Cool math books

Straight-up math books:

  1. ‘Understanding Analysis’ by Abbott
  2. ‘The Art of Proof’ by Beck
  3. ‘Contributions to the Founding of the Theory of Transfinite Numbers’ by Cantor
  4. ‘What Is Mathematics?’ by Courant & Robbins
  5. ‘The Mathematical Experience’ by Davis and Hersh
  6. ‘Introduction to Mathematical Thinking’ by Devlin
  7. ‘Journey Through Genius: The Great Theorems of Mathematics’ by Dunham
  8. ‘One Two Three … Infinity’ by Gamow
  9. ‘Book of Proof’ by Hammack
  10. ‘Mathematics: a Human Endeavor’ by Jacobs
  11. Mathematics and the Imagination’ by Kasner and Newman
  12. ‘Surreal Numbers’ by Knuth
  13. ‘The Pleasures of Counting’ by Korner
  14. ‘Proofs and Refutations: The Logic of Mathematical Discovery’ by Lakatos, Worall, and Zahar
  15. ‘The World of Mathematics’ by Newman
  16. ‘Numbers: Rational and Irrational’ by Ivan Niven (as well as other stuff in this series)
  17. ‘The Gentle Art of Mathematics’ by Pedoe
  18. ‘The Mathematical Tourist’ by Peterson
  19. ‘Mathematical Snapshots’ by Steinhaus
  20. ‘The Joy of x: A Guided Tour of Math, from One to Infinity’ by Strogatz
  21. ‘Mind Tools: the five levels of mathematical reality’ by Rucker
  22. ‘Math Girls’ by Yuki
  23. Math on Trial: How Numbers Get Used and Abused in the Courtroom by Leila Schneps

Other Resources:

  1. Jump Math (for kids)
  2. Khan Academy
  3. Keith Devlin’s Coursera course “Introduction to Mathematical Thinking”
  4. A math book list for kids
  5. Martin Gardner’s stuff (this for example)
  6. ‘Men of Mathematics’ by Bell, if you like soap operas featuring math
  7. ‘Gödel, Escher, Bach: an Eternal Golden Braid’ by Hofstadter, if you like philosophy
  8. ‘A Mathematician’s Apology’ by Hardy

Please comment on this page if you have something to add. Also feel free to give your opinions on the above, since I haven’t actually read them.

  1. December 1, 2012 at 9:33 am

    Morris Kline has a number of well-regarded overview books. I’m most familiar with the excellent ‘Mathematics in Western Culture’, but see also ‘Mathematics for the Nonmathematician’, which is a textbook for a liberal arts course in mathematics. For something more specific in focus (though still remarkably wide-ranging), Petr Beckmann’s ‘A History of Pi’ is highly recommended.

    There are some marvellous books in the list already. ‘What Is Mathematics?’ is an excellent starting point for a self-learner. ‘Proofs and Refutations’ and ‘The Mathematical Experience’ should be required reading for all working mathematicians.

    Liked by 4 people

    • Rob
      January 21, 2016 at 10:50 am

      It’s Morris Klines’ Mathematics and the Physical World for me. I read it in my second year at University. It was the closest I have come to a religious experience.

      Liked by 2 people

  2. suevanhattum
    December 1, 2012 at 10:20 am

    How could I forget Math Girls?! Anime-style story line, and real math. I plan to re-read it this December, to see if I can understand why the sum of the alternating harmonic series is pi2/6. I just looked up the website ( and found out that Math Girls 2 will be out in December. Perfect holiday gift for me!

    Liked by 1 person

  3. December 1, 2012 at 11:50 am

    The Joy of X is based on a New York Times series of a couple of years ago. I just received the book and haven’t gotten a chance to read it yet but did read the series. The series was great and I expect the book to be too. But in the interest of full disclosure, Steven Strogatz is a friend. A great book (not written by a friend—I don’t even know him) that I’m about a third of the way through is Math in 10 Lessons: The Grand Tour. It’s a pure mathematics book that tries to show those in the humanities, as well as scientists and other non- mathematicians, how mathematicians view their discipline.

    Liked by 1 person

  4. December 1, 2012 at 3:51 pm

    Ummm… thanks for the spelling correction, but surely you don’t have to be nasty. Khan Academy is an amazing site, and he really started something which I for one appreciate as a mother. My oldest son learned a lot of physics from him.

    Liked by 2 people

    • Michael Paul Goldenberg
      December 2, 2012 at 8:41 am

      Where was I nasty? Because I suggested that there are far better math vids and named some?

      Liked by 1 person

      • Ross
        January 13, 2013 at 10:49 pm

        “Surely you can do better” comes off, at best, as a bit haughty. Worse, it seems a bit snotty, condescending, patronizing, or all three. ( I suppose it could have been delivered innocently, by assuming the exact right “tone”, but the first reaction is to take it as described; your reply indicates that’s correct.)

