100 books like Synthetic Philosophy of Contemporary Mathematics

By Fernando Zalamea, Zachery Luke Fraser (translator),

Here are 100 books that Synthetic Philosophy of Contemporary Mathematics fans have personally recommended if you like Synthetic Philosophy of Contemporary Mathematics. Shepherd is a community of 10,000+ authors and super readers sharing their favorite books with the world.

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Book cover of Quantum Computing Since Democritus

Ran Spiegler Author Of The Curious Culture of Economic Theory

From my list on scholarly and popular-science books that both pros and amateurs can enjoy.

Why am I passionate about this?

I am an academic researcher and an avid non-fiction reader. There are many popular books on science or music, but it’s much harder to find texts that manage to occupy the space between popular and professional writing. I’ve always been looking for this kind of book, whether on physics, music, AI, or math – even when I knew that as a non-pro, I wouldn’t be able to understand everything. In my new book I’ve been trying to accomplish something similar: A book that can intrigue readers who are not professional economic theorists, that they will find interesting even if they can’t follow everything.

Ran's book list on scholarly and popular-science books that both pros and amateurs can enjoy

Ran Spiegler Why did Ran love this book?

A simple (not perfect) test of whether you’re going to love this book: Just check out the author’s blog, called “shtetl-optimized”. The style is similar: sharp, funny, mixing professional theoretical Computer Science with broader takes.

I am still in the middle of the book, and nevertheless, I’m happy to recommend it. As an amateur with superficial CS knowledge, I am enjoying this introduction to classical complexity theory and the basic theory of quantum computation.

Aaronson’s distinctive style makes the ride all the more enjoyable. It’s neither a “real” textbook nor a pop-science book. It’s in a weird space somewhere in between, and I love it!

By Scott Aaronson,

Why should I read it?

3 authors picked Quantum Computing Since Democritus as one of their favorite books, and they share why you should read it.

What is this book about?

Written by noted quantum computing theorist Scott Aaronson, this book takes readers on a tour through some of the deepest ideas of maths, computer science and physics. Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible…


Book cover of The Joy of Abstraction: An Exploration of Math, Category Theory, and Life

Rocco Gangle Author Of Diagrammatic Immanence: Category Theory and Philosophy

From my list on mathematics for the philosophically inclined.

Why am I passionate about this?

Philosophy’s core questions have always obsessed me: What is real? What makes life worth living? Can knowledge be made secure? In graduate school at the University of Virginia I was drawn to mathematically formalized approaches to such questions, especially those of C. S. Peirce and Alain Badiou. More recently, alongside colleagues at Endicott College’s Center for Diagrammatic and Computational Philosophy and GCAS College Dublin I have explored applications of diagrammatic logic, category theory, game theory, and homotopy type theory to such problems as abductive inference and artificial intelligence. Philosophers committed to the perennial questions have much to gain today from studying the new methods and results of contemporary mathematics.

Rocco's book list on mathematics for the philosophically inclined

Rocco Gangle Why did Rocco love this book?

From a strictly philosophical perspective, the emergence of category theory as a unifying paradigm rivaling set theory is probably the most important development in mathematics in the last half-century.

But for philosophers without a lot of mathematical background, learning even its rudiments can be daunting. Among many introductory texts (Lawvere and Schanuel, Awodey, Riehl, Spivak), Cheng’s book stands out as perhaps the friendliest and most accessible.

She does not forego rigor, but she isn’t afraid to put aside precise formalism when necessary for intuition and clearer understanding. Her book takes the reader from mathematical beginnings through category theory’s core constructions to glimpses of higher-order categories (one of Cheng’s areas of expertise).

A mathematically novice philosopher who wants to understand the basics of category theory couldn’t do better.

By Eugenia Cheng,

Why should I read it?

1 author picked The Joy of Abstraction as one of their favorite books, and they share why you should read it.

What is this book about?

Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no formal mathematical background needed. The book brings abstract mathematical ideas down to earth using examples of social justice, current events, and everyday life - from privilege to COVID-19 to driving routes. The journey begins with the ideas and workings of abstract mathematics, after which you will gently climb toward more technical material,…


Book cover of Philosophy and Model Theory

Rocco Gangle Author Of Diagrammatic Immanence: Category Theory and Philosophy

From my list on mathematics for the philosophically inclined.

Why am I passionate about this?

Philosophy’s core questions have always obsessed me: What is real? What makes life worth living? Can knowledge be made secure? In graduate school at the University of Virginia I was drawn to mathematically formalized approaches to such questions, especially those of C. S. Peirce and Alain Badiou. More recently, alongside colleagues at Endicott College’s Center for Diagrammatic and Computational Philosophy and GCAS College Dublin I have explored applications of diagrammatic logic, category theory, game theory, and homotopy type theory to such problems as abductive inference and artificial intelligence. Philosophers committed to the perennial questions have much to gain today from studying the new methods and results of contemporary mathematics.

