrational numbers are just symbols in a measure, not real numbers.
This may temporarily comfort mathematicians' broken hearts, but it can't really solve the problem. With the discovery of new irrational numbers, more and more people support the existence of irrational numbers, and irrational numbers have become a problem that must be faced and solved. Until 1872, German mathematician Dai Dejin defined irrational numbers by "division of rational numbers" and established the theory of real numbers. Irrational numbers have been righted and gained legal status in mathematics.
The first mathematical crisis triggered by hippasus lasted for more than 2000 years, and it was completely solved. If hippasus's soul is still stranded in the Mediterranean, is it a smile or sadness at this time?
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