        Liked by 1 person

    • Spicyrunner
      March 24, 2013 at 11:08 pm

      I LOVE LOVE LOVE I’m a neuropsychologist assessing children with learning problems…and having such high quality *tutoring* available for FREE is a Godsend for the kiddos I work with. My kiddos just want to know HOW to solve the problems on their homework!!!!

      Liked by 1 person

  5. Charles monneron
    December 1, 2012 at 7:47 pm

    “Meta math, the quest for Omega” by Gregory Chaitin is as mind bending than GEB

    Liked by 1 person

  6. Nikki
    December 2, 2012 at 12:35 pm

    Surreal Numbers was my very first cool math book, recommended by the same French mathematician who told me about the Nicolas Bourbaki. More recently I enjoyed reading Poincare’s Conjecture.

    Liked by 2 people

  7. Silvia Adduci
    December 6, 2012 at 7:23 am

    Have you tried The Puzzling Adventures of Dr Ecco, by Dennis Shasha?

    Liked by 1 person

  8. rustam
    December 7, 2012 at 12:10 am

    I suggest you add “Who Is Fourier?: A Mathematical Adventure” to your list.

    Liked by 1 person

  9. January 7, 2013 at 4:07 am

    Late to the party, I suggest “The enjoyment of Mathematics” by Rademacher&Toeplitz, maybe old fashioned but I remember having a lot of fun .

    Liked by 1 person

    • Luis
      June 29, 2014 at 7:12 pm

      Rademacher & Toeplitz is in the top 20. They are not afraid of tackling intricate topics and bringing them down to high school level (that is, good high school). But I must say that these expositions never get old fashioned – only Hollywood does.

      Liked by 1 person

  10. pdtillman
    January 14, 2013 at 1:58 pm

    Do you have a recommendation for a good introduction to Bayesian statistics? I’m particularly interested in comparing Bayesian vs. frequentist statistics. And my statistical skills are pretty rusty ;-[

    TIA, Pete Tillman
    Consulting Geologist (retired), Arizona and New Mexico (USA)

    Liked by 1 person

    • January 14, 2013 at 3:37 pm

      Try Gelman’s book, Bayesian Data Analysis. He also writes a blog .

      Liked by 3 people

    • charles
      March 2, 2013 at 2:21 am

      Try Probability Theory: The Logic of Science by E. T. Jaynes. It’s a great read and has a very good introduction to probability. The math gets heavy pretty quickly but the text alone is worth the book.

      John Kruchke’s book Doing Bayesian Anaysis is a first rate tutorial suitable for those of us who don’t think in intregals.

      Liked by 1 person

    • Jorge Reyes-Spindola
      May 16, 2017 at 8:33 am

      As a more general introduction to Bayes’ theorem, I would recommend “The Theory That Would Not Die. How Bayes’ rule cracked the Enigma code, hunted down Russian submarines and emerged truimphant from two centuries of controversy.” by Sharon Bertsch McGrayne. It’s a history of Bayes’ theorem and its applications. Great book.

      Liked by 1 person

      • Albanius
        May 16, 2017 at 8:50 am

        “The Theory That Would Not Die” is a good read, but it is a narrative history, with focus on personalities, not math.
        For the math, I suggest “Scientific Reasoning: The Bayesian Approach” (3rd Ed) by Colin Howson and Peter Urbach.
        Here is the blurb:
        ‘This user-friendly, comprehensive course in probability and statistics as applied to physical and social science explains the probability calculus, distributions and densities, and the rivals of Beyesianism – the classical, logical, and subjective theories. Howson and Urbach clearly lay out the theory of classical inference, the Neyman-Pearson theory of significance tests, the classical theory of estimation, and regression analysis. The work is controversial, but gives a fair and accurate account of the anti-Bayesian views it criticizes. The authors examined the way scientists actually appeal to probability arguments, and explain the ‘classical’ approach to statistical inference, which they demonstrate to be full of flaws. They then present the Bayesian method, showing that it avoids the difficulties of the classical system. Finally, they reply to all the major criticisms levelled against the Bayesian method, especially the charge that it is “too subjective”.’

        Liked by 1 person

  11. Albanius
    January 16, 2013 at 4:04 pm

    Euler’s Gem: The Polyhedron Formula and the Birth of Topology by Richeson
    The Fractal Geometry of Nature by Mandelbrot
    How to Solve It by Polya
    How to Lie with Statistics by Huff and Geis

    Liked by 1 person

  12. January 29, 2013 at 12:21 am

    I think the best Book I’ve seen on teaching “proof” so far is “A Transition to Advanced Mathematics” by D. Smith et al. We used this for My “Foundations of Mathematics” course in college. And I still reference it! . What do you think?


