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Il meraviglioso mondo dei numeri
Acuto, ricco di aneddoti, piccole scoperte ed esempi divertenti, Il meraviglioso mondo dei numeri è un viaggio nella sorprendente terra della matematica e della geometria.
Alex Bellos incontra una tribù amazzonica che concepisce solo tre numeri (1, 2 e molti). Vola in Giappone da uno scimpanzè che sa contare. In Germania interroga il più veloce calcolatore mentale del mondo, in India un saggio indù. Risolve il mistero dello zero e dimostra che la diversa percezione del tempo di adulti e bambini è dovuta all'intuizione logaritmica. In uno stile comprensibile e rigoroso, spazia tra storia, filosofia e calcolo, tra paradossi logici e statistici. E dimostra come il mondo della matematica sia molto più variopinto e divertente di quello che di solito immaginiamo.
Alex Bellos incontra una tribù amazzonica che concepisce solo tre numeri (1, 2 e molti). Vola in Giappone da uno scimpanzè che sa contare. In Germania interroga il più veloce calcolatore mentale del mondo, in India un saggio indù. Risolve il mistero dello zero e dimostra che la diversa percezione del tempo di adulti e bambini è dovuta all'intuizione logaritmica. In uno stile comprensibile e rigoroso, spazia tra storia, filosofia e calcolo, tra paradossi logici e statistici. E dimostra come il mondo della matematica sia molto più variopinto e divertente di quello che di solito immaginiamo.
582 pages, Paperback
First published April 5, 2010
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About the author
Alex Bellos
70 books378 followers"I was born in Oxford and grew up in Edinburgh and Southampton. After studying mathematics and philosophy at university I joined the Evening Argus in Brighton as a trainee reporter. I joined the Guardian in 1994 as a reporter and in 1998 moved to Rio de Janeiro, where I spent five years as the paper’s South America correspondent. Since 2003 I have lived in London, as a freelance writer and broadcaster.
[...]
In 2003 I presented a five-part series on Brazil for the BBC, called Inside Out Brazil. My short films about the Amazon have been broadcast on the BBC, More 4 and Al Jazeera International."
[...]
In 2003 I presented a five-part series on Brazil for the BBC, called Inside Out Brazil. My short films about the Amazon have been broadcast on the BBC, More 4 and Al Jazeera International."
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June 14, 2017
This was a mixed bag for me. On one hand it’s an easy read, a beach read if you will, and it covers quite a lot of math’s ground in relatively little space. Most of the anecdotes and stories about former mathematicians I already knew, but it’s nice to have them all in one place. On the other hand the bock sometimes lacks a certain depth. It is noticeable that the author is trying to offer something to readers who have little or nothing to do with numbers and maths. Only those people would probably not want to read the book in the first place. The chapter on gambling (Slot/fruit machines, Roulette, Black-Jack) is too long, and my dear Gödel is missing completely!
A conditional recommendation for people who like to brush up on their maths and not beaten up by formulas.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
A conditional recommendation for people who like to brush up on their maths and not beaten up by formulas.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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December 2, 2016While I was reading this book , I noticed it was published by Bloomsbury and I remembered that a few years ago they were doing rather poorly until J.K.Rowling came along with a seven volume Christian parable for children and magically transformed their financial performance.
I might be the ideal audience for this book - turned off Maths at school, yet still mildly interested, bed bound and unwell , with limited reading choices, however I found it largely uninteresting built up of clusters of not particularly memorable anecdotes which I have, a few months on entirely forgotten. I now know that the maths of the shape of the fifty pence coin is much less interesting than I might have imagined, also that gambling is a mugs game - think I knew that from playing penny up at school or cards with my card counting father, and that the variability of weight of loaves of bread may be affected by sample variance and local factors as much as by the baker making smaller loaves. No magic here, and possibly therefore no magical bonuses for the publisher that year!
I might be the ideal audience for this book - turned off Maths at school, yet still mildly interested, bed bound and unwell , with limited reading choices, however I found it largely uninteresting built up of clusters of not particularly memorable anecdotes which I have, a few months on entirely forgotten. I now know that the maths of the shape of the fifty pence coin is much less interesting than I might have imagined, also that gambling is a mugs game - think I knew that from playing penny up at school or cards with my card counting father, and that the variability of weight of loaves of bread may be affected by sample variance and local factors as much as by the baker making smaller loaves. No magic here, and possibly therefore no magical bonuses for the publisher that year!
