When it comes to the discovery of irrational numbers, we have to mention a famous theorem in the history of mathematics, Pythagoras Theorem. The discovery of Pythagoras theorem is a great event in itself. At that time, the Pythagorean school was said to have held a grand celebration.

Realizing the existence of irrational numbers through Pythagoras theorem made people rethink logarithm, and even triggered the first mathematical crisis in the history of mathematics.

Euclid wrote Elements of Geometry.

To say that the most influential, lasting and printed book in the history of mathematics is probably Euclid's Elements of Geometry! On the basis of sorting out and summarizing the previous work, Euclid established geometry on several axioms.

This is the first axiom system in the history of mathematics, and its influence on later generations is self-evident. Until now, Euclidean geometry has been widely used in the teaching of basic mathematics in various countries. In modern times, Lobachevsky, Riemann and others thought about the fifth postulate and established new geometry.

Arabic numerals

Around 870 AD, decimal numbers including zero appeared in India, which were later introduced into Arabia and evolved into today's Indo-Arabic numbers. The use of decimal Arabic numerals has greatly promoted the research and use of mathematics and its worldwide spread.

Establishment of analytic geometry

1637, Descartes published Geometry, which marked the birth of analytic geometry. The birth of analytic geometry linked algebra and geometry, brought the development of mathematics into a new world, and a large number of new mathematical ideas and new disciplines began to appear.

Mathematics has entered the era of variable mathematics from constant mathematics, and function has become an important research object of mathematics. The study of function, such as the tangent of function curve, promotes the generation of analysis. It can be said that the injection of new ideas in analytic geometry has given mathematics unprecedented vitality.

The rigidity of analytical science

The invention of calculus is definitely a milestone in the history of mathematics. The birth of calculus has produced a large number of topics, attracting a large number of outstanding mathematical masters, including Newton, Leibniz, Cauchy, Lagrange, Weisstras and others. After obtaining a lot of rich results, people began to pay attention to the rigor and refinement of analysis.

Especially after the work of Cauchy and Wilstrass, the concepts of function, limit, derivative and differential are given accurately, which makes the analysis rigorous. In a short time after that, many mathematicians even thought that mathematics had no work to do.

In fact, modern analysis has just started, but in any case, extreme thinking is a powerful tool that enables human beings to think about "infinite or infinite" problems! Besides analyzing its own development, it is also widely used in other branches of mathematics.