100 books like The Joy of Abstraction

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!

Zalamea’s book is the perfect introduction and survey if you want to understand how developments in contemporary mathematics are relevant to current philosophy.

Zalamea’s own approach follows closely in the steps of Peirce, Lautman, and Grothendieck, merging pragmatism, dialectics, and sheaf theory, but he also engages the work of dozens of other key mathematicians and philosophers coming from different points of view, sometimes cursorily, always tantalizingly.

No philosopher can read this book without a quickened heartbeat and eager plans to clear shelf space for some of the many volumes of mathematics and philosophy of mathematics canvassed here by Zalamea.

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.

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.

I love all of Eugenia’s books, she is a cool mathematician working to educate the public about real mathematics – a subject of deep explorations and connected ideas.

Eugenia shares the creativity in mathematics, and the importance of pushing against boundaries, including the gender boundaries that often stop girls and women going forward in STEM. Her playful use of mathematical ideas to disrupt the myths of narrow and inequitable mathematics and the dominance of men in the field, is so fascinating, especially for those of us perturbed by the inequities in STEM.

This is a great book for those who would like to love mathematics a little more than they do now.

Great Circles is a unique tale of the life and works of mathematicians, scientists, philosophers, poets, and other literary figures. It is collections of circles of thoughts and implications that return on themselves as if they are gravitationally attached to some core red dwarf of universal meaning.  

I loved reading this book. One moment I was into the math, and in the next, I was immersed in a relevant poem or was personality attached to some math or a philosophical thought about a connection of a poem with the math. It was a ride more than a read. It is a calming cognitive exercise on tour through and between chapters – mind wandering not permitted-- with a smooth comfort of thought as if Grosholz is in the room (or perhaps in your brain) reading and guiding.  

The poetry is gripping and wonderfully placed between the appropriate background materials. 

The author explains the importance of abstraction in logic, demonstrating its three main components: paths made of long chains of logic, packages made of a collection of concepts structured into a new compound unit, and pivots to build bridges to previously disconnected places.

Eugenia Cheng does an excellent job of abstracting principles of logic to better understand challenging real-world societal issues such as affirmative action and cancer screening. I found it quite compelling to understand how and why she came to her positions on various issues, through her axiom that "avoiding false negatives is more important than avoiding false positives." I appreciated the expertise by which she weaved numerous hard topics, in both mathematics and social justice, into a coherent and compelling narrative.

This book has haunted me for years. For what is it, exactly, that gives it such enduring popularity? After all, it was first published in 1936, yet is still in print today. In his autobiography, Hogben remarks on the importance of eye-catching illustrations but speculates that its success may instead be because the book contains – most unusually for a 'popular' work – exercises and answers, making it more suitable for self-teaching. Whatever the real answer, his book must surely have something to teach anyone – like myself – who aspires to bring mainstream mathematics to life for the general public.

Polya was a great mathematician who knew what counted (after all, he made major contributions to combinatorics, the mathematics of counting). He thought hard about what he was doing when working on problems in mathematics, developing a mental process that lead to creative breakthroughs and solutions. Polya’s problem-solving method is broadly applicable to domains other than mathematics, and this book features many nice puzzles to improve your thinking.

Algorithm design is challenging because it often requires flashes of sudden insight which seem to come out of the blue. But there is a way of thinking about problems that make such flashes more likely to happen. I try to teach this thought process in my books, but Polya got there first.

I love this book because it illustrates how a deep understanding of one subject area (mathematics) can help develop a deeper understanding of another (biology). This is a common theme in my teaching. I love how the author links the two fields of mathematics and biology in a way that is accessible to people in both fields.

This book will extend the knowledge of anyone working in the interdisciplinary area of mathematical biology and encourage the reader to see the value of viewing the world through interdisciplinary eyes.