Rocco's book list on mathematics for the philosophically inclined

Rocco Gangle Why did Rocco love this book?

Far too many math books are written in a style so terse and ungenerous that all but the most mathematically gifted readers hardly have a fair chance of understanding.

On the other hand, the discursive style of much philosophy of mathematics gains readability at the expense of formal rigor. Button and Walsh strike the perfect balance in this exceptionally rich introduction to model theory from a distinctively philosophical perspective.

There’s no getting around the fact that the mathematics of model theory is hard going. But this book works through all the relevant proofs in clear and detailed terms (no lazy “we leave this as an exercise for the reader”), and the authors are always careful to motivate each section with well-chosen philosophical concerns right up front.

An Everest, but worth it.

By Tim Button, Sean Walsh,

Why should I read it?

1 author picked Philosophy and Model Theory as one of their favorite books, and they share why you should read it.

What is this book about?

Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics.
But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of…


Book cover of Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy

Rocco Gangle Author Of Diagrammatic Immanence: Category Theory and Philosophy

From my list on mathematics for the philosophically inclined.

Why am I passionate about this?

Philosophy’s core questions have always obsessed me: What is real? What makes life worth living? Can knowledge be made secure? In graduate school at the University of Virginia I was drawn to mathematically formalized approaches to such questions, especially those of C. S. Peirce and Alain Badiou. More recently, alongside colleagues at Endicott College’s Center for Diagrammatic and Computational Philosophy and GCAS College Dublin I have explored applications of diagrammatic logic, category theory, game theory, and homotopy type theory to such problems as abductive inference and artificial intelligence. Philosophers committed to the perennial questions have much to gain today from studying the new methods and results of contemporary mathematics.

Rocco's book list on mathematics for the philosophically inclined

Rocco Gangle Why did Rocco love this book?

The Univalent Foundations program in foundations of mathematics launched by Voevodsky and others in the past decade and a half has contributed to a promising new paradigm unifying computation, mathematics, logic, and proof theory.

Understanding the core elements of this research program, Homotopy Type Theory, is essential for contemporary philosophers who want to engage directly with current developments in mathematics and computer science.

Corfield is a well-established name in philosophy of mathematics, and this book is the best introduction to Homotopy Type Theory for philosophers.

Working within themes and problematics that will be familiar to philosophers with a basic background in logic, Corfield covers the elementary constructions of homotopy types from a logical point of view and provides plenty of provocative suggestions for how these formal tools might reinvigorate philosophical research today.

By David Corfield,

Why should I read it?

1 author picked Modal Homotopy Type Theory as one of their favorite books, and they share why you should read it.

What is this book about?

"The old logic put thought in fetters, while the new logic gives it wings."

For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory.

Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New…


Book cover of Proofs and Refutations

William Byers Author Of How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics

From my list on thinking, creativity, and mathematics.

Why am I passionate about this?

I'm a mathematician but an unusual one because I am interested in how mathematics is created and how it is learned. From an early age, I loved mathematics because of the beauty of its concepts and the precision of its organization and reasoning. When I started to do research I realized that things were not so simple. To create something new you had to suspend or go beyond your rational mind for a while. I realized that the learning and creating of math have non-logical features. This was my eureka moment. It turned the conventional wisdom (about what math is and how it is done) on its head.

William's book list on thinking, creativity, and mathematics

William Byers Why did William love this book?

Lots of people have a priori ideas about what mathematics is all about but Lakatos had the brilliant idea of looking at what actually happened. His book is all about one famous theorem: “for all regular polyhedra, V – E + F =2, where V is the number of vertices, E is the number of edges, and F is the number of faces.  Think of a cube where V=8, E = 12, F = 6.  

We tend to think that mathematics proceeds from a well-defined hypothesis to conclusion. But that is only the finishing step. Along the way the definitions keep changing as do the hypotheses and even the conclusion. Everything is moving! This is what makes doing mathematics so exciting!

By Imre Lakatos,

Why should I read it?

1 author picked Proofs and Refutations as one of their favorite books, and they share why you should read it.

What is this book about?

Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a…


Book cover of The Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science

Elizabeth E. Botchis Author Of Awakening the Holographic Human: Nature's Path to Healing and Higher Consciousness

From my list on healing ourselves and our planet.

Why am I passionate about this?

