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Foolproof, and Other Mathematical Meditations
A non-mathematician explores mathematical terrain, reporting accessibly and engagingly on topics from Sudoku to probability.
Brian Hayes wants to convince us that mathematics is too important and too much fun to be left to the mathematicians. Foolproof, and Other Mathematical Meditations is his entertaining and accessible exploration of mathematical terrain both far-flung and nearby, bringing readers tidings of mathematical topics from Markov chains to Sudoku. Hayes, a non-mathematician, argues that mathematics is not only an essential tool for understanding the world but also a world unto itself, filled with objects and patterns that transcend earthly reality. In a series of essays, Hayes sets off to explore this exotic terrain, and takes the reader with him.
Math has a bad dull, difficult, detached from daily life. As a talking Barbie doll opined, “Math class is tough.” But Hayes makes math seem fun. Whether he's tracing the genealogy of a well-worn anecdote about a famous mathematical prodigy, or speculating about what would happen to a lost ball in the nth dimension, or explaining that there are such things as quasirandom numbers, Hayes wants readers to share his enthusiasm. That's why he imagines a cinematic treatment of the discovery of the Riemann zeta function (“The 1972. The Afternoon tea in Fuld Hall at the Institute for Advanced Study in Princeton, New Jersey”), explains that there is math in Sudoku after all, and describes better-than-average averages. Even when some of these essays involve a hike up the learning curve, the view from the top is worth it.
Brian Hayes wants to convince us that mathematics is too important and too much fun to be left to the mathematicians. Foolproof, and Other Mathematical Meditations is his entertaining and accessible exploration of mathematical terrain both far-flung and nearby, bringing readers tidings of mathematical topics from Markov chains to Sudoku. Hayes, a non-mathematician, argues that mathematics is not only an essential tool for understanding the world but also a world unto itself, filled with objects and patterns that transcend earthly reality. In a series of essays, Hayes sets off to explore this exotic terrain, and takes the reader with him.
Math has a bad dull, difficult, detached from daily life. As a talking Barbie doll opined, “Math class is tough.” But Hayes makes math seem fun. Whether he's tracing the genealogy of a well-worn anecdote about a famous mathematical prodigy, or speculating about what would happen to a lost ball in the nth dimension, or explaining that there are such things as quasirandom numbers, Hayes wants readers to share his enthusiasm. That's why he imagines a cinematic treatment of the discovery of the Riemann zeta function (“The 1972. The Afternoon tea in Fuld Hall at the Institute for Advanced Study in Princeton, New Jersey”), explains that there is math in Sudoku after all, and describes better-than-average averages. Even when some of these essays involve a hike up the learning curve, the view from the top is worth it.
248 pages, Kindle Edition
Published September 22, 2017
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750 people want to read
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Displaying 1 - 16 of 16 reviews
November 19, 2017
The last time I enjoyed a popular maths book as much as this one was reading Martin Gardner’s Mathematical Puzzles and Diversions as a teenager. The trouble with a lot of ‘fun’ maths books is that they cover material that mathematicians consider fascinating, such as pairs of primes that are only two apart, which fail to raise much excitement in normal human beings.
Here, all the articles have something a little more to them. So, even though Brian Hayes may be dealing with something fairly abstruse-sounding like the ratio of the volume of an n-dimensional hypersphere to the smallest hypercube that contains it, the article always has an interesting edge - in this case that although the ‘volume’ of the hypersphere grows up to the fifth dimension it gets smaller and smaller thereafter, becoming an almost undetectable part of the hypercube.
If that doesn’t grab you, many articles in this collection aren’t as abstruse, covering everything from random walks to a strange betting game. What's more, an extra delight for me is that Hayes throws in a lot of computing reflections, even including snippets of code as a way of explaining some processes. I particularly loved the exploration of pseudorandom and quasirandom numbers (not the same thing) and their implications for Monte Carlo methods.
The only times I felt Hayes loses it a bit is when he gets too heavily into research mode and gives us more detail than we need. For example, he digs into the origins of the story of the young Gauss adding up 1 to 100 almost instantaneously at school. His exploration of this mathematical legend is impressive, but he enumerates every possible source and route for the various versions of the legend to have originated, taking us to a level that feels unnecessarily complete. Similarly he lost me a bit when he tries to forensically examine why a Victorian mathematician who calculated pi to 707 places went wrong from the errors that he made in his calculations. But this kind of over-detailed analysis is rare.
I suspect the ideal reader is someone who has an aged physics, maths or computer science degree, who is still aware of (say) what Monte Carlo methods or eigenvalues are in a vague sense, but needs some gentle reminders. The essential, however, is to have a sense of wonder in discovery. For people like us it’s a brilliant book.
Here, all the articles have something a little more to them. So, even though Brian Hayes may be dealing with something fairly abstruse-sounding like the ratio of the volume of an n-dimensional hypersphere to the smallest hypercube that contains it, the article always has an interesting edge - in this case that although the ‘volume’ of the hypersphere grows up to the fifth dimension it gets smaller and smaller thereafter, becoming an almost undetectable part of the hypercube.
