Euclid (Euclid, top 300- top 275? ) Ancient Greek mathematician.

The printed volume of this book is second only to the Bible, and it is the first systematic work in the history of mathematics, and also the first western-language masterpiece translated into Chinese. Originally known as Euclid Geometry, it was changed to Geometry Elements when translated by Xu Guangqi in Ming Dynasty. In volume 13 of this book, starting from five postulates and five axioms, a geometric deduction system is constructed. This method, which is loyal to the physical world and only uses a set of axioms to prove theorems, is a great progress of human thought. This book has been circulated since the time of writing, and it has had a lasting and significant impact on human activities. Before the appearance of non-Euclidean geometry in19th century, it was always the main source of geometric reasoning, theorems and methods.

2. Arithmetic research (1798)

Gauss (C.F.Gauss, 1774- 1855), a German mathematician.

The title of "king of mathematics" can be said to be an extremely appropriate tribute to Gauss. He ranks with Archimedes and Newton as the greatest mathematicians in history. His famous saying "Mathematics, the Queen of Science; Arithmetic, the queen of mathematics ",appropriately expressed his views on the key role of mathematics in science. He published this book at the age of 24, which is one of the most outstanding achievements in the history of mathematics, and systematically and extensively expounded the influential concepts and methods in number theory. This overthrew the theory and method of world mathematics in 18, and opened up a rigorous analysis road in the middle of 19 century with innovative number theory. Gauss's argument is extremely cautious and has three principles: "Less; But to be mature "; Don't do anything more.

3. Geometric function (1854).

B.Riemann (1826- 1866) is a german mathematician.

Riemann is one of the most creative mathematicians in19th century. Although he didn't live to be 40 years old and wrote few books, almost every article opened up a new field. This article is Riemann's inaugural speech when he was a university lecturer at the University of G? ttingen. It is one of the most famous speeches in the history of mathematics, and its title is Hypothesis on the Basis of Geometry. Riemann independently put forward non-Euclidean geometry in his speech, namely "Riemann geometry", also known as elliptic geometry. His unique and brave thoughts on space geometry have had a far-reaching impact on modern theoretical physics and become the geometric basis of Einstein's theory of relativity.

4. Basis of general theory of polymerization (1883).

Cantor (G.Cantor, 1845- 19 18) is a German mathematician.

Set theory founded by Cantor is one of the greatest achievements of19th century. This book is Cantor's monograph on set theory. He greatly promoted the development of analysis and logic by establishing the basic skills of dealing with infinity in mathematics, and derived a new thinking mode about the nature of numbers by virtue of the ideas about infinity in ancient and medieval philosophical works.

5. Geometric function (1899).

D.Hilbert (1862- 1943) is a German mathematician.

Hilbert is a giant in the whole generation of international mathematics. /kloc-The vigorous mathematical tradition initiated by Gauss, Dirichlet and Riemann in the 0/9th century was more prominent and famous in the first 30 years of the 20th century mainly because of Hilbert. In this book, Hilbert uses geometric examples to illustrate the processing method of axiomatic system set theory, which marks the turning point of axiomatic processing of geometry. Hilbert's famous saying "I must know, and I will know" sums up his passion to devote himself to mathematics and make it develop to a new level with his lifelong career.

6. General measure theory and probability theory (1929).

Andrei Andrey Kolmogorov (A.N.Kolmogorov, 1903- 1993) is a Soviet mathematician.

Andrei Andrey Kolmogorov is the most influential Soviet mathematician in the 20th century. He contributed creative general theories to many branches of mathematics. This paper is a famous work on probability, which was accepted as a complete axiom of probability theory in the following 50 years. 1937 published the book "Analysis Methods of Probability Theory", which expounded the principle of stochastic process theory without aftereffect, marking a new period of the development of introductory theory.

7. Formulated undecidable propositions about mathematical principles and related systems (193 1).

K godel (1906- 1978) is an Austrian-born American mathematician.

In this paper, Godel gives the famous Godel proof, the content of which is: In any strict mathematical system, there must be a proposition, and the axioms in this system cannot prove its establishment or non-establishment. Therefore, it cannot be said that the basic axioms of arithmetic will not be contradictory. This proof became the symbol of mathematics in the 20th century, and it is still influential and controversial. It ended nearly a century of mathematicians' efforts to establish axioms that can provide a strict foundation for all mathematics.

8. Element Mathematics I-XXXIX, 1939-)

The book is signed by Boolean Biacchi, who is not a person, but a group of mathematicians who have great influence on modern mathematics. In the 1930s, it was composed of a group of young mathematicians in France. They organized the mathematical knowledge accumulated by human beings for a long time into an orderly and profound system according to the mathematical structure. Nearly 40 volumes of Principles of Mathematics have become classic works, the starting point and reference guide of many research work, and the mainstream of the booming mathematical science. No one knows when this masterpiece will be finished. But this system, together with other contributions of Bourbaki School to mathematics, is unique in the history of mathematics.