Math themed books

April 22, 2022 8:50 PM

I would love to find more books (hardcopy) along the lines of Zebrowski's A History of the Circle. It explores way more than I thought and makes a nice desk reference for someone for whom math has always remained a mystery. With more books like this the mystery may open up.

I enjoy anything by Alex Belos, and Willers' The Bedside Book of Algebra is amazingly useful, as well as The Mathematics Lover's Companion (links to an interesting NZ bookshop I didn't know of).

I'm currently trying to get a copy of Foolproof and other Mathematical Meditations, and have started reading Kline's Mathematics For The Nonmathematician.

I'm not interested in New Scientist type compendiums as they lack a theme. Adam Spencer's stuff misses the sweet spot too as does Woo's World of Math, along with Ben Orlin's offerings and much of Matt Parker. I also get turned off if anything is too gamified (but practical puzzles are good), or only uses sport metaphors/analogies.

Themes could include other shapes (and solids), circle/polygon packing, algebra, but also spatial statistics, mathematical ecology - anything spatial. Equations fine as long as basics are explained - Zebrowski does this well.

posted by unearthed to Science & Nature (22 answers total)

I enjoyed Fermat's Last Theorem, aka Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem.
posted by NotLost at 9:17 PM on April 22, 2022 [2 favorites]

I found The Nature and Growth of Modern Mathematics by Edna E. Kramer so interesting when I borrowed it from my library that when I was later able to afford it, I bought a new hardback version.

The book explains mathematical topics but also has fascinating short biographical articles about famous mathematicians. All presented in roughly a chronological order so you can see how newer math was built on older math foundations.
posted by TimHare at 9:41 PM on April 22, 2022 [1 favorite]

I quite enjoyed MeFite escabeche (aka Jordan Ellenberg)'s Shape and How Not to be Wrong. I especially liked the latter book, but you might enjoy the geometry focus of Shape.

The Logician and the Engineer is a sneaky good book that starts with colorful anecdotes about George Boole and and Claude Shannon and ends up walking through what are basically diagrams for logic gates, and how once they are sorted out they can be combined to make modern computers.
posted by mark k at 10:11 PM on April 22, 2022 [3 favorites]

All my book recommendations are old style.
Mathematics for the Million: A Popular Self-Educator [1936] by Lancelot Hogben is archived so you can browse its 600+ pages to see if it might suit. Hogben was one of a group of leftie scientists of the 1930. "I like Scandinavians, skiing, swimming and socialists who realize it is our business to promote social progress by peaceful methods. I dislike football, economists, eugenicists, Fascists, Stalinists, and Scottish conservatives. I think that sex is necessary and bankers are not" There are several editions in the archive.
posted by BobTheScientist at 11:08 PM on April 22, 2022 [1 favorite]

I think Mathematics and Logic by Mark Kaç and Stanislaw Ulam is a vastly under-appreciated little gem of a book.

It was published in 1968 as a Britannica Perspective for the 200th Anniversary of the great encyclopedia, and it starts from very elementary beginnings but gets into real mathematics more rapidly than any similar book I’m aware of. Within the first 15 pages, for example, you’ll find yourself in a discussion of the the fact that every quadratic irrational has a periodic continued fraction, and that the golden mean is by one measure the most irrational of all numbers in the sense that is the most difficult to approximate with rationals, followed by Louiville's proof of the existence of transcendental numbers (numbers which aren’t roots of any algebraic equation) by constructing one, which preceded by a few years (IIRC) Cantor's demonstration that there were 'more' transcendentals than rationals and algebraic irrationals combined, and a remark that many eminent mathematicians were horrified by Cantor's work:

This striking conclusion perturbed and even shocked many mathematicians. The great Poincare found it reason enough to fight Cantorism, casting his vote against it in a famous phrase: "... n'envisager jamais que les objets susceptibles d'etre defini dans un nombre fini des mots" ("... never consider objects except those that can be defined in a finite number of words").