  13. Krishnan
    February 11, 2013 at 8:32 pm

    Books by John Allen Paulos (Innumeracy for example)


  14. charlie
    February 14, 2013 at 12:36 pm

    What about “God Created Integers” by Stephen Hawking?


    • Dr Edwin Coleman
      November 2, 2016 at 6:14 pm

      I think not.
      This consists of original papers, like Godel’s On Formally …, and is quite unsuitable as intro material.
      Hawking’s contribution seems to consist in putting his name on the cover.


  15. February 14, 2013 at 5:01 pm

    You might also consider From Zero To Infinity by Constance Reid.


  16. February 18, 2013 at 5:10 pm

    I would also add ‘A Radical Approach to Lebesgue’s Theory of Integration’ by Bressoud. This is a textbook on measure and integration, but the historical progress of the theory is told as the subject matter develops. A good complement to #3 might be ‘Georg Cantor’ by Dauben. I haven’t read #3, but this book gives a great detailed look into the work of Cantor, without being too technical, and also looks at his life.


    • Higby
      May 9, 2013 at 4:57 pm

      Yeah, the historical perspective — always missing in under/grad courses.

      Typically, math concepts are presented as ex nihilo. But when you look more deeply, you see how it is cobbled together from bits of this and parts of that.


  17. JJ
    February 21, 2013 at 9:34 am

    Bob Moses & Charles Cobb. Radical Equations: Civil Rights from Mississippi to the Algebra Project. Beacon Press, 2002.

    Jeffrey Isaac. 1999. “The Algebra Project & Democratic Politics,” Dissent (Winter).

    Highly recommended for trying to draw the analogy between the importance of verbal literacy to the struggle for voting rights in the 1960s and the importance of math literacy for poor/minority kids in contemporary America – if, of course, we hope them to have the opportunities of political & economic citizenship. Ella Baker meets quadratic equations.

    The project has been running since the mid-1980s and raises all sorts of interesting political issues (hence the Isaac piece) but gets relatively little attention.

    Liked by 1 person

  18. Phil H
    February 26, 2013 at 5:23 am

    “The Princeton Companion to Mathematics” edited by Gowers, Barrow-Green and Leader.

    Liked by 1 person

  19. Louis Bruno
    March 4, 2013 at 12:02 pm

    I just came across your list (and site) and would like to suggest a few title I have enjoyed. One of the first books to get me interested in math was “Fermat’s Last Theorem” by Simon Singh, followed by several of Martin Gardner’s articles and books, “In Code” by Sarah Flannery, and several large reference-style compendiums that prove quite useful in trying to get a handle on new subjects, “Mathematics, From the Birth Of Numbers” by Jan Gullberg, “The VNR Concise Encyclopedia Of Mathematics” by W. Gellert et al, Martin Gardner’s :The Colossal Book of Mathematics:, and Dr. Richard Elwes’s “Mathematics 1001”.

    Most recently, I just finisthed Nate Silver’s “The Signal and The Noise” and “Connected” by Nicholas A. Christakis.

    I hope these suggestions help a bit and the site continues to provide such an interesting contribution to a fascinating subject.


  20. March 20, 2013 at 12:48 am

    I love this book God Created Integers by Stephen Hawking


  21. May 5, 2013 at 4:09 pm

    This is my favorite – ‘A Million Random Digits with 100,000 Normal Deviates’. Not for the book but for the good read in Amazon’s comments about it.


  22. Glen S. McGhee
    May 10, 2013 at 9:07 am

    Donald MacKenzie, Statistics in Britian 1865 – 1930: The Social Construction of Scientific Knowledge (1981).

    Galton, Pearson, and Fisher were all eugenists — it should never be forgotten that Galton’s statistics first emerged as a powerful rhetorical device for the advancement and promotion of the eugenics movement, and for the justification of mass sterilizations of inferior classes. Unfortunately, one group did in fact succeed on such a massive scale that it still horrifies and haunts humanity.

    Does anyone remember Florence Nightingale’s rose chart? “In 1859 Nightingale was elected the first female member of the Royal Statistical Society and she later became an honorary member of the American Statistical Association” (wikipedia).

    Liked by 1 person

  23. May 19, 2013 at 1:21 pm

    Brian Butterworth, The Mathematical Brain;

    Graham Farmelo, ed., It Must Be Beautiful: Great Equations of Modern Science;

    Robert Kaplan, The Nothing that Is: A Natural History of Zero;

    E. T. Jaynes, Probability Theory: The Logic of Science (corrected ed.);

    David Acheson, From Calculus to Chaos.


  24. May 19, 2013 at 1:23 pm

    Glen, I remember Florence Nightingale’s rose chart. Brilliant innovation. You can find it along with other wonderful exhibits in Edward Tufte’s The Visual Display of Quantitative Information (2nd ed.).


