Pythagoras devoted his life to mathematical research. He was the first person to make mathematics beyond the scope of business needs. His hard work promoted the development of mathematics, especially in geometry. He thinks numbers are the most basic elements in mathematics, and divides them into odd numbers and even numbers. Pythagoras put forward the theory of irrational numbers and the concepts of point, line, surface and space in geometry. He thinks that it can be expanded into six equilateral triangles, four right triangles and three regular hexagons with a point as the center on the plane, which is the conclusion he has drawn on the basis of careful observation of the surrounding things and independent research.

Pythagoras' most outstanding achievement in mathematics is that he discovered Pythagoras' theorem. Pythagoras found that there seems to be a special relationship between the three sides of a right triangle on a tile. So, it first writes an A on one right-angled side, a B on the other right-angled side and a C on the hypotenuse, and uses A, B and C to represent the lengths of the three sides of the triangle respectively. Two adjacent black triangles form a square with an area of a = a, and the other two adjacent black triangles form a square with an area of b = b. Four adjacent black-and-white triangles are combined into a larger square with an area of c = c, and its area is equal to the sum of the areas of two small squares. From this, he obtained the relationship between the three sides of a right triangle: the square of a+the square of b = the square of c.