At that time, Pythagoras School was an important mathematical school in ancient Greece. They think that all numbers can be represented by integers or ratios of integers. However, one of their students, hippasus, found that the hypotenuse of an isosceles right triangle could not be represented by an integer. This discovery is called "the first mathematical crisis" because it subverts an important theory of Pythagoras school.
Hippasus found that if the length of the two right sides of a right triangle is 1, then the length of the hypotenuse is √2. But √2 is not an integer or the ratio of two integers, and the Pythagorean school cannot accept this result. They tried to deny the discovery and even threw hippasus into the sea and drowned.
However, the development of mathematics is inevitable. Later, people accepted the fact that √2 is an irrational number and began to study more irrational numbers. The solution of this crisis finally led to the introduction of the concept of real numbers in mathematics, including rational numbers and irrational numbers.
The first mathematical crisis had a far-reaching impact on mathematics. It promotes the development of mathematics and makes people start to study new mathematical theories and methods. At the same time, it also promoted the development of philosophy and made philosophers begin to think about the essence and significance of mathematics. In addition, it also has an impact on the development of science and technology, allowing scientists to explore the nature and laws of natural phenomena.
The influence of the first mathematical crisis on the field of mathematics;
1. This crisis has promoted the development of mathematics. Before the crisis, mathematicians mainly studied some basic problems in arithmetic and geometry. The first mathematical crisis prompted them to start studying new mathematical theories and methods, such as algebra and calculus, which became the basis of modern mathematics.
2. The first mathematical crisis also promoted the development of philosophy. Before the crisis, philosophers mainly paid attention to natural philosophy and metaphysics. The first mathematical crisis prompted them to think about the essence and significance of mathematics and explore the relationship between mathematics and the real world. This has led to the emergence of some important ideas in the field of philosophy, such as Plato's idealism and Aristotle's positivism.
3. The first mathematical crisis also affected the development of science and technology. Before the crisis, the development of science and technology was relatively slow. The first mathematical crisis prompted scientists to explore the nature and laws of natural phenomena and put forward some important scientific theories, such as the law of universal gravitation and electromagnetic wave theory.