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 is a sequel to Alex Bellos's bestseller Alex's Adventures in Numberland, but more focused on applications of mathematics to the real world, especially through physics. Many of these were known to me, particularly when they involved calculus, but I greatly enjoyed Alex's distinctive and novel way of putting across sophisticated ideas, in part by interspersing them with personal interviews with mathematicians of all kinds.  

This may seem an odd choice, but as a maths popularizer I need to know all that I can about why some people find the main elements of the subject so difficult. I found Doug French's book exceptionally helpful in this respect, even though it is aimed principally at high school teachers. This is partly because he focuses throughout on the most important mathematical ideas and difficulties. Moreover, the scope is wider than the title suggests, for he also ventures imaginatively into both geometry and calculus.

In my opinion, Prof. Axler's book is the best way to learn the formal proofs of linear algebra theorems.

My undergraduate studies were in engineering, so I never learned the proofs. This is why I chose this book to solidify my understanding of the material; it didn't disappoint! Already, in the first few chapters, I learned new things about concepts that I thought I understood.

The book contains numerous exercises which were essential for the learning process. I went through the exercises with a group of friends, which helped me stay motivated. It wasn't easy, but all the time I invested in the proofs was rewarded by a solid understanding of the material.

I highly recommend this book as a second book on linear algebra.