The link is to a pdf in order to give you a flavor of the book, which is available in a Dover edition.
posted by jamjam at 11:40 PM on April 22, 2022 [1 favorite]

Chaos: Making a New Science by James Gleick
The Information: A History, a Theory, a Flood by James Gleick
posted by SweetLiesOfBokonon at 12:26 AM on April 23, 2022 [2 favorites]

With the caveat that I haven't read A History of the Circle - maybe The Quantum Astrologer's Handbook: a history of the Renaissance mathematics that birthed imaginary numbers, probability, and the new physics of the universe (review halfway down at that link). I bought it for a family member and ended up reading it myself too. When I was choosing the book, I also looked at some on this list. I've also had The Mathematics of Life and Death recommended.
posted by paduasoy at 12:58 AM on April 23, 2022

Larry Gonick's The Cartoon Guide to Calculus might do for calculus what Zebrowski's book does circles (and related). Gonick has extensive mathematical training, but dropped out of graduate school at Harvard to focus on cartooning. His Cartoon History books are excellent and I think he brings a similar sensibility to the Calculus book.

What sets the cartoon calculus book apart is the fun it uses to explore concepts. Yes, there will be a formula here and there, but they'll be part of the story when they come up. I've tried (unsuccessfully) to get my colleague in several math departments to adopt this book as a calculus text, just as a fun teaching experiment for a year. As weird and unconventional many mathematicians can be personally, they can also be surprisingly resistant to go against math traditions.
posted by El_Marto at 4:00 AM on April 23, 2022 [4 favorites]

Ditto Gonick's cartoon Guide to Physics, maybe.
posted by sebastienbailard at 4:02 AM on April 23, 2022

It's hella expensive, but Kronecker Wallis's edition of Euclid's elements looks amazing. If you can't shell out the big bucks, this is a perfectly decent student version. Euclid was a very clear writer, and working through the foundations of geometry is a really cool experience.
posted by hydropsyche at 5:35 AM on April 23, 2022

Looking in my own library, the closest I found was Sextant by David Barrie. It purports to trace the development of navigation, but is really much more about the age of exploration than the math.
posted by SemiSalt at 6:15 AM on April 23, 2022 [1 favorite]

I came in here to recommend Fermat's Enigma, which got me started on the road to a math PhD when I read it in high school.
posted by number9dream at 7:28 AM on April 23, 2022 [1 favorite]

Imagining Numbers: (particularly the square root of minus fifteen) by Barry Mazur is very much in the vein of Fermat's Enigma, where it carefully lays out, from simple principles, the process of getting one's head around the more complex and conceptual elements of imaginary numbers. There's also poetry.
posted by OHenryPacey at 9:15 AM on April 23, 2022

I find maths fascinating but mystifying, and if I was tested and told I had dyscalculia or something similar I wouldn't be surprised. Numbers mean nothing to me, much to my chagrin.

Nonetheless, A Introduction to Mathematics by Alfred North Whitehead (link is to the PDF on Project Gutenberg but you can buy hard copies easily) actually showed me the link between algebra and geometry in a way I could understand. It really is the only book that has ever made me feel that maybe maths is not entirely out of my reach.

Seconding The Information: A History, a Theory, a Flood by James Gleick (and, as always, search for what Richard Feynman had to say if you don't mind videos)
posted by underclocked at 11:41 AM on April 23, 2022 [1 favorite]

Four books about individual numbers:
e: The Story of a Number by Eli Maor
An Imaginary Tale: The Story of i by Paul J. Nahin
A History of Pi by Petr Beckmann
The Nothing That Is: A Natural History of Zero by Robert Kaplan
posted by indexy at 11:46 AM on April 23, 2022

I'm a fan of Shape referred to above.

Another one I liked was Chances Are: Adventures in Probability.

