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Mathematics: Without the Boring Bits
Can you outrun a bullet?
How do you build an electronic brain?
Could you slow down time?
How do you unleash chaos?
From Plato's classification of regular polyhedra to making a million on the stock market, How to Solve the Da Vinci Code gives you everything you need to understand how numbers work, and the impact they have on our lives every day.
How do you build an electronic brain?
Could you slow down time?
How do you unleash chaos?
From Plato's classification of regular polyhedra to making a million on the stock market, How to Solve the Da Vinci Code gives you everything you need to understand how numbers work, and the impact they have on our lives every day.
223 pages, Hardcover
First published December 30, 2010
20 people are currently reading
195 people want to read
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Displaying 1 - 14 of 14 reviews
April 6, 2015
Really, it’s my fault that mathematics gets such a bad rap.
And by me, I mean math teachers in general. And by math teachers, I actually mean the pedagogical paradigm in which most of us are embedded, and the questionable premises of the educational system that encourages such pedagogy. Math anxiety is often caused by general test anxiety, combined with a lingering sensation that there is “one right answer,” as well as a misunderstanding what math is and how we use it. Other factors: parents communicating anxiety/resisting innovative ways of teaching, and a generalized anti-intellectual snobbery in our society in which those who are interested in how the world works are “geeks” and “nerds.” (This is independent of the fact that, in recent years, geekdom and nerdery has become trendy. Capitalist structures might be co-opting the symbols and fashions of geek culture, but that doesn’t translate into broader tolerance or embracing of geek interests.)
With How to Solve the Da Vinci Code and 34 Other Really Interesting Uses of Mathematics (I hate the title), Richard Elwes sets out to make some of the most important fields or problems in math more accessible to the layperson. This is a worthy goal. From the titles of his other books, it looks like this is Elwes’ pet cause: he likes to break mathematics into small but fascinating facts, problems, or ideas that he can explore in five-minute chunks. As a result, this is the sort of book you can dip in and out of, say at bedtime, for a number of evenings. You don’t have to remember a lot or pay attention to a plot.
Nor does Elwes demand much in the way of memory or understanding. He covers some of the basics of algebra in the earlier chapters, but even understanding those is not a requirement. This book doesn’t so much teach you mathematics as it describes the different types and fields of mathematics and some of the most interesting results or problems from them. Perhaps the most complicated concept you really want to understand is prime numbers: if you know what those are, then you’re good.
Some of Elwes’ explanations are great. Within this are many “standard” explanations that I’ve seen before and skimmed—that being said, I am a mathematician and a math educator and a math enthusiast, so what’s familiar to me is not necessarily familiar to you, and this might be someone’s first exposure to Russell’s paradox or the theory of sets or graph theory. So that’s not a negative in my book, just an observation that the more mathematically-inclined have likely come across most of the content here, in one place or another.
On a related note, I want to stress that this really is a survey of mathematical results. Some chapters are longer than others, but none go into the type of depth one wants for a truly comprehensible explanation of what’s going on. To reiterate: you won’t learn a lot of math here; you’ll learn about math. Also valuable and important, but it’s a keen distinction.
For me, some of the highlights were: Chapter 7, “How to unleash chaos” (chaotic systems and strange attractors); Chapter 15, “How to arrange the perfect dinner party” (Ramsey’s theorem); Chapter 18, “How to draw an impossible triangle” (non-Euclidean geometry); Chapter 19, “How to unknot your DNA” (knot theory); and Chapter 23, “How to build the perfect beehive” (2D/3D tesselation and packing). I like these chapters because they taught me something or reminded me of something I had forgotten, or Elwes’ explanations are particularly thoughtful and useful. For example, the knot theory chapter doesn’t just talk about knots—as the title implies, he mentions DNA, enzymes, proteins, etc. It’s a reminder that mathematical discoveries end up having applications in places you wouldn’t suspect.
That’s another thing that this book does well. In chapters such as the one on the four-colour theorem, or Benford’s law, Elwes emphasizes two important and related things about mathematics. Firstly, mathematical discoveries don’t always happen in isolation or as strokes of genius. We tend to tell those stories, because they are exciting. But for something like Benford’s law or the four-colour theorem, the discoveries build on decades (or centuries) of work. Several mathematicians independently notice something cool, make a conjecture, fail to prove it, and discard it—only for another generation to succeed where they didn’t. Math is a progressive, ongoing effort.
