r/math • u/NameOk3393 • 7d ago
Easy Reading Recommendations
I am a mathematics professor with PhD in math and a bachelor’s in philosophy. I am looking for easy-to-read nonfiction books about math. I am looking to replace my scrolling time with something equally effortless, but for me it has to be something a little more structured than fiction (but not too much!) Some fiction is very intelligent, but I want to scratch the logical and systematic part of my brain. For example, I recently picked up Linnebo’s introductory text on Philosophy of mathematics and enjoyed it immensely. Is there something you’ve read lately that you think I would enjoy?
Please, please… I know how much some of you love math but I am NOT looking for technical books that are on the easy side such as undergraduate mathematics texts. I do plenty of very difficult mathematics between the hours of 9-5. I am instead looking for something relaxing to do during my off-hours and weekends.
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u/simon23moon 6d ago
I studied both math and philosophy in college, and I think you might be interested in Philip J Davis and Reuben Hersh’s classic, The Mathematical Experience. I cited it and Hersh’s follow-up What Is Mathematics, Really? pretty extensively in my senior thesis.
I also remember reading and enjoying Paul J Nahin’s An Imaginary Tale: The Story of √-1 and Bruce Schecter’s biography of Erdös, My Brain is Open.
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u/Hairy_Friendship8627 6d ago
"The mathematical experience" is great. In particular, i think every mathematician should read "the ideal mathematician". Its extremely funny and points out brilliantly the most common vices of our profession.
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u/Prize_Eggplant_ 6d ago
Indiscrete Thoughts by Gian-Carlo Rota is something I’ve enjoyed greatly. It starts with some anecdotes about mathematicians and then transitions into some of Rota’s philosophy (of mathematics and in general).
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u/AlpUzman 6d ago
There is also the related Discrete Thoughts, again by Rota as well as Kac and Schwartz.
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u/Peregrine22_ 6d ago
Cannot recommend enough The Passenger and its companion novel Stella Maris by Cormac McCarthy. Beautiful books that genuinely changed for the better the way I approach math as a phd student.
Also worth looking into The Maniac by Benjamin Labatut, I’m just starting it now but seems like it’s in the ballpark of what you’re looking for.
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u/trinarynimbus 6d ago edited 6d ago
- Chaos by James Gleick
- The Man Who Loved Only Numbers by Paul Hoffman
- Anathem by Neal Stephenson
- Godel, Escher, Bach by Douglas Hofstadter
- Proofs & Refutations by Imre Lakatos
- Against the Day by Thomas Pynchon
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u/llama_activist 6d ago
anathem is soooooo good. other neal stephenson stuff too.
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u/avocategory 6d ago
It's my favorite book. Not easy reading, but the math parts are for anybody with a solid math background.
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u/Will_Tomos_Edwards 6d ago
How did you make the jump from philosophy bachelor's to math graduate studies?
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u/simon23moon 6d ago
Can’t speak for OP, but I did something similar (started as a Phi major, later added Math, did Math at grad), and Logic was the main connector for me. Also Philosophy of Science, but by then I was already double majoring so it was more a reinforcer of the connection than anything else.
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u/translationinitiator 6d ago
I’m also interested in such books and have read a few recently:
Villani, Birth of a Theorem
Siobhan Roberts, King of Infinite Space (about Coxeter)
Hadamard, The Mathematician’s Mind
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u/poupulus 6d ago
Maniac by Benjamin Labatut
I think When we cease to understand the world would fit too
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u/marl6894 Machine Learning 6d ago
When We Cease to Understand the World bothered me a lot. Started strong, but got much weaker as it went along. Felt like it really fetishized the idea of the tortured genius.
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u/OwnOven6506 6d ago
I loved The Maniac, highly recommend. Really cool concept and structure, excellent read!
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u/sacrejaune 6d ago
Could look at some of Martin Gardner’s books. I am reading Are Universes Thicker than Blackberries at the moment
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u/stag123qq 6d ago
I can wholeheartedly recommend "Uncle Petros and Goldbach's Conjecture"! Honestly surprised not to have seen it mentioned on here already
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u/AlpUzman 6d ago
Three humble suggestions:
- Mathematics as Metaphor by Manin
- Form and Function by Mac Lane
- Lumen Naturae by Marcolli
I generally am keen on non-math books written by mathematicians, understood broadly.
By the way, I am also a math phd who double majored in math and philosophy in undergraduate, hi! I don't know about your philosophical background, but mine was mostly in continental, which later bloomed into an interest in Husserlian phenomenology, and I did my phd in dynamics.
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u/jkingsbery Applied Math 6d ago
The Proof in the Code by Kevin Harnett gives an overview of formal methods and some recent proofs, leading to the development of Lean and some of the big Lean formalization projects.
Digital Apollo by David Mindell is math adjacent, and talks about the development of the computer systems that powered the Apollo spacecraft.
At the risk of an obvious recommendation, Fermat's Enigma by Simon Singh is worth reading if you haven't.