  25. Chris
    May 19, 2013 at 9:13 pm

    T. Korner has written several books other than “Pleasures of Counting” that are pretty accessible. His two Fourier Analysis books are written at an mid-undergraduate level, and his game theory book is at an advanced high school/early undergraduate level. Also both are full of fun stories. And very relevant since Fourier methods and their extensions have been so important over the past two centuries in so many fields, both pure and applied.

    I wish I could suggest a good applied computational mathematics book. Sadly I don’t think there’s a great book out there yet. Also it’s a moving target, since the best languages, methods, libraries, and problems change from decade to decade.


  26. May 22, 2013 at 12:56 pm

    Thanks for the list. I emailed some links like Jump Math to my friends. Its really awesome. You did hard job to manage all these great resources here. Keep it up..upper…uppest! :p


  27. Richard L King
    May 27, 2013 at 6:42 am

    Back when the world was young, and I was even younger (about 10), I came across a book called Mathematician’s Delight by W W Sawyer. I can honestly say this book changed my life (very much for the better!).

    I’m glad to see it’s still in print. It’s the kind of thing that should be left lying around innocently to catch the attention of inquisitive young minds, even if it does contain words (such as ‘slide rule’) that have disappeared from common usage!

    Oh yes, the slide rule… another life changer…


  28. Dave Baum
    June 13, 2013 at 10:16 pm

    Thanks for the list of books. I had already read and enjoyed more than a few on the list and now I have several new titles to add to my reading queue.

    One additional suggestion is “The Math Book” by Pickover. It’s more history than mathematics, but can serve as a great (albeit brief) introduction to numerous topics. The illustrations are wonderful. For bonus points read it concurrently with “The Physics Book”.


  29. June 18, 2013 at 10:27 am

    I would agree with Dave about The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics by Clifford A. Pickover. It’s definitely worth a read and is a good one to recommend to people.

    As is Math on Trial: How Numbers Get Used and Abused in the Courtroom. Which I found to be a fascinating read and the tension really grips you.


  30. Zathras
    July 15, 2013 at 1:31 pm

    I just came across this post. To the list I would add Conceptual Mathematics: A First Introduction to Categories:

    No other book I know of gets students involved in the deep issues of math earlier than this one.


  31. David B. Chorlian
    August 5, 2013 at 2:50 pm

    W.K. Clifford’s _The Common Sense of the Exact Sciences_. In my previous existence as a high school math teacher I was always looking for ways to get beyond the purely manipulative approach featured in most textbooks to bring some insight into mathematical thinking. This book is one of the best.

    Liked by 1 person

  32. Reuben Shiffman
    October 8, 2013 at 10:13 am

    Please recommend an introductory textbook on statistics and probability. Many thanks, RS


  33. October 8, 2013 at 8:18 pm

    Wonderful – for general math problems, Knuth’s first volume (Computing?) has more problems with a breadth of difficulty, from 8th grade arithmetic to Fermat’s last theorem (unsolved when he published). For some philosophy with statistics & probability, Polya’s Mathematics and Plausible Reasoning volumes one and two (he show data proving that the different number of spots on a die “loads” it, I’ve forgotten who rolled 12 dice more than 23,000 times, but it’s covered with the requisite probability calculations – then he forgets to tell you why this was done in the first place. Then Gamma (Euler’s Constant) by Havil and The Story of sqrt(-1) by Nahim. The last two cover the history of both concepts (and Nahim debunks the importance of factoring x^2+1=0 as motivatomg “imaginary” numbers).


    • Chris
      May 23, 2017 at 10:31 pm

      The author of An Imaginary Tale (one of my favorite “numbers”) is Paul H. Nahin. Which is a wonderful book. He also wrote another one about about Euler’s Formula titled Dr. Euler’s Fabulous Formula: Cures Many Mathematical Ills (plus lots of other entertaining math books, that all require a piece of paper and pencil available for working the stuff out yourself!).

      When I was gainfully employed as a structural dynamics engineer Euler’s Formula formed the basis of almost everything I did, including switching between the time and frequency domains with Fourier transformations. I wore an embroidered Euler’s Formula during our local Science March, unfortunately it did not occur to me until later I should have added the words “This is how we bounce.” (… and if I was really on the ball I would have had a picture of Galloping Gertie!)

      Which is why my other picks would include the previously mentioned A History of Pi and “e:” The Story of a Number. It is kind of a “get you to know your tools” situation. 😉

      Oh, wait… another important number: Zero: The Biography of a Dangerous Idea by Charles Seife.


  34. October 11, 2013 at 1:38 pm

    ‘What Is Mathematics?’ by Courant & Robbins – My all-time favorite.

    Liked by 1 person

  35. Farrukh
    October 23, 2013 at 1:10 am

    I was going to suggest WW Sawyer’s books as well but you beat me to it! I had a friend in high school who hated math and had a lot of trouble understanding the abstract stuff. He read “A Mathematician’s Delight” and magically fell in love with math! Hard to believe, but it’s a true story.

