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Which mathematics books have a great influence on the history of mathematics? What are the names of these books?
1, the element of Euclid

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

The print run of this book is second only to that of the Bible. It is the first systematic work in the history of mathematics, and it is also the first western language masterpiece translated into Chinese. Its original name was Euclidean geometry, which was changed to Geometry Elements when translated by Xu Guangqi in Ming Dynasty. This book has 13 volumes. Starting from five postulates and five axioms, it constructs a geometric deduction system, which is not false to the physical world and only relies on a set of axioms to realize logical reasoning. This is a great progress in 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 is 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. As a result, the mathematical theory and method of 18 world were overthrown, and the strict analysis road of 19 century was opened up with innovative number theory. Gauss's "But Be Mature": "Don't leave anything to do further".

3. Geometrical radiation (1854).

German mathematician B. Riemann (1826- 1866).

Riemann is one of the most creative mathematicians in19th century. Although he didn't live to be 40 years old and didn't have many works, almost every one opened up new fields. This is Riemann's inaugural speech when he was a university lecturer at the University of G? ttingen, and it is one of the most famous speeches in the history of mathematics, entitled "Assumptions on Geometric Basis". In the speech, Riemann independently proposed non-Euclidean geometry, that is, "Riemann geometry".

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. Geometrical radiation (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 became more prominent and famous in the first 30 years of the 20th century. In this book, Hilbert illustrates the processing method of axiomatic system set theory with geometric examples, which marks a turning point in axiomatic processing of geometry. Hilbert famously said, "I must know, and I will know."

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 masterpiece about probability, and in the following 50 years, it is recognized as a complete axiom of probability theory. 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-American mathematician.

Godel gave the famous Godel proof in this paper, 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, if we can't say the basic axiom of arithmetic, there will be no contradiction. This proof became the symbol of mathematics in the 20th century, and it is still influential and controversial. It ends mathematicians' attempts to establish axioms that can provide a strict foundation for all mathematics in the past century.

8. Mathematical element I-XXXIX, 1939-)

The book is signed by Boolean Biacchi. He is not a person, but a group of mathematicians who have great influence on modern mathematics. In 1930s, a group of young French mathematicians arranged the mathematical knowledge accumulated by human beings for a long time according to the mathematical structure, forming a coherent and profound system. Principles of Mathematics has been published in nearly 40 volumes, becoming a classic. It has become the starting point and reference guide of many research work and the mainstream of the booming mathematical science. No one can say when this masterpiece will be completed, but this system, together with other contributions of Bourbaki School to mathematics, is unique in the history of mathematics.