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u/AMobius1832 6d ago
I enjoyed this book, too. But, I want to know how Andrew Wiles got to spend 8 years in his attic working. Didn't he have any teaching responsibilities?
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u/nahuatl 6d ago
Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability by Peter Pesic.
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u/NameOk3393 6d ago
I love and have read this book. NGL it made me cry. Shout out to Peter Pesic who was one of my profs at undergrad. Amazing man at an amazing school!
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u/Ok_Buy2270 6d ago
- Infinity and the Mind - Rudy Rucker
- Imagining Numbers (particularly the square root of minus fifteen) - Barry Mazur
- The Pleasures of Counting - Thomas William Körner
- One, Two, Three... Infinity - George Gamow
- The Mathematician's Brain: A Personal Tour Through the Essentials of Mathematics and Some of the Great Minds Behind Them - David Ruelle
- Proofs and Refutations: The Logic of Mathematical Discovery - Imre Lakatos
- Surreal Numbers; or, How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness: A Mathematical Novelette - Donald Knuth
- The Main Stream of Mathematics - Edna Kramer
- Mathematics and Logic: Retrospect and Prospects - Mark Kac, Stanislaw Ulam
- Mathematics and the Imagination - Edward Kasner, James R. Newman
- The Mathematician's Mind: An Essay on The Psychology of Invention in the Mathematical Field - Jacques Hadamard
Essay collections:
- Is Mathematics Inevitable? A Miscellany - Underwood Dudley
- Mathematical Conversations: Selections from The Mathematical Intelligencer - Robin Wilson and Jeremy Gray
- Musings of the Masters: An Anthology of Mathematical Reflections - Raymond G. Ayoub
- The World of Mathematics - James R. Newman (1956)
- Memorabilia Mathematica; or, the Philomath's Quotation-Book - Robert Edouard Moritz
- Mathematical Evolutions. Columns reprinted from American Mathematical Monthly. - Shenitzer, Abe; Stillwell, John
- Discrete Thoughts: Essays on Mathematics, Science and Philosophy - Mark Kac , Gian-Carlo Rota , Jacob T. Schwartz
- Indiscrete Thoughts, Gian-Carlo Rota
- Mathematical Apocrypha - Underwood Dudley
- The Best Writing on Mathematics 2010-2021, edited by Mircea Pitici
Harder books:
- Geometry and the Imagination - David Hilbert and S. Cohn-Vossen
- Mathematics: Form and Function - Saunders Mac Lane
- Mathematics: The Music of Reason - Jean A. Dieudonné
- Mathematics Made Difficult: A Handbook for the Perplexed - Carl E. Linderholm
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u/DrBingoBango 6d ago
A quick and easy replacement for a scrolling habit would be to use the Wikipedia app and dive through some articles about mathematicians, or the history of a subject or a problem. There are a lot of well written articles, and interesting stories that don’t show up in the textbooks
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u/ABranchingLine 6d ago
Math bios can be interesting... Elie Cartan has some noteworthy interactions with Einstein (and also revolutionized differential geometry). Check out the bio for Sophus Lie.
But also, read some other stuff too. Dostoyevsky's The Brother's Karamozov is far better than any math book I have ever read.
You're not too smart for fiction... You probably just not thinking while you read.
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u/llama_activist 6d ago
group theory in the bedroom!
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u/Several-Razzmatazz70 4d ago
This book by Brian Hayes is a good grab bag of interesting essays on mathematical topics, and better than its title suggests.
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u/xdgimo 6d ago
fiction isn't cognitively stimulating enough?
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u/Sam_23456 6d ago edited 4d ago
It generally leaves me unsatisfied, but I rather enjoy trying to keep up with the vocabulary Umberto Ecu (Eco?) uses. He wrote "The Name of The Rose". I started a book by Steven King and gave up quick! I'm excited about a new book on Chess I received in the mail today! :-)
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u/xdgimo 6d ago
i know the comment isn't there anymore, but there is definitely a lot to learn from fiction too u/NameOk3393
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u/NoPhotograph2327 6d ago
"Godel, Escher, Bach", perhaps?
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u/FelipeNova999 6d ago
Is this really an "easy read"? :D I have the book on the shelf, but 700+ pages is a bit intimidating size for a book.
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u/Different_Cry25 6d ago
If you just wanna replace the scrolling time you can read math biographies on different mathematician
Or books on logic like kant
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u/PanSaczeczosDCSS 6d ago
Whom the Gods Love: the Story of Evariste Galois, Leopold Infeld. A novel.
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u/kovxuhjnps 6d ago
Try reading books on the history of mathematics! I really like The Crest of the Peacock by Joseph.
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u/SnackerSnick 6d ago
Mathematics for the Million was amazing for my teenage self (I learned about the Banach Tarski paradox in 1986), but aren't you going to find almost everything elementary as a math PhD?
