From beginner-friendly introductions to comprehensive textbooks on the philosophy of mathematics, this page features books to suit any learning style. It’s important to note that there is no single best book on the philosophy of mathematics. The best book for you will depend heavily on your preferred learning style and the amount of time/energy you’re willing to spend reading.
It’s also worth noting that it is not a list of personal recommendations. Personal book recommendations tend to be highly subjective, idiosyncratic, and unreliable. This list is part of a collection of over 100 philosophy reading lists which aim to provide a central resource for philosophy book recommendations. These lists were created by searching through hundreds of university course syllabi, internet encyclopedia bibliographies, and community recommendations. Links to the syllabi and other sources used to create this list are at the end of the post. Following these links will help you quickly find a broader range of options if the listed books do not fit what you are looking for.
Here are the best books on the philosophy of mathematics in no particular order.
Mathematics: A Very Short Introduction – Timothy Gowers
Publisher description: The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questions about the mathematical community (such as “Is it true that mathematicians burn out at the age of 25?”) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.
Philosophy of Mathematics – Øystein Linnebo
Publisher description: A sophisticated, original introduction to the philosophy of mathematics from one of its leading contemporary scholars.
Mathematics is one of humanity’s most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is trying to answer that question: the philosophy of mathematics.
Written by Øystein Linnebo, one of the world’s leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms….
The Oxford Handbook of Philosophy of Mathematics and Logic – Stewart Shapiro
Publisher description: Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas.
This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines….
An Historical Introduction to the Philosophy of Mathematics: A Reader – Russell Marcus & Mark McEvoy
Publisher description: A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject.
An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject….
The following sources were used to build this list:
University Course Syllabi:
- Philosophy of Mathematics – PHIL 162 | Stanford University
- Philosophy of Mathematics – PHIL 436 | University of Nevada
You might also be interested in the following reading lists:
- The Best Introductory Philosophy Books
- The Best Books on Formal Logic
- The Best Books on the Philosophy of Language
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- Find the best philosophy books on a wide variety of topics with this collection of over 120 philosophy reading lists.
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A History of Western Philosophy in 500 Essential Quotations – Lennox Johnson
Category: Reference | Length: 145 pages | Published: 2019
Publisher’s Description: A History of Western Philosophy in 500 Essential Quotations is a collection of the greatest thoughts from history’s greatest thinkers. Featuring classic quotations by Aristotle, Epicurus, David Hume, Friedrich Nietzsche, Bertrand Russell, Michel Foucault, and many more, A History of Western Philosophy in 500 Essential Quotations is ideal for anyone looking to quickly understand the fundamental ideas that have shaped the modern world.