    Richard L King :
    Back when the world was young, and I was even younger (about 10), I came across a book called Mathematician’s Delight by W W Sawyer. I can honestly say this book changed my life (very much for the better!).
    I’m glad to see it’s still in print. It’s the kind of thing that should be left lying around innocently to catch the attention of inquisitive young minds, even if it does contain words (such as ‘slide rule’) that have disappeared from common usage!
    Oh yes, the slide rule… another life changer…


  36. barry spivack
    October 26, 2013 at 5:26 pm

    Cathy – great blog
    I am looking for a book on time series analysis for the layman. Can you recommend something?Thanks


  37. November 29, 2013 at 2:11 pm

    The book that I like the most among those enlisted above is ‘What Is Mathematics?’ by Courant & Robbins. Thanks for sharing the links.

    Khan Academy has always served me as a wonderful resource. I recommend it to my kiddos so often.


  38. December 1, 2013 at 6:58 am

    I’d suggest adding “Wolfram MathWorld” — the online compendium on mathematics: . Not entertaining, but amazingly thorough. And it’s free!


  39. Albanius
    December 12, 2013 at 9:03 am

    Love and Math, by Edward Frenkel (just published, late 2013), intertwines an exciting autobiography (struggling through antisemitism, excluded from Moscow State U in the 1980s USSR, getting an exit visa to be a visiting prof at Harvard at age 21 while still an undergraduate!) with a serious effort to explain his research in the Langlands program for the general reader. Much more math than most popular math book, especially in the endnotes.


  40. January 20, 2014 at 2:21 pm

    What about Mathematics for the Millions by Hogben or Thompson’s Calculus for the common man. In fact the entire series of Books on Mathematics for the Common man are fantastic


  41. Phil Harmsworth
    January 28, 2014 at 6:24 am

    Kasner and Newman’s ‘Mathematics and the Imagination’ – old but good (and available as a free download at Really inspired me as a kid.
    Cundy and Rollet ‘Mathematical Models’. Ditto.
    Fuse ‘Unit Polyhedron Origami’
    Yandell ‘The Honors Class Hilbert’s Problems and Their Solvers’
    Dars, Lesne and Papillault ‘The Unravellers Mathematical Snapshots’. This one is more about mathematicians than mathematics. It’s look at the mathematicians at the IHÉS: if you can’t go there, this is the next best thing.


  42. Jim Netter
    March 12, 2014 at 10:10 am

    A few of my non-technical favorites that haven’t been mentioned:
    Dunham’s “Mathematical Universe” and “Euler: The Master of Us All”
    Mandelbrot: “The Fractal Geometry of Nature”
    Derbyshire (yes, I know): “Prime Obsession” and “Unknown Quantity”
    Eli Maor: “Trigonometric Delights”, “To Infinity and Beyond”, “e: The Story of a Number”
    Kanigel’s Ramanujan biography
    Edna Kramer’s “Nature and Growth of Modern Mathematics”
    various titles by Raymond Smullyan and Ian Stewart
    and a seconding for the works of Martin Gardner – I’m rereading his collection “Penrose Tiles and Trapdoor Cyphers” and it’s way cool


  43. Tim McGrath
    May 4, 2014 at 11:50 pm

    Kalid Azad at does a great job of presenting the subject on an intuitive level.


  44. Jay
    May 13, 2014 at 11:25 am

    Courant and Robbins was my great introduction to math when I was in junior high. The Laktos book I read many years later. Although I was a math major, it discusses many topics in proving things that had worried me in my courses. I would add Gödel’s Proof by Nagel, Newman and Hofstadter. An update of a monograph from the ’60s, it presents a very understandable explanation of the First Incompleteness theorem. Another book, Incompleteness by Goldstein, covers much of the same ground but weaves in the philosophical implications of the theorem and some biographical background on Godel.

    Liked by 1 person

  45. warrack
    June 27, 2014 at 1:53 pm

    Stanislaw Ulam’s “Adventures of a Mathematician” is one of the most fascinating books I ever read. Also Littlewood’s “A Mathematician’s Miscellany” is, in my opinion, rather more interesting than his friend Hardy’s “Apology”.


  46. warrack
    June 27, 2014 at 2:00 pm

    Also Tim Gowers’s “A Very Short Introduction to Mathematics” is a tour de force, and beautifully written. He once amusingly commented that his Princeton Companion might also be titled “A Very Long Introduction to Mathematics”


  47. Aaron Silberstein
    July 3, 2014 at 3:28 pm

    “Math on Trial” was written by Schneps and Colmez 🙂


  48. Colin Davies
    September 26, 2014 at 5:23 pm

    How about Danica McKellar’s books?