Aside from the mathematical concepts, both of these books are also well-written (ie. from a language point of view!). I'm a fan of math and science books that have some exuberance to them. :)
posted by storybored at 1:01 PM on April 23, 2022

I recommend Measurement by Paul Lockhart . It's quite different from most of the books recommended here so far. It isn't about mathematics (that is, history, biography, philosophy, with the mathematical content summarized or paraphrased). It is mathematics --- it starts with simple geometry and develops calculus and differential equations. It is accessible and self-contained -- it doesn't assume you know anything about these subjects when you begin. It's almost 400 pages, but large print with several hand-drawn diagrams on almost every page. There is a fair amount of philosophy and even some memoir, but they are there to support the development of the math.

This book appears to be part of Lockhart's remedy to the problems he described in his well-known essay The Mathematician's Lament.
posted by JonJacky at 1:46 PM on April 23, 2022 [2 favorites]

I also recommend Mathematics: A Very Short Introduction by Timothy Gowers. Unlike Lockart (upthread) he touches on many topics instead of presenting a single line of development, but like Lockhart he presents mathematics from the inside -- the reader participates in the discovery. Both are good at conveying that mathematics creates an independent self-contained reality with its own internal logic.
posted by JonJacky at 4:50 PM on April 23, 2022

Similar to the Hogben book is Aaron Bakst’s Mathematics: Its Magic and Mastery from the same era. I found this book fascinating in elementary school and as an early teenager. The chapters tend to be self contained, so you can jump around if you like.
posted by wittgenstein at 8:17 AM on April 24, 2022 [1 favorite]

This is really far outside of the books you've mentioned and might not even count as math at all, won't teach you to solve any problems, and might be controversial in some circles, but I've found Edward Tufte's books, starting with The Visual Display of Quantitative Information are a very readable discussion of how one can think about thinking about spatial and dimensional things. It's written for an audience who will be producing plots, but is a fun read for people who only expect to interpret them.

This is also a pretty far removed, but I've heard very good things about Geoffrey B. West's Scale: The Universal Laws of Growth. . . (I sadly haven't actually read it yet. But, I've read many of his technical papers and heard him speak to a general audience before, and I would be surprised if it isn't interesting and anchored in non-obvious spatial insights.)
posted by eotvos at 2:12 PM on April 24, 2022 [2 favorites]

I recommend Measurement by Paul Lockhart .

Thanks so much for this. My copy arrived earlier today, together with Arithmetic, also by Lockhart. I appreciate MetaFilter in general. In this particular case, I had no idea these books existed.
posted by kingless at 1:58 PM on April 26, 2022

Response by poster: That sounds great TimHare, along the lines of Willer.

mark k, Shape sounds like the thing, affordable too - books very $ in NZ.

jamjam - I hope the contents of Mathematics and Logic lives up to the neat cover! It looks semi-approachable and I like Dover Editions.

The Information sounds like a helpful reference thanks SweetLiesOfBokonon.

I'd forgotten about Gonick thanks El_Marto.

hydropsyche, I've seen that in the library, beguiling graphics. It somehow reminded me of a book in my own library Hierarchy : Perspectives for Ecological Complexity.. Really useful for understanding; scale, erosion, pollen, vegetation surveys ... and explains hard topics (like higher dimension numbers) - in a way that makes them applicable, good text and graphics.

Thanks underclocked, Whitehead it is then, math for me too about not seeing connections, apparently I was bright with numbers until I was about 10. Since then mostly a mystery.

JonJacky. Lockhart looks exciting (and makes me smile too via his video)!, I've ordered a copy, and I'll interloan Timothy Gowers.

Bakst's cover is the sort of book I pick off the shelf - I judge literal books by their covers, (people, more by their walk at hundred yards).

I've also just found Vaclav Smil's Didn't even know Smil wrote actual books. Numbers Don’t Lie: 71 Things You Need to Know About the World.

I've found Belos and Willers make for enjoyable relaxing reading while learning less formally, and many of your suggestions above promise similar, as well as thanks to NotLostnnnnn, BobTheScientist, paduasoy, SemiSalt, number9dream, OHenryPacey, indexy, eotvos for some serious desk works to take me further.
posted by unearthed at 11:38 PM on May 1, 2022 [3 favorites]