This page contains links to articles from the Princeton Companion to Mathematics. While some of these articles are available on the book’s website, most of the rest are from the respective authors’ webpages. These may be pre-prints or drafts, and may thus differ in content and formatting from the print version.

Many of these links are also drawn from Terence Tao’s series of posts on the Companion. Timothy Gowers, the chief editor of this book, also writes about it on his blog.

I hope I’m not infringing any copyrights. After all, these links are readily available on the authors’ webpages. But if this does infringe some law somewhere, let me know and I’ll take down the offending links.



Part I Introduction
I.2 The Language and Grammar of Mathematics  (Timothy Gowers)

Part II The Origins of Modern Mathematics
II.2 Geometry  (Jeremy Gray)
II.6 The Development of the Idea of Proof (Leo Corry)
II.7 The Crisis in the Foundations of Mathematics (José Ferreirós)

Part III Mathematical Concepts
III.9 Compactness and Compactification (Terence Tao)
III.14 Designs (Peter Cameron)
III.16 Differential Forms and Integration (Terence Tao)
III.18 Distributions (Terence Tao)
III.27 The Fourier Transform (Terence Tao)
III.29 Function Spaces (Terence Tao)
III.35 Hamiltonians (Terence Tao)
III.60 Moduli Spaces (David Ben-Zvi)
III.78 Ricci Flow (Terence Tao)
III.83 The Schrödinger Equation (Terence Tao)

Part IV Branches of Mathematics
IV.1 Algebraic Numbers (Barry Mazur)
IV.2 Analytic Number Theory (Andrew Granville)
IV.3 Computational Number Theory (Carl Pomerance)
IV.4 Algebraic Geometry (Frank Sottile)
IV.5 Arithmetic Geometry  (Jordan Ellenberg)
IV.6 Algebraic Topology (Burt Totaro)
IV.12 Partial Differential Equations (Sergiu Klainerman)
IV.18 Enumerative and Algebraic Combinatorics (Doron Zeilberger)
IV.19 Extremal and Probabilistic Combinatorics (Michael Krivelevich, .ps file)
IV.20 Computational Complexity (Oded Goldreich & Avi Wigderson, .ps file)
IV.21 Numerical Analysis (Llyod Trefethen)
IV.25 Probabilistic Models of Critical Phenomena (Gordon Slade,  and a clarification here)

Part V Theorems and Problems
V.10 Fermat’s Last Theorem (Timothy Gowers)
V.15 Gödel’s Theorem (Peter Cameron)
V.23 Mostow’s Strong Rigidity Theorem (David Fisher)
V.28 From Quadratic Reciprocity to Class Field Theory (Kiran S. Kedlaya)
V.35 The Weil Conjectures (Brian Osserman)

Part VI Mathematicians
VI.61 Jules Henri Poincaré (1854-1912)  (June Barrow-Green)

Part VII The Influence of Mathematics
VII.2 Mathematical Biology (Michael Reed)
VII.4 The Mathematics of Traffic in Networks (Frank Kelly)
VII.5 The Mathematics of Algorithm Design (Jon Kleinberg)
VII.6 Reliable Transmission of Information (Madhu Sudan)
VII.8 Mathematics and Economic Reasoning (Partha Dasgupta)

Part VIII Final Perspectives
VIII.2 “Why Mathematics?” You Might Ask (Michael Harris)
VIII.5 Mathematics: An Experimental Science (Herbert Wilf)
VIII.6 Advice to a Young Mathematician  (Michael Atiyah, Béla Bollobás, Alain Connes, Dusa McDuff, Peter Sarnak)

Two more articles by Terence Tao that seem to have been excluded from the final book:
Phase Space
Generalized Solutions

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