And something we don’t make clear often enough in the classroom is that new mathematical research is still ongoing at a furious pace. We present math as an accomplished, finished product: here’s how you find the missing side of a triangle; the Babylonians knew how to do it, and now you do too! But like science, mathematics isn’t a stable set of knowledge. It behoves us to raise awareness among the general public of how people research math and what we still research. Elwes points to the Clay Institute’s Millennium Prizes as one example. He also mentions a few other questions that remain open problems. While it’s true that genuine mathematics research is not for the faint of heart or the interested amateur, that tends to be true of any specialized discipline. Math is not necessarily more difficult or special in this regard.
How to Solve the Da Vinci Code is not the warmest of math books I’ve read. Elwes’ tone is conversational, yes, and has a hint of humour to it. However, the broad strokes of his descriptions necessarily make them less personal than they might otherwise be. He tells a story in most of the chapters, but it’s not with the same level of vivacity that other authors often employ. Instead, his style is one step up from an encyclopedia article. Again, this isn’t really a positive or negative in and of itself—it depends on what you want from a book like this. I, personally, want to know more about the author. I want to know where they’re coming from, what interests them, and hear them tell the story of mathematics from their perspective. We don’t get that here—Elwes never inserts himself into the text—and I feel like that’s unfortunate. But others might find it more objective and informative.
Would I recommend? Not for someone like me, who has read a lot of math books and studied math. For neophytes and laypeople? Maybe, depending on the person. I’d rather find a book that gets them more excited about one specific thing, rather than throw everything at them like Elwes does here. Maybe this book is best for someone who already likes math, has a passing interest or understanding of it, and wants to sort of survey the field and see what kinds of things are out there. In that case, there’s definitely 35 good ideas here.
And by me, I mean math teachers in general. And by math teachers, I actually mean the pedagogical paradigm in which most of us are embedded, and the questionable premises of the educational system that encourages such pedagogy. Math anxiety is often caused by general test anxiety, combined with a lingering sensation that there is “one right answer,” as well as a misunderstanding what math is and how we use it. Other factors: parents communicating anxiety/resisting innovative ways of teaching, and a generalized anti-intellectual snobbery in our society in which those who are interested in how the world works are “geeks” and “nerds.” (This is independent of the fact that, in recent years, geekdom and nerdery has become trendy. Capitalist structures might be co-opting the symbols and fashions of geek culture, but that doesn’t translate into broader tolerance or embracing of geek interests.)
With How to Solve the Da Vinci Code and 34 Other Really Interesting Uses of Mathematics (I hate the title), Richard Elwes sets out to make some of the most important fields or problems in math more accessible to the layperson. This is a worthy goal. From the titles of his other books, it looks like this is Elwes’ pet cause: he likes to break mathematics into small but fascinating facts, problems, or ideas that he can explore in five-minute chunks. As a result, this is the sort of book you can dip in and out of, say at bedtime, for a number of evenings. You don’t have to remember a lot or pay attention to a plot.
Nor does Elwes demand much in the way of memory or understanding. He covers some of the basics of algebra in the earlier chapters, but even understanding those is not a requirement. This book doesn’t so much teach you mathematics as it describes the different types and fields of mathematics and some of the most interesting results or problems from them. Perhaps the most complicated concept you really want to understand is prime numbers: if you know what those are, then you’re good.
Some of Elwes’ explanations are great. Within this are many “standard” explanations that I’ve seen before and skimmed—that being said, I am a mathematician and a math educator and a math enthusiast, so what’s familiar to me is not necessarily familiar to you, and this might be someone’s first exposure to Russell’s paradox or the theory of sets or graph theory. So that’s not a negative in my book, just an observation that the more mathematically-inclined have likely come across most of the content here, in one place or another.
On a related note, I want to stress that this really is a survey of mathematical results. Some chapters are longer than others, but none go into the type of depth one wants for a truly comprehensible explanation of what’s going on. To reiterate: you won’t learn a lot of math here; you’ll learn about math. Also valuable and important, but it’s a keen distinction.
For me, some of the highlights were: Chapter 7, “How to unleash chaos” (chaotic systems and strange attractors); Chapter 15, “How to arrange the perfect dinner party” (Ramsey’s theorem); Chapter 18, “How to draw an impossible triangle” (non-Euclidean geometry); Chapter 19, “How to unknot your DNA” (knot theory); and Chapter 23, “How to build the perfect beehive” (2D/3D tesselation and packing). I like these chapters because they taught me something or reminded me of something I had forgotten, or Elwes’ explanations are particularly thoughtful and useful. For example, the knot theory chapter doesn’t just talk about knots—as the title implies, he mentions DNA, enzymes, proteins, etc. It’s a reminder that mathematical discoveries end up having applications in places you wouldn’t suspect.