June 23, 2015
Alex Bellos is a gifted writer who has embarked on a mission to popularize mathematics. He makes a frank observation that should give pause to any reader: “By age 16, schoolkids have learned almost no math beyond what was already known in the mid-seventeenth century, and likewise by the time they are 18, they have not gone beyond the mid-eighteenth century.” What ensues is both a historical tour and spontaneous encounters with some of the most eccentric people currently operating on the fringes of mathematics.
From its onset, the book is playful. It opens with Chapter Zero rather than the conventional Chapter One. Bellos proceeds with a revelatory anecdote illustrating our own socialized mania for quantification. His overriding theme is that preconceptions shaped by culture and biological hard-wiring are unconsciously embedded in our thinking. “...[U]nderstanding quantities in terms of exact numbers is not a universal intuition; it is a product of culture....[R]atios are much more important for survival in the wild than the ability to count.” Those ratios might include a pride of lions assessing the relative strength of interlopers in their territory, or a monkey assessing which tree will reward the best return of fruit for energy expended. A surprising experiment entailed asking kindergarteners to map numbers along a line. Their lines tended to compress the distances between higher numbers — a logarithmic as opposed to linear depiction. Experiments with an Amazonian tribe showed they judged five dots to be five times more than one dot, but characterized ten dots as two times more than five dots, a distance of five increments vs. two: an understanding of quantity based on ratios, not enumeration.
Bellos's promised excursion begins with the invention of zero, a number so basic to all calculations that it is easy to forget that it needed to be invented. He concludes the journey with a chapter that defies both intuition and cultural pre-conceptions. It is a chapter that discusses Euclid's Fifth Postulate, which came to be reformulated as the Parallel Postulate: “Given a line and a point not on that line, then there is at most one line that goes through the point and is parallel to the original line.” The postulate works for a flat plane (at most one line) and a spherical plane (e.g. there are no straight straight lines passing through the north pole and that are parallel to the equator). Then, Bellos introduces the hyperbolic plane, a surface with negative curvature. It's a construct that almost defies visualization. The example he offers is a localized section that resembles a pringle. Mathematicians are familiar with the form as represented by Professor Daina Taimina's model constructed from crochet work. Even today's 3-D printers cannot replicate her models (http.//3dprint.com/8013/3d-printed-math).
It's a shock to realize that hyperbolic space only gets the reader up to the 19th century. To usher the reader into the 20th century Bellos explores the ideas of Georg Cantor and David Hilbert on infinity. “Cantor's heresy was to treat infinity as an entity in itself.” By working with correspondences between infinite sets he characterized some infinite sets as countable (aleph), and others as non-countable (beth). To complete that leg of the journey, Bellos books us into the marvelous “Hilbert Hotel.”
Between the beginning and end of his book, Bellos covers an eclectic mix of topics. Pythagoras' Theorem, zero, pi, Cartesian coordinates, prime numbers, Fibonnaci's sequences, Recamán's sequence, the golden mean, and probability theory mingle with side-trips into Vedic mathematics, mnemonic techniques for memorizing number sequences, competitions to produce the longest decimal expansion of pi, a visit to Peter Hopp's slide rule collection, designer Piet Hein's superegg, and a legion of sudoku enthusiasts. The book is written for the non-mathematician. However, exposure to first year algebra and geometry would be helpful. I have had both, but even after careful reading, there were still many sections that left me puzzled. The chapter on Vedic Mathematics was insightful, but I still do not see how this method can be considered easier than the traditional method I was taught. I was completely lost in the two chapters devoted to probability. Although Bellos claims in his introduction that the narrative is more or less chronological, this is true only on a chapter by chapter basis, since the material is presented thematically. The key question, however, is did I find the book interesting? The answer is a resounding YES! Bellos introduced me to people and ideas I never dreamed existed.
NOTES
This book was originally published in the U.K. as ALEX'S ADVENTURES IN NUMBERLAND. In my opinion it was a more appropriate title, mirroring some of the spirit of Lewis Carroll's verbal playfulness. In an interview Bellos was asked if he thought math was the universal language. Bellos responded in part: “...math is not just a universal language but also a language of universals....” (http://intelligenttravel.nationalgeog...) Moreover, his goal is not to instruct, any more than the goal of THROUGH THE LOOKING GLASS is a manual on chess-playing. Bellos wants to pique our curiosity, and maybe even expand a few brain cell connections.