Lilli Botchis, PhD, is a psycho-spiritual counselor, educator, and vibrational medicine developer with four decades of experience in advanced body/soul wellness and the development of higher consciousness. Her expertise includes botanicals, gems, color, flower essences, bio-energy therapies, and holographic soul readings. Lilli is an alchemist, mystic, and translator of Nature’s language as it speaks to our soul. A brilliant researcher in the field of consciousness, she understands the interconnectedness of Nature and the human being and is known as an extraordinary emissary of the natural world. Lilli has been inducted into the Sovereign Order of St. John of Jerusalem, Knights Hospitaller. Many seek her out for her visionary insights and compassionate wisdom.

Elizabeth's book list on healing ourselves and our planet

Elizabeth E. Botchis Why did Elizabeth love this book?

According to Michael Schneider, "The universe may be a mystery, but it's no secret." This book is a comprehensive yet simple visual guide to understanding the hidden meaning in the mathematical composition of all physical form. It is fun and fascinating to discover the sacred geometry visible throughout nature, in flowers, crystals, plants, shells, and the human body. You don't have to be a mathematician to see the beauty and symmetry of these patterns in every expression of God's creation, once revealed.

By Michael S. Schneider,

Why should I read it?

1 author picked The Beginner's Guide to Constructing the Universe as one of their favorite books, and they share why you should read it.

What is this book about?

Discover how mathematical sequences abound in our natural world in this definitive exploration of the geography of the cosmos

You need not be a philosopher or a botanist, and certainly not a mathematician, to enjoy the bounty of the world around us. But is there some sort of order, a pattern, to the things that we see in the sky, on the ground, at the beach? In A Beginner's Guide to Constructing the Universe, Michael Schneider, an education writer and computer consultant, combines science, philosophy, art, and common sense to reaffirm what the ancients observed: that a consistent language of…


Book cover of Descartes' Dream: The World According to Mathematics (Dover Books on Mathematics)

Ian Stewart Author Of Flatterland: Like Flatland Only More So

From my list on to find out why math isn’t what you think.

Why am I passionate about this?

As a kid I read every popular math book I could lay my hands on. When I became a mathematician I wanted to do more than teaching and research. I wanted to tell everyone what a wonderful and vital subject math is. I started writing popular math books, and soon was up to my neck in radio, TV, news media, magazines... For 12 years I wrote the mathematical Recreations Column for Scientific American. I was only the second mathematician in 170 years to deliver the Royal Institution Christmas Lectures, on TV with a live tiger. The University changed my job description: half research, half ‘outreach’. I had my dream job.

Ian's book list on to find out why math isn’t what you think

Ian Stewart Why did Ian love this book?

Mathematicians are constantly baffled by the public’s lack of awareness, not just of what mathematics does, but what it is. Today’s technological society functions only because of a vast range of mathematical concepts, techniques, and discoveries, which go far beyond elementary arithmetic and algebra. This was one of the first books to tackle these misunderstandings head on. It does so by examining not just the math and what it’s used for, but the social structures, the ‘conditions of civilization’ that have brought us to this curious state: utterly dependent on math, almost universally unaware that we are. 

By Philip J. Davis, Reuben Hersh,

Why should I read it?

1 author picked Descartes' Dream as one of their favorite books, and they share why you should read it.

What is this book about?

"A passionate plea against the use of formal mathematical reasoning as a method for solving mankind's problems. . . . An antidote to the Cartesian view that mathematical and scientific knowledge will suffice to solve the central problems of human existence." — The New York Times
"These cogitations can and should be read by every literate person." — Science Books and Films
"A warning against being seduced or intimidated by mathematics into accepting bad science, bad policies, and bad personal decisions." — Philadelphia Inquirer
Rationalist philosopher and mathematician René Descartes visualized a world unified by mathematics, in which all intellectual…


Book cover of The Lives of Literature: Reading, Teaching, Knowing

Robert F. Barsky Author Of Clamouring for Legal Protection: What the Great Books Teach Us about People Fleeing from Persecution

From my list on to help us harness the ‘classics’ to address crises.

Why am I passionate about this?

I have taught a broad array of humanities and social sciences courses over the years, sometimes employing case studies from the realm of law, most notably stories about undocumented migrants, refugees, or homeless people. I’ve also had occasion to teach in law schools, usually in ways that bridge the gap between the legality of forced displacement, and the lived experiences of those who have done it. I won a Rockefeller Foundation grant to write my newest book, Clamouring for Legal Protection, in which I considered the idea that we can learn a lot about refugees and vulnerable migrants with references to people we know well: Ulysses, Dante, Satan, and even Alice in Wonderland.

Robert's book list on to help us harness the ‘classics’ to address crises

Robert F. Barsky Why did Robert love this book?