That’s another thing that this book does well. In chapters such as the one on the four-colour theorem, or Benford’s law, Elwes emphasizes two important and related things about mathematics. Firstly, mathematical discoveries don’t always happen in isolation or as strokes of genius. We tend to tell those stories, because they are exciting. But for something like Benford’s law or the four-colour theorem, the discoveries build on decades (or centuries) of work. Several mathematicians independently notice something cool, make a conjecture, fail to prove it, and discard it—only for another generation to succeed where they didn’t. Math is a progressive, ongoing effort.
And something we don’t make clear often enough in the classroom is that new mathematical research is still ongoing at a furious pace. We present math as an accomplished, finished product: here’s how you find the missing side of a triangle; the Babylonians knew how to do it, and now you do too! But like science, mathematics isn’t a stable set of knowledge. It behoves us to raise awareness among the general public of how people research math and what we still research. Elwes points to the Clay Institute’s Millennium Prizes as one example. He also mentions a few other questions that remain open problems. While it’s true that genuine mathematics research is not for the faint of heart or the interested amateur, that tends to be true of any specialized discipline. Math is not necessarily more difficult or special in this regard.
How to Solve the Da Vinci Code is not the warmest of math books I’ve read. Elwes’ tone is conversational, yes, and has a hint of humour to it. However, the broad strokes of his descriptions necessarily make them less personal than they might otherwise be. He tells a story in most of the chapters, but it’s not with the same level of vivacity that other authors often employ. Instead, his style is one step up from an encyclopedia article. Again, this isn’t really a positive or negative in and of itself—it depends on what you want from a book like this. I, personally, want to know more about the author. I want to know where they’re coming from, what interests them, and hear them tell the story of mathematics from their perspective. We don’t get that here—Elwes never inserts himself into the text—and I feel like that’s unfortunate. But others might find it more objective and informative.
Would I recommend? Not for someone like me, who has read a lot of math books and studied math. For neophytes and laypeople? Maybe, depending on the person. I’d rather find a book that gets them more excited about one specific thing, rather than throw everything at them like Elwes does here. Maybe this book is best for someone who already likes math, has a passing interest or understanding of it, and wants to sort of survey the field and see what kinds of things are out there. In that case, there’s definitely 35 good ideas here.
April 4, 2022
Gives an inspiring, but very brief, introduction to a variety of areas within the mathematical realm. I really enjoyed reading these short essays on topics ranging from chaos theory to the mathematics of knots. Very little previous mathematical knowledge is needed in order to be able to appreciate this book.
July 28, 2012
Despite what the introduction claims, I'm not sure how "accessible" this book is to non-mathphiles. But for me (with a life-long fascination with numbers and 16 years in the classroom teaching mathematics) it was a terrific collection of short essays on numerous topics, including the dinner party problem, the four-color map problem, Cantor's theory of sets, and lots more. This book has the single best explanation of Euler's Formula (e^iπ + 1 = 0) that I've ever seen in print. And it completely blew my mind showing Ramanujan and Hardy's estimate of the number of partitions of any number n. (If you don't know what that means, the book actually does a very good job explaining that particular topic.) My only qualms with the book were a few over-simplifications, which were no doubt done to make the text more "accessible" but unfortunately led to some inaccuracies. Also, the order of the topics seemed really haphazard. Chapter 31 deals with a topic in probability, chapter 32 jumps to physics, and then chapter 33 is back onto another probability topic. These are small criticisms, though - overall, this was a very enjoyable read, highly recommended for all lovers of math.
June 26, 2012
A cute little maths book highlighting some interesting stories and tidbits about popular maths concepts. The initial chapter (on how to solve every equation there has ever been) was really well written and that and the chapter on Zeno's paradox were quite topical for me as they were things I was currently discussing in the classroom and it gave me some food for thought.
Overall though, the book suffers in that it doesn't really have a well defined audience. It left me frustrated by simplifying many concepts and for not getting gritty enough. It could be argued that this is not a book for people who know maths already, but the book does make a few big jumps in explanations making it a little difficult for the novice. To me, it was a book that didn't know what type of book it wanted to be.
Each chapter covers an independent topic. This frustrated me as I like to go on a journey with a book from the first page to the last page. This one was like reading 34 short stories. Strangely unsatisfying....
Overall though, the book suffers in that it doesn't really have a well defined audience. It left me frustrated by simplifying many concepts and for not getting gritty enough. It could be argued that this is not a book for people who know maths already, but the book does make a few big jumps in explanations making it a little difficult for the novice. To me, it was a book that didn't know what type of book it wanted to be.
Each chapter covers an independent topic. This frustrated me as I like to go on a journey with a book from the first page to the last page. This one was like reading 34 short stories. Strangely unsatisfying....