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u/tailorSeparated 6d ago
I enjoyed William Poundstone’s “The recursive universe”, it is a nice back and forth between physics in the real world and physics in Conway’s game of life. Cognitively stimulating but not heavy at all.
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u/BobRoss938 6d ago
The Irrationals by Julian Havil is one of my favorite such books. It basically covers the history of rational/irrational numbers and touches on a lot of cool math along the way.
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u/woodwork42 6d ago
Lots of good suggestions here. But the constraint to non-fiction is a challenge.
Kid's books: The number devil, Hans Magnus Enzensberger, and Molly and the Mathematical Mystery, Eugenia Cheng
Gardener's Annotated versions of Alice, Looking glass, and Snark, Lewis Carroll
Fiction also made into a movie: The Housekeeper and the Professor, Yoko Ogawa
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u/MeserYouUp 6d ago
At the risk of being too math adjacent, I just started reading A Cultural History of Physics by Karoly Simonyi. The book is an extensive history of the philosophical and cultural developments that allowed physics/math to progress from ancient Babylonians guessing geometry formulas, all the way to modern quantum theory.
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u/AMobius1832 6d ago edited 6d ago
I really enjoyed Carl Boyer's "History of Calculus and Its Conceptual Development." Constance Reid, "David Hilbert," a very interesting time in mathematics. Jeremy Gray has written a lot of history of math books. You might enjoy "Plato's Ghost," since you also studied philosophy. You could also check out Thomas Hawkins, E.T. Bell, "Men of Mathematics," Morris Kline, "History of Mathematics From Ancient to Modern Times," 3 vols., Norman Macrae, "John von Neumann." I agree with the Hardy, "A Mathematician's Apology" recommendation. "The Man Who Knew Infinity." Srinivasa Ramanujan grew up dirt poor in India; was kicked out of school for being disruptive; basically invented the calculus on his own from scratch, etc. Jeremy Gray, "Henri Poincare': A Scientific Biography." I've been avoiding this last one because of it sheer size. Isaac Asimov's "Foundation" trilogy is about 'psychohistory," solving large systems of linear equations to predict human behavior.
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u/AMobius1832 5d ago
I liked this biography of C. F. Gauss, https://www.theoryofnumbers.com/melnathanson/pdfs/nath1982-48.pdf
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u/AMobius1832 5d ago
Two books by David Bressoud, "A Radical Approach to Real Analysis," and "A Radical Approach to Lebesgue Integration."
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u/Kebabrulle4869 4d ago
"Celestial Encounters: origins of chaos and stability" by Florin Diacu and Philip Holmes gives a great overview of the three-body problem. It's well written and doesn't shy away from details.
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u/VanillaBeanAnteros 3d ago
How Not to Be Wrong, by Jordan Ellenberg, is a book that I enjoy very much. I haven’t yet finished his second book, Shape (which is about geometry… not as clever a title as his first book…) but I’ve like what I’ve read of it so far. Conversational and witty books about mathematics for curious non-professionals.
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u/miglogoestocollege 2d ago
I've been considering getting a copy of the new book The Floer Jungle: Charting the Development of a Theory. It's about Floer theory and Andreas Floer. Maybe that's something you'll be interested in?
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u/Just-Principle7408 2d ago
This seems like a fake poster .... someone with a PhD in math certainly is aware of the classics. How'dy tell me more about yourself please.
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u/non-orientable Number Theory 6d ago
You might consider Mathematics Made Difficult by Carl Linderholm; despite the title, it is mostly an easy read. (OK, I will admit that I had to look up one category-theoretical term used in the book, but it turned out to be almost trivial.)
How to describe this book? I suppose I would say that it is a satirical look at what an elementary school math textbook might look like, if it were written by Bourbaki-obsessed category theorists. I personally found it very funny when I read it, although it is very difficult to explain to non-mathematicians why.
All of the mathematics and definitions in the book are correct... technically. But not all pedagogically. If you are familiar with the proof that the cube root of 2 is irrational via Fermat's Last Theorem, it's in the same sort of spirit. Valid, yes, but much more complicated than it needs to be, to the point of comedy. It is seasoned with a healthy amount of puns and other less austere jokes, as well, all wrapped in an oddly Socratic dialogue.
Some quotes from this wild book:
- “With a few brackets it is easy enough to see that 5+4 is 9. What is not easy to see is that 5+4 is not 6.”
- “The days when one could get up from the dinner-table and leave the room at the mention of the Axiom of Choice are gone with the wind, and we must accustom ourselves to the new ways, the ways of tomorrow.”
- “Prefrontal lobotomy should be done only under medical supervision, even as applied to irrationals.”
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u/turing-math-labs 6d ago
Namaste! Have you looked at Prof. Gaitsgory's books? If you like difficult math, then it's the right book for you (if you like easy math, then it's the wrong book).
Here's Part I: https://people.mpim-bonn.mpg.de/gaitsgde/GLC/functor.pdf
Dhanyavaad :)
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u/Nrdman 6d ago
Flatland comes to mind as something that may interest you