Weinstein takes the age-old question – what is literature? – and transforms it into why we (would want to) read literature. For him, literature changes us, allows us to be someone else, and provides us insight into the world we inhabit, and many more worlds we haven’t. He reads a broad array of works, from Sophocles to James Joyce and Toni Morrison, and thinks about such issues as identification, empathy, and sympathy with those we come to ‘know’ through our reading.

By Arnold Weinstein,

Why should I read it?

1 author picked The Lives of Literature as one of their favorite books, and they share why you should read it.

What is this book about?

Mixing passion and humor, a personal work of literary criticism that demonstrates how the greatest books illuminate our lives

Why do we read literature? For Arnold Weinstein, the answer is clear: literature allows us to become someone else. Literature changes us by giving us intimate access to an astonishing variety of other lives, experiences, and places across the ages. Reflecting on a lifetime of reading, teaching, and writing, The Lives of Literature explores, with passion, humor, and whirring intellect, a professor's life, the thrills and traps of teaching, and, most of all, the power of literature to lead us to…


Book cover of The Collapse of Chaos: Discovering Simplicity in a Complex World

Michael Edgeworth McIntyre Author Of Science, Music, and Mathematics: The Deepest Connections

From my list on to get you past selfish-gene theory.

Why am I passionate about this?

I’m a scientist at the University of Cambridge who’s worked on environmental research topics such as jet streams and the Antarctic ozone hole. I’ve also worked on solar physics and musical acoustics. And other branches of science have always interested me. Toward the end of my career, I became fascinated by cutting-edge issues in biological evolution and natural selection. Evolution is far richer and more complex than you’d think from its popular description in terms of ‘selfish genes’. The complexities are central to understanding deep connections between the sciences, the arts, and human nature in general, and the profound differences between human intelligence and artificial intelligence.

Michael's book list on to get you past selfish-gene theory

Michael Edgeworth McIntyre Why did Michael love this book?

It achieves an important and unusual cross-fertilization between two very different kinds of expertise. Both authors are highly innovative, and creative, thinkers, Cohen in biology and Stewart in mathematics.

Cohen is a biologist fascinated by the complexity observed in the living world, and Stewart is an expert on the mathematics of chaos and complexity. The result is a profound and multifaceted view of many natural phenomena, and of evolution in particular. It becomes very clear how selfish-gene theory fails to take account of important evolutionary mechanisms.

By Jack Cohen, Ian Stewart,

Why should I read it?

1 author picked The Collapse of Chaos as one of their favorite books, and they share why you should read it.

What is this book about?

Moving on from his books on chaos ("Does God Play Dice?") and symmetry ("Fearful Symmetry"), the author of this book deals with the wider field of complexity theory. The book tackles the question of how complexity arises in nature, of how life overcomes chaos and entropy to create developing order. Co-written with biologist Jack Cohen, the book will range across the central areas of modern science, from quantum mechanics and cosmology to evolution and intelligence, looking at the central questions of order, chaos, reductionism and complexity.


Book cover of Cosmos

Ursula Goodenough Author Of The Sacred Depths of Nature: How Life Has Emerged and Evolved

From my list on an ecospiritual orientation.

Why am I passionate about this?

I’m working with others to develop what we call a religious naturalist orientation or an ecospiritual orientation, and these books have deeply guided my path and inspired the writing of my own book. 

Ursula's book list on an ecospiritual orientation

Ursula Goodenough Why did Ursula love this book?

Astronomer Carl Sagan can be said to have launched the ecospiritual/religious naturalist trajectory with this book, upon which the TV series was based, later writing: A religion that stressed the magnificence of the universe as revealed by modern science, might be able to draw forth reserves of reverence and awe hardly tapped by the conventional faiths. Sooner or later such a religion will emerge.”

Two seminal quotes: “The nitrogen in our DNA, the calcium in our teeth, the iron in our blood, the carbon in our apple pies were made in the interiors of collapsing stars. We are made of starstuff.” “We are a way for the cosmos to know itself.”

By Carl Sagan,

Why should I read it?

7 authors picked Cosmos as one of their favorite books, and they share why you should read it.

What is this book about?

* Spacecraft missions to nearby planets
* The Library of ancient Alexandria
* The human brain
* Egyptian hieroglyphics
* The origin of life
* The death of the sun
* The evolution of galaxies
* The origins of matter, suns and worlds

The story of fifteen billion years of cosmic evolution transforming matter and life into consciousness, of how science and civilisation grew up together, and of the forces and individuals who helped shape modern science. A story told with Carl Sagan's remarkable ability to make scientific ideas both comprehensible and exciting.


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