## Brief introduction

"History of Mathematics" was first published in 1968, and a revised edition was issued in 1991. Although both are old, they are not outdated as historical materials of mathematics. This is just like the characteristic of mathematics: only in mathematics, there is no major correction-only expansion. For example, once the Greeks developed the deductive method, they were right and always right in terms of what they did. Euclid is not complete, his work has been greatly expanded, but no correction is needed. His theorem, all theorems, are valid today.

This book condenses the development of mathematics for thousands of years into this chronicle. From the Greeks to Gödel, mathematics has always been brilliant, celebrities have appeared in large numbers, and the rise and fall of ideas are clearly visible everywhere. Moreover, although tracking the development of European mathematics, the author did not ignore the contributions of Chinese, Indian, and Arab civilizations. There is no doubt that this book is (and will always be) a classic one-volume historical work on mathematics and the mathematicians who created this subject. Both academic and readable, this book can serve as a good introduction to this topic, and it is also a good reference book.

## About the author

Boyer (Carl B. Boyer, 1906~1976), an outstanding historian of mathematics, and a member of the International Academy of the History of Science. He received his Ph.D. degree from Columbia University in 1939, and served as a professor of mathematics at Brooklyn College in 1952, and served as the vice chairman of the American Society for the History of Science from 1957 to 1958. He mainly studies the history of mathematics and science, and his main works include "History of the Conceptual Development of Calculus", "History of Analytical Geometry" and "Rainbow: From Myth to Mathematics".

[Introduction to the revisionist]

Uta C. Merzbach (1933～ ), Ph.D. in History of Mathematics and Science, Harvard University, Honorary Curator of Mathematics Library of Smithsonian Institution He has authored books such as "A Hundred Years of American Mathematics" and "The Biography of Gauss".

## Recommended by famous experts

Boyer and Metzbach condensed the development of mathematics for thousands of years into this fascinating chronicle. From the Greeks to Gödel, mathematics has always been brilliant, celebrities have appeared in large numbers, and the rise and fall of ideas are clearly visible everywhere. Moreover, although tracking the development of European mathematics, the author did not ignore the contributions of Chinese, Indian, and Arab civilizations. There is no doubt that this book is (and will always be) a classic one-volume historical work on mathematics and the mathematicians who created this subject.

——William Dunham

*Journey Through Genius, The Great Theorems of Mathematirs*

When we read a book like "History of Mathematics", what we get is a picture of the frame structure, which is constantly higher, wider, and more beautiful. It is more magnificent and has a foundation. Besides, the structure today is as immaculate and effective as when Thales came up with the earliest geometric theorem nearly 2,600 years ago.

——Isaac Asimov

Excerpt from the preface of this book

This book is one of the most useful and comprehensive in the subject of mathematics One of the introductions.

——Joseph W. Dauben (Joseph W. Dauben)

City University of New York

It is both academic and readable. This book can serve as a good introduction to this topic. Theory, it is also a good reference book at the same time.

——J. J. David Bolter

University of North Carolina

Author of "Turing's Man" (*Turing's Man*)< /p>

## Chinese Table of Contents

Foreword 1

Revision Preface 1

First Edition Preface 1

Chapter 1 Origin< /p>

The concept of number/early cardinal numbers/the origin of number language and calculation/the origin of geometry/

Chapter 2 Egypt

Early records/hieroglyphics Symbols/Ames papyrus/single fraction/

Arithmetic operations/algebra problems/geometric problems/triangle ratio/Moscow papyrus/deficiencies of Egyptian mathematics/

Chapter 3 Messo Untamia

Cuneiform records/positional notation/fractions based on sixty/basic operations/algebra problems/quadratic equations/cubic equations/Pythagoras ternary arrays/ Area of Polygons/Geometry as Applied Mathematics/Imperfections of Mesopotamian Mathematics/