If that doesn’t grab you, many articles in this collection aren’t as abstruse, covering everything from random walks to a strange betting game. What's more, an extra delight for me is that Hayes throws in a lot of computing reflections, even including snippets of code as a way of explaining some processes. I particularly loved the exploration of pseudorandom and quasirandom numbers (not the same thing) and their implications for Monte Carlo methods.
The only times I felt Hayes loses it a bit is when he gets too heavily into research mode and gives us more detail than we need. For example, he digs into the origins of the story of the young Gauss adding up 1 to 100 almost instantaneously at school. His exploration of this mathematical legend is impressive, but he enumerates every possible source and route for the various versions of the legend to have originated, taking us to a level that feels unnecessarily complete. Similarly he lost me a bit when he tries to forensically examine why a Victorian mathematician who calculated pi to 707 places went wrong from the errors that he made in his calculations. But this kind of over-detailed analysis is rare.
I suspect the ideal reader is someone who has an aged physics, maths or computer science degree, who is still aware of (say) what Monte Carlo methods or eigenvalues are in a vague sense, but needs some gentle reminders. The essential, however, is to have a sense of wonder in discovery. For people like us it’s a brilliant book.
April 25, 2023
Perché la matematica dà sempre sorprese
Nelle prime righe di questo libro Hayes scrive "la matematica è troppo divertente per essere lasciata solo ai matematici". Aggiunge inoltre che lui non è un cittadino di Matelandia, ma una persona che si è trasferita lì e ha cercato di comprendere usi e costumi dei suoi cittadini. In effetti la sua formazione è più da informatico, tanto che negli anni '80 teneva la rubrica di Computer Recreations sullo Scientific American, mentre ora scrive su American Scientist. Lo troviamo così a dissezionare il famosissimo aneddoto di Gauss bimbetto e la somma della serie di numeri trovata al volo, tracciando le innumerevoli versioni per capire come il folklore matematico abbia man mano abbellito la storia; nel frattempo spiega come la differenza tra l'approccio del giovane Carl Frederick e quello di un programma al computer abbia ripercussioni importanti. Ma molte di queste meditazioni matematiche, pur non entrando a fondo nella teoria sottostante, sono davvero interessanti: segnalo quella sui numeri quasicasuali, sullo spettro del Riemannio (una correlazione a prima vista inimmaginabile tra gli zeri della zeta di Riemann e gli spettri degli elementi chimici), su un modo alternativo alla virgola mobile di memorizzare i numeri su un computer, che permette di aumentare l'ampiezza dei numeri rappresentabili conservando una estrema precisione nei valori prossimi allo zero, e soprattutto il gioco di Zenone. Una gioia per appassionati e semplici turisti!
Nelle prime righe di questo libro Hayes scrive "la matematica è troppo divertente per essere lasciata solo ai matematici". Aggiunge inoltre che lui non è un cittadino di Matelandia, ma una persona che si è trasferita lì e ha cercato di comprendere usi e costumi dei suoi cittadini. In effetti la sua formazione è più da informatico, tanto che negli anni '80 teneva la rubrica di Computer Recreations sullo Scientific American, mentre ora scrive su American Scientist. Lo troviamo così a dissezionare il famosissimo aneddoto di Gauss bimbetto e la somma della serie di numeri trovata al volo, tracciando le innumerevoli versioni per capire come il folklore matematico abbia man mano abbellito la storia; nel frattempo spiega come la differenza tra l'approccio del giovane Carl Frederick e quello di un programma al computer abbia ripercussioni importanti. Ma molte di queste meditazioni matematiche, pur non entrando a fondo nella teoria sottostante, sono davvero interessanti: segnalo quella sui numeri quasicasuali, sullo spettro del Riemannio (una correlazione a prima vista inimmaginabile tra gli zeri della zeta di Riemann e gli spettri degli elementi chimici), su un modo alternativo alla virgola mobile di memorizzare i numeri su un computer, che permette di aumentare l'ampiezza dei numeri rappresentabili conservando una estrema precisione nei valori prossimi allo zero, e soprattutto il gioco di Zenone. Una gioia per appassionati e semplici turisti!
October 26, 2023
I've learned to take publisher's blurbs with a grain of salt, but the one for Foolproof describes exactly what this interesting book delivers. Hayes is a scientist and writer, one who has the unique ability to make math understandable and accessible to non-mathematicians, and he has written a book that is accurate, informative, and highly enjoyable. His enthusiasm makes the reader want to truly understand the topics he covers in these 13 essays. I enjoyed and learned from each one of them, with the last one about proof in mathematics being my favorite. Who wouldn't love a discussion about proofs that prove something is impossible?