    Liked by 1 person

  49. Aaron Lercher
    October 1, 2014 at 4:22 pm

    Symmetry by Hermann Weyl


  50. Steve Cox
    December 4, 2014 at 6:46 pm

    No one has suggested The Art of Mathematics by Jerry King. How odd.


  51. December 14, 2014 at 5:16 pm

    Another author of excellent general introductory books, Sherman K. Stein (emeritus professor at U.C. Davis) “Mathematics, the Man Made Universe” and “Strength in Numbers”. I strongly second the remarks about W.W. Sawyer. He went out from Cambridge to start a Department of Mathematics in the Gold Coast (now Ghana), and I believe wrote some of the books to foster an interest in mathematics there.


  52. March 4, 2015 at 6:12 am

    You have a great list of math books many of which I have never read, and I plan to check them out. There is one book that stands out in my mind that is not on your list. The book “Five Equations that Changed the World” is an excellent read and I highly recommend it.


  53. March 11, 2015 at 9:54 am

    I have a little math book designed for folks who don’t like math and have avoided the subject. In “Math for Grownups,” I take readers through the basic math they need on a daily basis, to manage their finances, garden, do DIY projects, and bake. Through funny and engaging real-world problems, readers are introduced to the concepts behind basic calculations. I would be honored to have you take a look and include it in the list. (My second book, “Math for Writers,” takes the same approach for journalists and freelance writers. But that’s a pretty niche readership.)


  54. March 14, 2015 at 1:13 am

    I recommend “The Geometry of Multivariate Statistics” for those of you interested in gaining a deep conceptual understanding of applied statistics and linear algebra. Understanding the geometric interpretation of vector and matrix operations seems much more intuitive than thinking of the topic as an algorithm that blindly leads to a result.


  55. April 7, 2015 at 1:54 am
    • Stephen Cox
      December 20, 2015 at 1:40 am

      Very good book.


  56. May 20, 2015 at 3:21 pm

    I will gladly plug (which I co-author) and and (which I do not).


  57. September 5, 2015 at 9:40 pm

    “The Joy of X” is really not a ‘cool math book’. Maybe it is just where I am now but I got no brain buzz from any of it. Moderately interesting but not cool.


  58. Florian
    November 3, 2015 at 8:19 am

    My suggestion: “How not to be wrong” by Jordan Ellenberg. Even though it’s aimed at a non-mathematical audience, explaining how various fields of math (with a focus on probability theory though) apply to everyday life, I as a mathematician also had great fun reading it.


  59. January 7, 2016 at 9:58 pm

    Shameless self-plug: for a precalculus, mechanics, and calculus all-in-one textbook, with zero bullshit in it, check out the noBS guide to math an physics


  60. February 19, 2016 at 12:43 am

    “Why is there a philosophy of mathematics at all?”, by Ian Hacking. This is very much a philosophy book, not a mathematics one, but it’s written to present the author’s personal viewpoint in the context of previous viewpoints rather than as a survey or textbook or even as an argument, so I found it much more readable than anything else on the subject.

    I’d like to warn people away from “Godel, Escher, Bach”, because I think it’s wrong in a subtle way which is very hard for people who don’t have philosophy experience to realize the flaws, and Hofstader doesn’t give any pointers at all to arguments against his views.


  61. June 15, 2016 at 3:55 pm

    Good ideas! I’d like to shamelessly plug my book, Hacking Math Class with Python. All the code needed to explore many traditional math topics like solving equations and factoring polynomials to creating fractals and 3D Graphics. It could be an intermediate step to implementing your (or KW’s) excellent ideas on “The Future of Math Education.”


  62. Robert Baillie
    August 12, 2016 at 3:51 pm

    I would recommend any book by either Ian Stewart or John Allen Paulos.


  63. Anne
    August 27, 2016 at 5:41 pm

    Cathy, which books would you recommend for engineers who haven’t worked with math since college?


  64. September 6, 2016 at 3:31 pm

    I recommend “Road To Reality” by Roger Penrose; it’s somewhat advanced but is a great treatise on modern physics and the mathematics behind our current understanding of the laws of the universe.


  65. September 6, 2016 at 6:10 pm

    I’ve read some of these. Good list. Like to add another book which suggests how to fix an anomaly in the pipeline for getting more into STEM careers in general: “Long STEM Roads for Life”, subtitle Math Education and STEM Careers- see


  66. Celia Baruchin
    September 8, 2016 at 12:21 pm

    Thanks for your terrific, informative appearance on the Brian Lehrer show today on WNYC, and congratulations on the publication of your book! I’m looking forward to sharing your blog with my 17 y/o daughter!


  67. brianbuchbinder
    September 8, 2016 at 9:24 pm

    Totally with you on the Cantor. But you left out Nagel’s “Godel’s Proof” which if I can understand it, is a clear exposition of the theorem. GEB was great, but doesn’t really give you the mathematical joy of the Gödel discovery.


