Books like Mathematical Writing — picked by fans

I think about this book every day, even though it was written almost 25 years ago, and the edition I read explained how to manage your paper file folders! (One of my most-used apps, the to-do manager Things, is built on this system.)

I love how much time this book has saved me as I juggle running several businesses, staying active in my hobbies, and running a household. Allen’s approach to capturing your ideas and then deciding how to organize them so that you can keep track of what needs your attention is both simple and really profound.

For athletes who need to be as efficient as possible to reserve time and energy for training, this book is a lifesaver.

This book provides a systematic account of how to understand and structure mathematical proofs. Its approach is almost entirely syntactic, which is the opposite of how I naturally think – I tend to generate arguments based on examples, diagrams, and conceptual understanding. But that difference, for me, is precisely what makes this book so valuable. Solow gives a no-nonsense, practical, almost algorithmic approach to interpreting logical language and to tackling the associated reasoning. His book thereby provides the best answer I know of to the “How do I start?” problem so often encountered when students begin constructing proofs.  

Many undergraduate mathematics books – even those aimed at new students – are dense, technical, and difficult to read at any sort of speed. This is a natural feature of books in a deductive science, but it can be very discouraging, even for dedicated students. Houston’s book covers many ideas useful at the transition to proof-based mathematics, and he has worked extensively and attentively with students at that stage. Consequently, his book maintains high mathematical integrity and has lots of useful exercises while also being an unusually friendly read.

Research in cognitive psychology has revealed a lot about human learning and how to make it more effective. Most mathematics students – and indeed their professors – know very little about this research or how to apply it. Weinstein and Sumeracki’s book explains how psychologists generate evidence on learning, gives a basic account of human cognitive processing, explains some strategies for effective learning, and gives tips for applying them. It is not about mathematics and it certainly will not make advanced mathematics simple, but I think that we would all have an easier time if we were more aware of some common misunderstandings about learning and effective ways to improve 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.

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 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.

This is a fascinating analysis of the works of Copernicus, Kepler, Galileo, Descartes, Hobbes, Gilbert, Boyle, and Newton. It not only establishes the reasons for the triumph of the modern perspective but also accounts for certain limitations in this view that continue to characterize contemporary scientific thought.

A criticism as well as a history of the change that made possible the rise of modern science, this volume is also a guide to understanding the methods and accomplishments of the great philosopher-scientists of the sixteenth and seventeenth centuries.

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.