December 23, 2022
Applied Math with a fun twist
The title “Mathematics without the Boring Bits” may be misread. It is not math for dummies or math for idiots or math without math.
I have encountered many math books that have a solution that did not need math and work backward in calculus or geometry or some other odd math discipline so that the student can use this discipline to locate the solution. Most real math problems are solved a lot more simpler in the real world. For example, how much airplane material does it take to make a 60-foot aircraft? Come on “Airplane material.” Give me a break.
Each discipline has its own language and methods. We keep remembering functions as Pi yet all the real calculations for volume are done in ¼ Pi or 0.785398163. An easy way to remember is to take 6 and go two up (78) then take 6 and go two down (54) or 0.7854 Place this number in a search engine and you will instantly see the truth of the matter.
This book cuts through the gobbledygook and still uses math to help us get an understanding of 35 key math ideas. In the process, it still uses practical math. Luckily if you forgot most of the math or are starting from scratch the book will bring you up to speed in a genital way.
There are lots of “marginal” diagrams to help. A great glossary and much other supporting information. The subject titles may be a little kitschy, however, the innards on each subject will allow you to go way beyond magazine articles and hold your own with any digital geek. Most of the concepts allow you to see the real world and are not just math games.
Again here are the kitschy titles just keep in mind underneath the title descriptions are real worthwhile concepts:
How to unleash chaos
How to survive a whirlpool
How to make a million on the stock market
How to outrun a speeding bullet
How to solve every equation there has ever been
How to slay a mathematical monster
How to excel at Sudoku
How to solve the Da Vinci Code
How to admire a mathematical masterpiece
How to count like a supercomputer
How to visit 100 cities in one day
How to arrange the perfect dinner party
How to paint the world in four colors
How to be alive and dead at the same time
How to draw an impossible triangle
How to unknot your DNA
How to find holes in the universe
How to feel at home in five dimensions
How to count to infinity
How to build a brain
How to bring down the Internet
How to ask an unanswerable question
How to avoid prison
How to mislead a jury
How to slow time
How to win at roulette
How to have beautiful children
How to talk to a computer
How to become a celebrity mathematician
How to square a circle
How to win the ultimate math prize
How to design a beautiful pattern
How to build the perfect beehive
How to detect fraud
How to create an unbreakable code
Do not let Homeland Security catch you reading the last subject.
The title “Mathematics without the Boring Bits” may be misread. It is not math for dummies or math for idiots or math without math.
I have encountered many math books that have a solution that did not need math and work backward in calculus or geometry or some other odd math discipline so that the student can use this discipline to locate the solution. Most real math problems are solved a lot more simpler in the real world. For example, how much airplane material does it take to make a 60-foot aircraft? Come on “Airplane material.” Give me a break.
Each discipline has its own language and methods. We keep remembering functions as Pi yet all the real calculations for volume are done in ¼ Pi or 0.785398163. An easy way to remember is to take 6 and go two up (78) then take 6 and go two down (54) or 0.7854 Place this number in a search engine and you will instantly see the truth of the matter.
This book cuts through the gobbledygook and still uses math to help us get an understanding of 35 key math ideas. In the process, it still uses practical math. Luckily if you forgot most of the math or are starting from scratch the book will bring you up to speed in a genital way.
There are lots of “marginal” diagrams to help. A great glossary and much other supporting information. The subject titles may be a little kitschy, however, the innards on each subject will allow you to go way beyond magazine articles and hold your own with any digital geek. Most of the concepts allow you to see the real world and are not just math games.
Again here are the kitschy titles just keep in mind underneath the title descriptions are real worthwhile concepts:
How to unleash chaos
How to survive a whirlpool
How to make a million on the stock market
How to outrun a speeding bullet
How to solve every equation there has ever been
How to slay a mathematical monster
How to excel at Sudoku
How to solve the Da Vinci Code
How to admire a mathematical masterpiece
How to count like a supercomputer
How to visit 100 cities in one day
How to arrange the perfect dinner party
How to paint the world in four colors
How to be alive and dead at the same time
How to draw an impossible triangle
How to unknot your DNA
How to find holes in the universe
How to feel at home in five dimensions
How to count to infinity
How to build a brain
How to bring down the Internet
How to ask an unanswerable question
How to avoid prison
How to mislead a jury
How to slow time
How to win at roulette
How to have beautiful children
How to talk to a computer
How to become a celebrity mathematician
How to square a circle
How to win the ultimate math prize
How to design a beautiful pattern
How to build the perfect beehive
How to detect fraud
How to create an unbreakable code
Do not let Homeland Security catch you reading the last subject.