A picture of Piet Hein's superegg can be found on https://en.m.wikipedia.org/wiki/superegg
Sloane's Online Encylopedia of Interger expressions is on http://oeis.org In addition to cataloging number sequences, there is a tool for converting the sequence into musical notes. (Quicktime needs to be loaded to play the music).
The Recamán's sequence is generated can also be played on https://m.youtube.com/#watch?v=z9Wbyr...
I read the Kindle edition, which I do not recommend. The formulas are input as images and do not enlarge so those parts are difficult to read.
From its onset, the book is playful. It opens with Chapter Zero rather than the conventional Chapter One. Bellos proceeds with a revelatory anecdote illustrating our own socialized mania for quantification. His overriding theme is that preconceptions shaped by culture and biological hard-wiring are unconsciously embedded in our thinking. “...[U]nderstanding quantities in terms of exact numbers is not a universal intuition; it is a product of culture....[R]atios are much more important for survival in the wild than the ability to count.” Those ratios might include a pride of lions assessing the relative strength of interlopers in their territory, or a monkey assessing which tree will reward the best return of fruit for energy expended. A surprising experiment entailed asking kindergarteners to map numbers along a line. Their lines tended to compress the distances between higher numbers — a logarithmic as opposed to linear depiction. Experiments with an Amazonian tribe showed they judged five dots to be five times more than one dot, but characterized ten dots as two times more than five dots, a distance of five increments vs. two: an understanding of quantity based on ratios, not enumeration.
Bellos's promised excursion begins with the invention of zero, a number so basic to all calculations that it is easy to forget that it needed to be invented. He concludes the journey with a chapter that defies both intuition and cultural pre-conceptions. It is a chapter that discusses Euclid's Fifth Postulate, which came to be reformulated as the Parallel Postulate: “Given a line and a point not on that line, then there is at most one line that goes through the point and is parallel to the original line.” The postulate works for a flat plane (at most one line) and a spherical plane (e.g. there are no straight straight lines passing through the north pole and that are parallel to the equator). Then, Bellos introduces the hyperbolic plane, a surface with negative curvature. It's a construct that almost defies visualization. The example he offers is a localized section that resembles a pringle. Mathematicians are familiar with the form as represented by Professor Daina Taimina's model constructed from crochet work. Even today's 3-D printers cannot replicate her models (http.//3dprint.com/8013/3d-printed-math).
It's a shock to realize that hyperbolic space only gets the reader up to the 19th century. To usher the reader into the 20th century Bellos explores the ideas of Georg Cantor and David Hilbert on infinity. “Cantor's heresy was to treat infinity as an entity in itself.” By working with correspondences between infinite sets he characterized some infinite sets as countable (aleph), and others as non-countable (beth). To complete that leg of the journey, Bellos books us into the marvelous “Hilbert Hotel.”
Between the beginning and end of his book, Bellos covers an eclectic mix of topics. Pythagoras' Theorem, zero, pi, Cartesian coordinates, prime numbers, Fibonnaci's sequences, Recamán's sequence, the golden mean, and probability theory mingle with side-trips into Vedic mathematics, mnemonic techniques for memorizing number sequences, competitions to produce the longest decimal expansion of pi, a visit to Peter Hopp's slide rule collection, designer Piet Hein's superegg, and a legion of sudoku enthusiasts. The book is written for the non-mathematician. However, exposure to first year algebra and geometry would be helpful. I have had both, but even after careful reading, there were still many sections that left me puzzled. The chapter on Vedic Mathematics was insightful, but I still do not see how this method can be considered easier than the traditional method I was taught. I was completely lost in the two chapters devoted to probability. Although Bellos claims in his introduction that the narrative is more or less chronological, this is true only on a chapter by chapter basis, since the material is presented thematically. The key question, however, is did I find the book interesting? The answer is a resounding YES! Bellos introduced me to people and ideas I never dreamed existed.
NOTES
This book was originally published in the U.K. as ALEX'S ADVENTURES IN NUMBERLAND. In my opinion it was a more appropriate title, mirroring some of the spirit of Lewis Carroll's verbal playfulness. In an interview Bellos was asked if he thought math was the universal language. Bellos responded in part: “...math is not just a universal language but also a language of universals....” (http://intelligenttravel.nationalgeog...) Moreover, his goal is not to instruct, any more than the goal of THROUGH THE LOOKING GLASS is a manual on chess-playing. Bellos wants to pique our curiosity, and maybe even expand a few brain cell connections.