  68. September 19, 2016 at 9:28 pm

    The Man who Loved Only Numbers by Hoffman about Erdos is a fascinating biography with some thought-provoking math problems that non-mathematicians can understand. On the kids’ list, I strongly recommend The Number Devil. Another good kids book is Sidesways Math From Wayside School.


  69. Sonja
    September 21, 2016 at 7:50 pm

    Anything by Raymond Smullyan, anything!!! 🙂

    Thanks so much for this splendid blog. You make me happy. 🙂


  70. October 10, 2016 at 7:20 am

    Your book is very important socially and relevant to what is happening all through the world of big data. People must understand how the Theory of Solving Ill-Posed Problems and VC theory applies to model making and also how important problem definition is to validation. We are building a world of self-fulfilling prophecy and true danger of information isolation and polarization. Prediction acts as a short circuit to debate; when the process for prediction development is misused, the prediction loses validity, yet few can detect that loss, especially in deep learning networks. Models are given authority they do not deserve!


  71. JPA
    October 12, 2016 at 2:08 am

    Not a technical book but I loved reading Fantasia Mathematica as a kid.


  72. November 8, 2016 at 2:41 pm

    I’m a developer that’s worked on big data systems, specifically with social media data mining. Your book Weapons of Math Destruction is a very important topic for all, especially software developers. Here’s the latest, go figure: facebook gets sued for discriminatory housing ads


  73. November 15, 2016 at 9:14 am

    Excelente selección de libros. Gracias


  74. David Bee
    November 30, 2016 at 10:45 pm

    Since your 10th book is Harold R. Jacobs’s gem Mathematics: A Human Endeavor, you should also list his other two books, namely Elementary Algebra and Geometry.

    Why? Because for anyone who wants to learn such, these two books, written in a style similar to MAHE, may just be the best textbooks on such ever WRITTEN.


  75. Andang
    December 2, 2016 at 10:58 am

    I recommend George Polya’s How To Solve It.


  76. Moon Virgo
    December 30, 2016 at 9:22 pm

    No Alex Bellos’ book recommendations? Wow. Tough Audience. I recommend his “Here’s looking at Euclid.” Lots of great history of math research on interesting and diverse contributions from around the world to the study of math. The chapter on India was such a revelation. And your book, Cathy, should be here too. Great book – so useful in advancing discourse intelligently and helping others see how math metrics can be used in damaging ways. Freakonimics is also great. Flatland too. Along with spin-offs Sphereland and Flatterland, though I see Ian Stewart made the list already in the comments.


  77. January 5, 2017 at 4:09 pm

    If advocating for your own book is verboten, please ignore or delete. My latest book, Painting By Numbers: How to Sharpen Your BS Detector and Smoke Out the Experts, is now available from Amazon (author Jason Makansi). I list Weapons of Math Destruction as one of a dozen for deeper insight. My hope is that Painting by Numbers will be regarded similarly to How to Lie with Statistics, still in my mind one of the simplest, clearest explanations of a complex field of math.


  78. February 10, 2017 at 6:23 pm

    “The Emperor’s New Mind” by Penrose. Lots of math and speaks to the heart of your criticism with ML and AI, Dr. O’Neil.


    • Dr Edwin Coleman
      February 10, 2017 at 6:46 pm

      I read that Penrose book when it first came out. Can’t fault his maths, tho not exactly pellucid. His philosophy is very amateurish however. You can’t “solve ” philosophical problems with scientific speculations.


      • April 26, 2017 at 3:23 pm

        I disagree. You have to know something about the world before you can do any meaningful philosophy. The Greeks were right. Earth-measuring comes first. Science helps contextualize experience into empirical chunks of data which can then be analyzed. You’ll find that Penrose’s book is deeply rooted in science and math in order to contextualize the nature of the inquiry. One can’t simply run off and start philosophizing if it’s not rooted in something observable and measureable. Penrose’s book is daunting and covers a lot of ground. It’s hard to connect the math and science to consciousness and its origins at first, or even second pass.

        Penrose is merely cautioning that simulating consciousness is not the same thing as consciousness itself. One can write very complex algorithms for passing Turing Tests, but it’s not a measure for assessing if there’s any deep contemplation or judgment going on. A computer can beat people at Go or Chess, but it doesn’t understand why the game is played at all or what it’s really doing. It’s just following a complex set of orders. It’s just taking data as input and spitting out a response based on the rules it was given.

        At the end of it all, AI is all about speed and efficiency. It’s a tool, not a God.