March 13, 2021
Really enjoyed this book for what it is. Each section is only a few pages long with a somewhat brief summary of a mathematical idea with the history of it explained, each section is like a little story and the way the author writes changes this from what could have been a boring look at math into something a little more interesting. Granted the ideas aren't massively fleshed out in the instances where they could be (some of the ideas are more complex than others) but you can hardly complain about that. Most the ideas were ones I'm already quite familiar with but I enjoyed reading little bits of history on them that I may not have known. If you've done certain puzzles or played games such as the ones in the Professor Layton games you'll also recognise some of these but this added and explains some of the mathematical elements to them which was fun as most the bigger ideas in this book (chaos theory, fractals, game theory, Fibonacci sequence, game of life, etc) are already quite well established in the more geeky parts of the internet.
July 29, 2018
Interesting and inspiring, linking some fundamental maths to the real world in bite size digestible chunks. After reading some of the sections I discussed interesting aspects with my boys (11 and 14) over breakfast, some of which was listened to a bit!
January 17, 2021
An eye opening book
May 9, 2015
Questo libro è stato pubblicato con una varietà di nomi diversi: magari l'avete visto intitolato "How to solve the DaVinci code", oppure "Math without the boring bits". (O più probabilmente non l'avete visto, di Elwes forse uscirà prima o poi Maths 1001 per Newton Compton). Ma è sempre lo stesso libro, facente parte della collana di Quercus "35 interesting uses of". Devo dire che in questa sua prima prova editoriale Elwes mi è parso ancora acerbo come divulgatore. Ovviamente non è colpa sua se alcuni di questi usi della matematica non sono poi così interessanti: però ho notato che più di una volta ha usato le ultime righe di uno dei capitoletti per accennare a generalizzazioni del tema. L'idea immagino fosse quella di far capire al lettore che non ci si ferma certo ai risultati mostrati in quelle poche pagine in gabbia fissa; il risultato pratico è che al lettore resta l'impressione di un libro tagliato a metà. Da questo punto di vita è molto meglio il suo Maths 1001, dove le definizioni in pillole sono così tante che è possibile ricomporre comunque un mosaico della matematica.
September 4, 2015
It's a good book for people who have an interest in mathematics. With lots of short chapters it is a good book to read in short chunks. I felt that was quite easy to dip into one or two chapters on the train in the morning. The fact that the chapters were treated separately is quite good if you are busy person and are likely to lose the plot of a book if you put it down a lot.
Richard Elwes sets out to make maths more accessible to "non-nerds", which don't get me wrong it's a good thing, however I felt that in places it was over-explained or over-simplified which could make it less interesting to more advanced mathematicians.
Its sarcastic, its amusing and it covers a good selection of interesting problems. (And you don't need to have a degree in maths to understand it!)
Richard Elwes sets out to make maths more accessible to "non-nerds", which don't get me wrong it's a good thing, however I felt that in places it was over-explained or over-simplified which could make it less interesting to more advanced mathematicians.
Its sarcastic, its amusing and it covers a good selection of interesting problems. (And you don't need to have a degree in maths to understand it!)
December 6, 2013
This is a wonderful book. Richard Elwes writes fluently about a subject for which he is clearly passionate. The book cover is a little sensationalist which is a pity; the book is really a whistle-stop tour through many of the most fascinating areas of mathematics, both traditional and modern, outlined in a very clear manner.
Where the book lacks depth(due to inherent complexity of a particular topic), it nonetheless leaves one feeling one has grasped the basics.
When you've finished this book, you will have had a good introduction to the broad sweep of mathematics and have been introduced to many notable mathematicians and their contributions, from Hippasus, through Euler and Hilbert, to Nash.
Where the book lacks depth(due to inherent complexity of a particular topic), it nonetheless leaves one feeling one has grasped the basics.
When you've finished this book, you will have had a good introduction to the broad sweep of mathematics and have been introduced to many notable mathematicians and their contributions, from Hippasus, through Euler and Hilbert, to Nash.
June 23, 2013
Entertaining look at maths principles and their use in the world. He covers a lot of territory, each chapter being just four pages, so I wonder if he had the time to space to get everything in. Certainly there were times when I felt the was a jump in logic that left me scratching my head and wondering how he could say what he just did. Maybe mathematicians would understand how he got there, but I felt I was left behind, usually somewhere down the third page of each article. But overall I enjoyed it.
January 18, 2012
This is a good book to keep around when you want something to read in short bits. It's not a book that you sit down to read cover to cover.
September 27, 2013
Its an entertaining whistlestop tour of some of the more fascinating parts of Maths, but treating each chapter separately means the book repeats itself in places.
Displaying 1 - 14 of 14 reviews