A picture of Piet Hein's superegg can be found on https://en.m.wikipedia.org/wiki/superegg
Sloane's Online Encylopedia of Interger expressions is on http://oeis.org In addition to cataloging number sequences, there is a tool for converting the sequence into musical notes. (Quicktime needs to be loaded to play the music).
The Recamán's sequence is generated can also be played on https://m.youtube.com/#watch?v=z9Wbyr...
I read the Kindle edition, which I do not recommend. The formulas are input as images and do not enlarge so those parts are difficult to read.
January 16, 2015
This is a fabulous chronicle of the most esoteric subject in existence!
Alex Bellos is witty, serious, engaging and if I may say so, utterly charming in his narration of the history of mathematics. He has organized the book in the way that allows him to be chronological while also taking diversions from time to time to connect with what's happening now in the field of mathematics.
He begins with a systematic exposition of the idea of numbers and the need for them and progresses steadily at a really comfortable pace to cover everything from shepherds using a hybrid base of numbers for counting their sheep to humans understanding incredibly weird and abstract concepts in mathematics with the help of crochet!
On this journey, he makes some astonishing revelations and keeps you thoroughly entertained. I'm an engineer, so I might be slightly better positioned to understand this text, but the format and language of the book assumes nothing of the reader (without being condescending) and explains every concept in a way that even a lay person will be able to follow.
It's no mean feat to be able to explain concepts like Zeno's paradox, regression to the mean, squaring a circle and Riemann's non-Euclidean geometry without using any equations. Bellos does that and more! He's juggling hardcore mathematics, entertaining (and often humorous) anecdotes and practical applications of math at the same time!
The most endearing aspect of the book is that it doesn't take sides. It is incredibly neutral in its treatment of all the branches of math, no matter how bogus they may seem (I'm looking at you, Vedic math). All the people in this book have been treated as creative artists and their work has been explored with childlike wonder.
There are many tidbits in the book that refresh your ideas of math. Indeed, for me this was a refresher of my entire math curriculum from school. And this book is also an answer (without actually trying to be) to all those people who ask – 'Why do we learn math if it has no real application in life?' Well, as amply demonstrated by Bellos, everything that is ever done in mathematics, be it silly games or idle curiosity, everything has been put to some use and had contributed to the progress of humanity.
If nothing, you should read this book to learn about an encyclopedia of sequences (that also converts them into music), to see the unbelievable impact of the invention of the electronic calculator, to imagine a world of rivalries between human equation solvers and where human calculators would indulge in math duels! But if showmanship is not your cup of tea, then there's a really good critical examination of Pascal's wager, an exploration of the wonders of Pascal's triangle and of course, a fitting end to the book with a mind-mangling (a term I learned from this book) discussion of Cantor's various infinities.
You must, must, must read this book. See the excerpts to know why (excerpts annotated with a lot of love)
Thirty-fourth book reviewed as part of the 130 Challenge| Read on my blog
Alex Bellos is witty, serious, engaging and if I may say so, utterly charming in his narration of the history of mathematics. He has organized the book in the way that allows him to be chronological while also taking diversions from time to time to connect with what's happening now in the field of mathematics.
He begins with a systematic exposition of the idea of numbers and the need for them and progresses steadily at a really comfortable pace to cover everything from shepherds using a hybrid base of numbers for counting their sheep to humans understanding incredibly weird and abstract concepts in mathematics with the help of crochet!
On this journey, he makes some astonishing revelations and keeps you thoroughly entertained. I'm an engineer, so I might be slightly better positioned to understand this text, but the format and language of the book assumes nothing of the reader (without being condescending) and explains every concept in a way that even a lay person will be able to follow.
It's no mean feat to be able to explain concepts like Zeno's paradox, regression to the mean, squaring a circle and Riemann's non-Euclidean geometry without using any equations. Bellos does that and more! He's juggling hardcore mathematics, entertaining (and often humorous) anecdotes and practical applications of math at the same time!
The most endearing aspect of the book is that it doesn't take sides. It is incredibly neutral in its treatment of all the branches of math, no matter how bogus they may seem (I'm looking at you, Vedic math). All the people in this book have been treated as creative artists and their work has been explored with childlike wonder.