Chapter 4 Ionian and Pythagorean School

Greece Origins/Thylus of Miletus/Pythagoras of Samos/

Pentagonal star of the Pythagorean school/Numerical mysticism/Arithmetic and cosmology/Graphic numbers/Proportion/ Athens Notation/Ionian Notation/

Arithmetic and Logic/

Chapter 5 The Age of Heroes

Activity Center/Crazo Minai’s Anaxagoras/Three famous problems/

Finding the area of the crescent shape/Lianbi/Hipias in Erlis City/Filolaus and Aceta in Tarentum /Double Cube//Incommensurability/Golden Section/Zeno's Paradox/Deductive Reasoning/Geometric Algebra/Democritus of Abdera/

Chapter 6 Plato and Aristotle German Times

Seven Arts of Liberal Arts/Socrates/Plato Polyhedron/Theodore of Cyrene

The Arithmetic and Geometry of Ross/Plato/The Origin of Analysis/Nidos Eudoxus/Exhaustive Method/Mathematical Astronomy/Menehemos/Cubic Doubling/Dinostratus and Ottolikos/Aristotle/Ancient The end of the Greek period/

Chapter 7 Euclid of Alexandria

Author of "Geometric Elements"/Other works/The purpose of "Geometric Elements"/definition and postulates/ Scope of Volume 1/Geometric Algebra/Volumes 3 and 4/Proportion Theory/Number Theory/Prime and Perfect Numbers/Incommensurability/Solid Geometry/Pseudo-Book/The Influence of "The Original Geometry"/

Chapter 8 The Mathematics of Syracuse

The Siege of Syracuse/The Principle of Leverage/The Principle of Hydrostatics/"The Art of Numbers and Sands"/

Measurement of Circles/Three Divisions Angle/Area of Parabolic Segment/Volume of Parabola/Spherical Section/"On the Sphere and Cylinder"/"The Set of Lemma"/Semi-regular Polyhedra and Trigonometry/"Method"/Volume of the Ball/"Method" Restoration/

Chapter 9 Apollonius

The lost works/recovering the lost works/Apollonios problem/round and

turnover Circle/"Conic Section Theory"/Name of Conic Section/Double Leaf Cone/Basic Attributes/Conjugate Diameter/Tangent and Harmonic Division/Three-line and Four-Line Trajectory/Intersecting Conic Section/Maximum and Minimum, Tangent and Orthogonal Line/ Similar Conic/Conic Focus/Use of Coordinates/

Chapter 10 Trigonometry and Surveying in Greece

Early Trigonometry/Aristak in Samos /Ella of Cyrene

Tosteni/Hiparks of Nicaea/Menelaus of Alexandria/Ptolemy's "The Greatest Theory"/360-degree circle/triangle The construction of the function table / Ptolemy's astronomy / Ptolemy's other works / optics and astrology / Helen of Alexandria / the principle of shortest distance / the decline of Greek mathematics/

Chapter 11 Greek mathematics Revival and Decline

Applied Mathematics/Diophantus of Alexandria/Nicomacus/Diophantine

The "Arithmetic" of Diagrams/Diophantine Problem/Diophantus Position in Algebra/Papps of Alexandria/ "Mathematics Compilation"/Papps' Theorem/Papps Problem/"Analysis Book"/Papps-Goulding's Theorem/Proclos of Alexandria/ Poitiu/The End of the Alexander Period/"Selected Greek Poems"/Byzantine Mathematics in the Sixth Century AD/

Chapter 12 China and India

The oldest document/" The Nine Chapters of Arithmetic/Magic Square/Chips/Abacus

and decimal decimals/π value/Algebra and Horner's method/13th century mathematics/arithmetic triangle/early mathematics in India/The rope method "/"Siddhamta"/Aliyah Vita/Indian Numbers/Symbols Representing Zero/Indian Trigonometry/Indian Multiplication/Long Division/Brahma Gupta/Brahma Gupta Formula/Indefinite Equation/Bashkala /"Li Luowati"/Ramanujan/