The best popular math book that I have read previously is How Not to be Wrong by Jordan Ellenberg. Foolproof deserves a place right next to it on the shelf of excellent mathematics books.
The best popular math book that I have read previously is How Not to be Wrong by Jordan Ellenberg. Foolproof deserves a place right next to it on the shelf of excellent mathematics books.
June 13, 2020
The chapters in this book had their origin in articles published by the author in the American Scientist magazine between 1998 and 2014. It consists in a very fine selection of topics on Mathematics and mathematical related topics, some bent on the historical (like the one about the legend of young Gauss summing the terms of an arithmetic progression, or the one about Markov work on Pushkin's poem Eugene Oneguin), others about strange, somewhat counterintuitive behaviors (like the factoidal distribution, or Zeno's wagering game). Even those about more standard stuff (so to speak), like the one titled "Playing ball in the nth dimension" have some nice surprises waiting the reader. I found this a very stimulating book on popularization of Mathematics.
March 17, 2020
Hayes is to math what Mary Roach is to science: a tour guide I'd follow anywhere. Thoroughly researched, sparklingly written. A total charmer.
September 28, 2019
Interesting... Skimmed some. Like through the multiple pages of historical research on the short story of young gauss.. Also skimmed the many pages on factoidal randomness etc... I agree with the author on his point about history of rigorous study in math history Instead of justskipping that and just telling of the glorified "aha" moments making it seem like it didn't dome from work and study :)... I wish I had a list to share but knowing the man behind the math does make it easier to remember for me... Back when I was spending long nights doing math homework I wrote a few history papers etc for english classes about math history etc... That really helped me... Aced that cal1 and cal2 class and still remember the struggle...
January 21, 2022
I guess I wish I was smart enough to love this book? Back in the day, I was the type of student who got annoyed with that other student who kept asking “But WHY do we have to learn about this??” With this book, I became that other student.
I found some of the essays harder to follow than others and it felt like the point of this writing was just beyond my reach for a lot of the time. I couldn’t truly follow a lot of the roundabout stories/tangents (no pun intended). It did make me laugh a couple of times though. It was not the book I had hoped it would be or maybe I’m not the math nerd I thought I was?
I found some of the essays harder to follow than others and it felt like the point of this writing was just beyond my reach for a lot of the time. I couldn’t truly follow a lot of the roundabout stories/tangents (no pun intended). It did make me laugh a couple of times though. It was not the book I had hoped it would be or maybe I’m not the math nerd I thought I was?
May 7, 2022
The author - a past columnist of Scientific American - explores the mathematical terrain : topics ranging from Markov chains to Sudoku. He traces the genealogy of well-worn anecdotes about a famous mathematical prodigy, speculates about what would happen to a lost ball in the nth dimension, talks about the role of randomness, pseudo-randomness, quasi randomness in Mathematics. While some of the expositions require a good knowledge of mathematics and could be heavy reading, one gets a good overview and appreciation of the topic even though it could heavy trundling through the article in some cases.
June 27, 2019
An interesting survey of a number of topics in mathematics, with some counterintuitive results in probability and in n dimensional geometry. My mathematics is a bit rusty but I could understand most of the reasoning. This a a good book for those who want to have a broader knowledge of the different areas of mathematics and be surprised by some contradictions or results. The author gives the history behind each area which made each topic more understandable and interesting.
August 20, 2021
I found the marketing on this book quite misleading since I still found it very heavy and not easy to understand (despite being written by a "non-mathematician") and many of the topics I also just thought were really not interesting if you're not hardcore into maths.
I wrote "How Not to Be Wrong: The Power of Mathematical Thinking" by Jordan Ellenberg and that was much more what I was looking for. Highly recommend that book.
I wrote "How Not to Be Wrong: The Power of Mathematical Thinking" by Jordan Ellenberg and that was much more what I was looking for. Highly recommend that book.
December 27, 2019
I was a bit concerned, at first, about how much Hayes makes of not being a mathematician. That's usually a signal that maths is about to be dismissed or misunderstood - but on the contrary, the outsider's viewpoint makes Foolproof fascinating. The topics it covers are all either new to me or covered in a way that's unusual, and I rate this book very highly.
December 18, 2020
The premise of the book was that Brian as a non mathematician was writing for other non mathematicians about math. It was comprised of 13 separate topics, about a quarter which I found interesting, and others fell flat. One a few topics, he got way too far into the weeds and for someone not familiar with math, may get lost.
August 18, 2020
Like another reviewer said this is one of the best pop-math books I’ve read. Everything is fresh and there’s little repetition of common stories and mathematics that are often repeated in other pop-math books.
April 28, 2024
One of the better collections of mathematical essays that I've read. A great selection of topics with some absolute bangers including the encoding of DNA and quasirandom numbers. It did feel a little lacking in the maths department.
May 6, 2018
More sophisticated than typical recreational mathematics books
October 18, 2023
Some great math history as well as clever problem-solving.
Displaying 1 - 16 of 16 reviews