Pythagoras was born on the island of Samos in the Aegean Sea (a small island in the eastern part of present-day Greece), and was a clever and studious man since his childhood, having studied geometry, natural sciences and philosophy under a famous teacher. Later on, because of his yearning for the wisdom of the East, he came to Babylon, India and Egypt after thousands of miles and absorbed the rich nutrients of Arabian civilization and Indian civilization and even Chinese civilization, and then returned to the island of Samos in about 530 B.C.E.. He later moved to Crotone in southern Italy and founded his own school, engaging in education and mathematical research at the same time.
Pythagoras and his school made many mathematical creations, and were especially interested in the patterns of change in the integers. For example, a number in which the sum of all the factors (except itself) is equal to itself is called a perfect number (e.g., 6, 28, 496, etc.), and a number in which itself is greater than the sum of its factors is called a surplus; a number in which the sum of its factors is less than the sum of its factors is called a deficit. They also discovered that "the sum of the squares of the two right-angled sides of a right triangle is equal to the square of the hypotenuse", which is called the Pythagorean Theorem in the West and the Pythagorean Theorem in China. Nowadays, there is the concept of "Pythagorean ternary array" in mathematics, which refers to the set of three arrays that can be used as the three sides of a right triangle. orthotetrahedron, orthohexahedron, orthoooctahedron, orthododecahedron and ortho icosahedron.
The Pythagorean school considered numbers to be the most sublime and mysterious, and by numbers they meant integers. "Number is everything," meaning that all kinds of relationships in the universe can be expressed in terms of integers or ratios of integers. However, a student named Hippasus discovered that a square with a side of length 1 and its diagonal (root 2) could not be expressed in terms of ratios of integers. This offended the school's creed, and a discipline was imposed: no one was allowed to reveal the secret of the existence of root 2 (i.e., irrational numbers). The na?ve Hippasus inadvertently spoke to someone about his discovery and was killed. But Root 2 soon caused a great revolution in mathematical thought. In the history of science, this event is called the "First Mathematical Crisis". The lesson left behind by the martyrdom of Root 2 is that there is no end to science, and that whoever draws a no-go area for science becomes an enemy of science, and is ultimately buried by science.
Unfortunately, the vigorous Pythagoras, in his later years, not only tends to be conservative academically, but also politically opposed to new things, and finally died.
Among the early mathematicians of ancient Greece, Pythagoras had the greatest impact. His storied life has left a multitude of amazing legends for future generations.
Pythagoras was born in Samos (a small island in the eastern part of Greece) and died in Tallinn (Taranto, southern Italy). He was both a philosopher, mathematician, and astronomer. As a young man, he traveled to Babylon and Egypt, as was customary for the children of wealthy families at the time, and was thus directly exposed to Eastern civilization. Upon his return, Pythagoras created a secret scholarly group in which politics, religion, and mathematics were united, and this group was known to later generations as the Pythagorean School. The activities of this school were all secret, shrouded in an incredible atmosphere of mystery. It is said that every newly enrolled student had to take an oath of secrecy and to join this school only for life. It was also the custom of the school to attribute all inventions to its leaders, and to keep them secret so that future generations would not know who invented them and when.
The Pythagorean Theorem (i.e., the Pythagorean Theorem) was another contribution of Pythagoras, and one of his students, Hippasus, discovered irrational numbers through the Pythagorean Theorem. Although this discovery broke Pythagoras's belief that all things in the universe are ratios of integers to whole numbers and led to Hippasus's tragic death, the theorem was a tremendous boost to the development of mathematics. In addition, Pythagoras also made some contributions to music, astronomy and philosophy, pioneering the geodesic theory that the sun, the moon and the five stars are spheres, floating and suspended in space.
Small story:
Pythagoras was invited to attend a rich dignitary's dinner, the owner of the luxurious palace-like restaurant is paved with square beautiful marble tiles, due to the meal is not late on the table, these hungry guests complained; the good observation and understanding of the mathematician but stared at the feet of these rules of the arrangement of these beautiful square tiles, but Pythagoras did not just appreciate the beauty of the tiles. But Pythagoras did not just admire the beauty of the tiles, but thought of their relationship to [number], so he took a brush and squatted down on the floor, chose a tile and drew a square with its diagonal AB as the side, and found that the area of this square was exactly equal to the sum of the areas of the two tiles. He was very curious, so two tiles put together the diagonal of the rectangle for another square, he found that the area of this square is equal to the area of five tiles, that is, the two strands as the side of the square and the sum of the area. So Pythagoras made a bold assumption: any right triangle, the square of its hypotenuse is exactly equal to the sum of the squares of the other two sides. That meal, the ancient Greek master of mathematics, the eyes have not left the ground.