Chapter 13 The Hegemony of Arabia

The Conquest of Arabia/Palace of Wisdom/"Algebra"/Quadratic Equation/< /p>

Father of Algebra/Geometrical Fundamentals/Algebraic Problem/A Problem Derived from Helen/Turk/Tabi Ibn-Kura/Arabic Numerals/Arabic Trigonometry/Abel Weifa With Kailaji/Albiruni and Alhazen/Omar Khayyam/Parallel Posts/Nasirdin/Al Kassi/

Chapter 14 Medieval Europe

From Asia to Europe/Byzantine Mathematics/Dark Age/Alcuum and

Gilbert/The Century of Translation/India—The Spread of Arabic Numerals/Book of Abacus/Fibonacci Sequence/Three Times Solution of Equations/Number Theory and Geometry/Jordanus/Novara’s Campanus/Thirteenth Century Academics/Medieval Kinematics/Thomas Bradwardin/Nicole Oresm/Form The Latitude/Infinite Series/The Decline of Medieval Scholarship/

Chapter 15 The Renaissance

Humanism/Nicolas of Cusa/Rege Montanus/Algebra in Geometry

Applications/A Transitional Figure/Nicholas Chukai’s "Arithmetic Three articles / Luca Paccioli's "Summary" / Leonardo Da Vinci / German Algebra / Cardano's "Dayan Shu" / the solution of the cubic equation / Ferrari's quartic equation Solution/Unsimplified cubic equations and complex numbers/Robert Reckold/Nicholas Copernicus/George Joachim Reticus/Petrus Ramis/Bombeli’s Mathematics"/Johannes Werner/Perspective Theory/Cartography/

Chapter 16 The Prelude to Modern Mathematics

François Veda/The Concept of Parameters/Analytical Techniques /Roots and coefficients

The relationship between Thomas Harriot and William Altred/See also Horner's method/Trigonometry and integration and difference/Trigonometric solutions of equations/John· Napier/The Invention of Logarithms/Henry Briggs/Jobster Burki/Applied Mathematics and Decimal Decimals/Algebraic Notation/Galileo/Pi Values/Restoration of Apollonius’ Theory of Tangency "/Infinitesimal Analysis/John Kepler/Galileo's "Two New Sciences"/Galileo and Infinity/Bonaventura Cavalieri/Spiral and Parabola/

Chapter 17 The era of Fermat and Descartes

The most important mathematician of the year/"Methodology"/The invention of analytic geometry/

The arithmetic of geometry/Geometric algebra/Classification of curves/Find Length of the curve/Identification of conic section/Normal and tangent/Cartesian geometric concept/Fermat's trajectory/High-dimensional analytic geometry/Fermat's differential method/Fermat's integral method/Gregory of Saint Vincent/Number theory /Fermat's theorem/Robval/Torízli/New curve/Dezag/

Projective geometry/Pascal/Probability/cycloid/

Chapter 18 Transition Period

Philip de Rahel/George Moore/Petro Mengoli/

François Van Schoten/Jean de Witte/ John Schud/Rene Francois de Sluse/Pendulum Clock/Involutes and Involutes/John Wallis/"Conic Theory"/"Infinite Arithmetic"/Christopher Ray En/Wallis formula/James Gregory/Gregory series/McKaite and Bronkel/Barrow’s tangent method/

Chapter 19 Newton and Leib Nitz

Newton’s early works/Binomial Theorem/Infinite Series/"Flow Number Method"/

"Principles"/Leibniz and Harmonic Triangles/Differential Triangles And infinite series / differential calculus / determinant, symbolic representation and imaginary numbers / logical algebra / inverse square law / conic theorem / optics and curves / polar coordinates and other coordinates / Newton's method and Newton's parallelogram / "Generalized Arithmetic"/ Later years/

