Euclid
Publication period: about 300 BC
Online version: interactive Java version
Summary: This is probably not only the most important work in geometry, but also the most important work in mathematics. It contains many important results of geometry and number theory and the first algorithm. It is still a valuable resource and a good guide to algorithms. More important than any particular result in this book, it seems that the greatest achievement of this book is to popularize logic and mathematical proof as a method to solve problems.
Importance: The creation, breakthrough, impact and summary of the project are the most modern and excellent (although it is the first, some achievements are still the most modern).
[Edit] Geometry
Descartes
Description: The Elements of Geometry was published by Descartes on 1637. This book has a great influence on the development of rectangular coordinate system, especially on the point on the plane represented by real numbers; In addition, there is a discussion about expressing curves through equations.
Importance: Project Pioneer, Breakthrough and Impact
Conceptual text (Begriffsschrift)
Gottlob Frege (Gottlob Frege)
Introduction: Published in 1879, the title Begriffsschrift is usually translated into conceptual writing or conceptual symbols; The full title of the overview equates it with "pure thinking formula language, modeling in arithmetic language". Frege's motivation for developing his formal logic system is similar to Leibniz's desire to find a calculator. Frege defined a logical calculation method on the basis of mathematics to support his research. Begriffsschrift is both the title of the book and the name of the calculation method defined in the book.
Importance: It can be said to be the most important logical work since Aristotle.
[Edit] Mathematical formula
Giuseppe Peano.
Introduction: Formulario mathematico, first published in 1895, is the first complete mathematics book written in a formal language. It contains expressions of mathematical logic and many important theorems of other branches of mathematics. Many concepts introduced in this book have become everyday concepts today.
Importance: influence
[Editor] Mathematical Principles (Mathematical Principles)
Bertrand Russell and alfred north whitehead.
Introduction: Principles of Mathematics is a trilogy based on mathematics, published by Russell and Whitehead at1910-1913. It is an attempt to deduce all mathematical truths by using well-defined axioms and reasoning rules in symbolic logic. Whether the axiomatic principle set can lead to contradictions and whether there are mathematical propositions that cannot be proved or falsified in this system still exist. These problems were solved by Godel's incomplete theorem in 193 1 in a somewhat disappointing way.
Importance: influence
[Editor] Godel's Incomplete Theorem
(? What about the formal invitation? Mathematical Principles and Mathematical Systems, Journal of Mathematics and Physics, Volume 38 (193 1). )
Godel
Online version: online version
Brief introduction: In mathematical logic, Godel's incomplete theorem (G? Del's incompleteness theorem is two famous theorems proved by Godel in 1930. The first incomplete theorem shows that:
For any formal system (1) that meets the following conditions, it is ω-consistent (ω-consistent), (2) it has a recursively definable axiom set and derivation rules, (3) the recursive relation of each natural number can be defined on it, and there is a formula of the system. According to the explanation of the system assumption, it expresses a fact about natural numbers, but it is not a theorem of the system.
Importance: breakthrough, influence
Arithmetic research (research and study of integer translation theory)
C.F.Gauss.
Introduction: Arithmetic Research is a textbook of number theory written by German mathematician C.F.Gauss. It was first published in 180 1 year. Gauss was 24 years old. In this book, Gauss accepted the number theory achievements of mathematicians such as Fermat, Euler, Lagrange and Legendre, and added his own important new achievements.
Importance: breakthrough, influence.
On prime numbers less than a given number.
Bernhard Riemann
Introduction: About prime numbers less than a given value (? How long is the term of office of the first prime minister? Sse) is a groundbreaking paper by Riemann, published in the monthly report of Berlin Academy of Sciences 1859 1 1. Although this is his only published paper on number theory, it contains the thoughts of dozens of researchers who have influenced 19 century until today. This paper mainly includes the definition, heuristic demonstration, proof outline and the application of powerful analysis methods; These have become the basic concepts and tools of modern analytic number theory.
Importance: breakthrough, influence
[Editor] Lecture Notes on Number Theory
Johann peter gustav lejeune dirichlet and Dai Dejin.
Introduction: Lecture Notes on Number Theory is a textbook on number theory compiled by German mathematicians Dirichlet and Dai Dejin, and published in 1863. The handout can be regarded as a watershed between the classical number theory of Fermat, Jacobi and Gauss and the modern number theory of Dai Dejin and riemann sum Hilbert. Dirichlet did not clearly define the central concept group of modern algebra, but many of his proofs showed that he had an implicit understanding of group theory.
Importance: breakthrough, influence
[Editor] Number theory, the historical method from Hammurabi to Legendre (number theory, the historical method from Hammurabi to legend).
Andre Weil
Introduction: The author is one of the greatest researchers in the field of number theory in the 20th century. This book involves 36 centuries of arithmetic works, but most of them are mainly used to carefully study and explain the work of Fermat, Euler, Lagrange and Legendre. The author hopes to bring readers to the workplace of the characters he describes and share their successes and failures. This is a rare opportunity to observe the historical development of a theme through the thoughts of one of the greatest practitioners.
Importance:
[Editor] Introduction to Number Theory
Godfrey Harold Hardy
Introduction: classic number theory textbook
Evolution and game theory.
John maynard smith
[Editor] Game theory and economic behavior.
(Game Theory and Economic Behavior, 3rd Edition, Princeton University Press 1953)
Morgan Stein (oskar morgenstern), Von Neumann (john von neumann).
Introduction: This book leads to the study of modern game theory as an important branch of mathematics. The author's work includes the method of finding the optimal solution of two-person zero-sum game.
Importance: influence, project creation, breakthrough
[Editor] About Numbers and Games
John conway
Introduction: This book is divided into two parts, {0, 1|}. The zero part is about numbers, and the first part is about games-including the value of games and some really playable games, such as Nim, Hackenbush, Col and Snort.
Importance:
[Editor] The way to win the math game.
Elwyn Berlekamp, john conway and Richard Guy.
Introduction: Information summary of mathematical games. First published in 1982, it is divided into two parts. One part focuses on combinatorial games and hyperreal numbers, and the other part focuses on some specific games.