  79. mazzy
    February 18, 2017 at 4:36 am

    – In Code: A Mathematical Journey
    – Fermat’s Engima
    – Mathematics: From the Birth of Numbers

    – Realm of Algebra, Isaac Asimov
    – Innumeracy: Mathematical Illiteracy and Its Consequences,
    Prof John Allen Paulos
    — Mathematician Reads The Newspaper,
    — A Mathematician Plays the Stock Market
    — Use to have a column called: “Who’s Counting”
    – Engineering Mathematics (I love the layout of this book)
    K. A. Stroud and Dexter J. Booth
    – The Misbehavior of Markets: A Fractal View of Financial Turbulence
    Benoit Mandelbrot, Richard Hudwon (More fractals)
    – Danica McKellar (actress/grad in math UCLA) has written some interesting math
    books designed for young women. They might appeal to some:
    — Girls Get Curves: Geometry Takes Shape,
    — Kiss My Math: Showing Pre-Algebra Who’s Boss,
    – Best video ever on exponential growth (1-8), Prof Bartlett
    – BBC Radio is awesome
    — Brief History of Mathematics
    — Philosphers Arms
    — In Our Time
    – Inquiring Minds podcast
    Guests like: Simon Singh, Jordan Ellenberg


  80. Chris
    May 25, 2017 at 12:41 am

    We are the folks who read math books for fun. We are not weird, we are interesting. I make no apologies.

    Who else would understand that knitting, crocheting, macrame and sewing are examples of applied topology? Forty years ago I used my Home Ec sewing ed. as examples of engineering design in a freshman intro engineering design course. Seriously, it applies!

    Also, I just finished a mobius scarf with two twists. The fabric had a shiny side and a matte side, so there was no transition between matte to shiny. It is definitely not “infinite”, but still kind of twisty. I did this because it was ombre dyed silk, and to make the transition between the colors (blue white green) more consistent I cut it into two pieces and made sure to sew blue to blue and green to green. It made a longer more narrow scarf… but still interesting. But definitely two distinct sides.

    When I mentioned this to another sewing friend she tried to correct me by saying it was an “infinite” scarf. Le sigh. She is a lawyer. Plus when she had to move back home to take care of her mother she gave me a $100 gift certificate to a fabric store from her previous employer, which I spent on silk for mobius scarves. I was not going to argue with her.


  81. Ross
    May 30, 2017 at 10:35 pm

    Michael Harris’ Mathematics Without Apologies.

    Erudite, fun, plenty of number theory, gossip, philosophy, heavily and intelligently footnoted.

    A lovely book.


    • albanius
      November 27, 2020 at 2:00 am

      Harris’ title alludes to Hardy’s classic A Mathematicians Apology.
      I read it mostly to learn what I could about recent developments, especially by Grothendieck and Langlands. It coruscates with brilliance, continually going off on hyperbolic tangents toward obscure but fascinating topics. That practice interrupts the flow of the exposition, making it a very difficult read — a whole less than the sum of its parts IMO.


  82. PaMar
    September 19, 2018 at 7:37 am

    I would suggest Logicomix, too.


  83. Skiwi
    September 27, 2018 at 9:58 pm

    I’d suggest Martin Gardner –


  84. Kate Georges
    February 3, 2019 at 4:03 pm

    For a book on higher math learning, I’d suggest The Definitive Guide to Learning Higher Mathematics, it’s from a smaller publisher, but their perspectives on learning and higher math are nontheless very refreshing.


  85. Thomas Wittlinger
    February 7, 2019 at 2:45 am

    >Essai Philosophique sur les Probabilit ́es< (Pierre-Simon de Laplace)
    “Laplace’s theories of cognitive illusions, heuristics, and biases” (Miller, Gelmann 2019)
    Yep ~ […] “A look at Laplace’s theories andreasoning is striking…”

    Click to access laplace21.pdf


  86. John Jones
    June 8, 2019 at 10:11 am

    I’d like to recommend “Mathematics made Difficult” by Carl E. Linderholm, Wolfe Publishing, London, 1971. It’s currently out of print, but a scanned version is available at

    Click to access math_hard.pdf

    It is not a suitable introduction to mathematics; in fact, it is largely incomprehensible without college-level math, and even if you have college-level math, you will not learn a lot from it. On the other hand, it is very funny, and deals with many questions other math books gloss over, such as whether the numbers we use for counting are the same numbers that we use for addition.


  87. RCD
    September 11, 2020 at 2:59 pm

    I got quite a bit out of Velleman’s “How to Prove It” and loved “A Tour of the Calculus” by Berlinski, whose prose was really fantastic.


  88. robj
    September 12, 2020 at 4:41 am

    “The Calculus Gallery: Masterpieces from Newton to Lebesgue” is another excellent book by William Dunham.


  89. November 13, 2021 at 9:20 pm

    Proofs and Refutations is a marvelous book, which everyone should read. For one thing, it tells us that even the good and great get it wrong sometimes, though they usually get definitions wrong and not theorems.


  90. January 25, 2023 at 4:57 pm

    Weapons of Math Destruction is a really good read for me of a subject I would not have thought capable of reading. Thank you


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