Chapter 20 Bernoulli’s Era

Bernoulli’s Family/Logarithmic Spiral/Probability and Infinite Series/Lobida’s Law/

< p> Exponential Calculus/Logarithm of Negative Numbers/St. Petersburg Paradox/Abraham DeMoffer/DeMoffer's Theorem/Roger Coates/James Sterling/Colin McLaughlin/Taylor Series/Analytics Home" Controversy/Clem's Law/Zienhouse Transformation/Solid Analytical Geometry/Michele Rolle and Pierre Valinon/Italian Mathematics/Parallel Postulate/Divergence Level Number/

Chapter 21 Euler’s Era

The life of Euler/Symbol/Foundation of analysis/Infinite series/

Convergent series and divergence Series/D'Alembert's life/Euler's identities/

D'Alembert and the limit/differential equations/Claire brothers/Ricatti and his son/probability theory/number theory/textbook/integrated geometry/solid Analytical Geometry/Lambert and Parallel Postions/Pei Shu and Elimination Method/

Chapter 22 Mathematics during the French Revolution

The era of revolution/The most important mathematician/1789 Previous publications/

Lagrange and Determinants/Committee of Weights and Measures/Conduce on Education/Monge as Administrator and Teacher/Descriptive Geometry and Analytic Geometry/Textbooks/La Croux Analytical Geometry of Tile Theory/Organizer of Victory/Metaphysics of Calculus and Geometry/"Position Geometry"/Intersections/Legendre's "Principles of Geometry"/Elliptic Integral/Number Theory/Function Theory/Variational Method/Lagrange Multiplier/Laplace and Probability Theory/Celestial Mechanics and Operators/Political Change/

Chapter 23 The Age of Gauss and Cauchy

A Summary of the 19th Century/Gauss: Early works/number theory/"Arithmetic Studies"

The treatment received/Gauss’ contribution to astronomy/Gauss’s middle age/The beginning of differential geometry/Gauss’s late work/Paris in the 1820s/Co West/Gauss and Cauchy Comparison/Non-Euclidean Geometry/Abel and Jacobi/Galois/Diffusion/British and Prussian Reform/

Chapter 24 Geometry

Meng Japanese School/Projective Geometry: Poncelet and Schaller/Comprehensive Metric Geometry:

Steiner/Comprehensive Non-Metric Geometry: Staudt/Analytic Geometry/Riemannian Geometry/High-dimensional Space/ Felix Klein/Algebraic Geometry in the Post-Lehman Era/

Chapter 25 Analysis

Berlin and Göttingen in the mid-nineteenth century/Riemann in Colombia Tingen/Geometry in

Mathematical Physics/Mathematical Physics in English-speaking Countries/Weilstrass and his students/Arithmeticization of Analysis/Cantor and Dedekin/ French analysis/

Chapter 26 Algebra

Introduction/English algebra and function calculation calculus/Boolean and logic

Algebra/Germany Morgan/Hamilton/Glassman and "Linear Extension Theory"/Cayley and Sylvester/Linear Associative Algebra/Algebraic Geometry/Algebraic Integers and Arithmetic Integers/Axioms of Arithmetic/

No. 27 Chapter Poincaré and Hilbert

An overview of the turn of the century/Poincaré/Mathematics and Physics His application/topology

/other fields and heritage/Hilbert/Invariant Theory/Hilbert's "Algebraic Number Field Theory"/Basic Geometry/Hilbert Problem/ Hilbert and Analytics/Waring’s Problem and Hilbert’s Work after 1909/

Chapter 28: All Aspects of the Twentieth Century

Overview/Integration and Measurement/ Functional Analysis and General Topology/Algebra/

Differential Geometry and Tensor Analysis/1930s and World War II/Probability Theory/ Homological Algebra and Category Theory/ Boolean Baji/Logic and Computation /Future outlook/

References

Total bibliography

Index of names and place names translated