There are many tidbits in the book that refresh your ideas of math. Indeed, for me this was a refresher of my entire math curriculum from school. And this book is also an answer (without actually trying to be) to all those people who ask – 'Why do we learn math if it has no real application in life?' Well, as amply demonstrated by Bellos, everything that is ever done in mathematics, be it silly games or idle curiosity, everything has been put to some use and had contributed to the progress of humanity.
If nothing, you should read this book to learn about an encyclopedia of sequences (that also converts them into music), to see the unbelievable impact of the invention of the electronic calculator, to imagine a world of rivalries between human equation solvers and where human calculators would indulge in math duels! But if showmanship is not your cup of tea, then there's a really good critical examination of Pascal's wager, an exploration of the wonders of Pascal's triangle and of course, a fitting end to the book with a mind-mangling (a term I learned from this book) discussion of Cantor's various infinities.
You must, must, must read this book. See the excerpts to know why (excerpts annotated with a lot of love)
Thirty-fourth book reviewed as part of the 130 Challenge| Read on my blog
January 7, 2012
Alex Bellos attempts to engage the general public in mathematics by describing maths in a way that anyone can understand. He commences by describing how different cultures use counting and numbers, and in many ways this is the most interesting part of the book. Several cultures, for instance, have no name for any quantity greater than about 4.
I have a degree in mathematics, but there were many things in the book that were new to me, and some that made my jaw drop. My feeling is though, that anyone without mathematical training may start to lose interest at about Chapter 5, when algebra is introduced. Probability, Number Theory, Geometry and Statistics follow, and in the limit as the page number tends to infinity, the book tends to resemble a maths textbook. Having said, as infinity was reached and the book finished, I was quite sad. There were six appendices to console me, however.
I think that non-mathsy people will enjoy at least the first half, perhaps more. The title is enough however, to put off my non-mathsy girlfriend, who accused me of being a "geek" for reading it.
Here are some of my favourite snippets:
The current record for reciting the digital expansion of pi from memory is held by Akira Haraguchi, a 60 year old retired engineer from Japan. In 2006, he was filmed in a public hall near Tokyo reciting pi to 100,000 decimal places. The performance took him 16 hours and 28 minutes. He used a mnemonic technique, assigning syllables to each number from 0 to 9 and then translating pi's decimals into words, which in turn formed sentences. The record for pi memorisation whilst juggling is held by Mats Bergsten (Sweden) who has recited 9778 digits while juggling three balls. (p162/163).
Ramanujan, in the early twentieth centiry, developed some remarkable infinite series for pi, including the mind blowing one on page 164 (can be seen at http://en.wikipedia.org/wiki/Ramanujan) without the help of computers. In the 1980s, presumably with the help of comupters, the Chudnovsky brothers developed an even more ferocious formula (p165).
In December 2009, the record for determining the digital expansion of pi was broken, and now stands at 2.7 trillion places (p 168).
The Great Internet Mesenne Prime Search (GIMPS) links about 75,000 computers across the world in the search for higher and higher prime numbers. The highest found (at the time of publication of the book) was 2^43112609-1, which is a number almost 13 million digits long (p 271).
"Regression (to the mean) is one of the least grasped but most useful mathematical concepts you need for a rational understanding of the world" (p 378).
I have a degree in mathematics, but there were many things in the book that were new to me, and some that made my jaw drop. My feeling is though, that anyone without mathematical training may start to lose interest at about Chapter 5, when algebra is introduced. Probability, Number Theory, Geometry and Statistics follow, and in the limit as the page number tends to infinity, the book tends to resemble a maths textbook. Having said, as infinity was reached and the book finished, I was quite sad. There were six appendices to console me, however.
I think that non-mathsy people will enjoy at least the first half, perhaps more. The title is enough however, to put off my non-mathsy girlfriend, who accused me of being a "geek" for reading it.
Here are some of my favourite snippets:
The current record for reciting the digital expansion of pi from memory is held by Akira Haraguchi, a 60 year old retired engineer from Japan. In 2006, he was filmed in a public hall near Tokyo reciting pi to 100,000 decimal places. The performance took him 16 hours and 28 minutes. He used a mnemonic technique, assigning syllables to each number from 0 to 9 and then translating pi's decimals into words, which in turn formed sentences. The record for pi memorisation whilst juggling is held by Mats Bergsten (Sweden) who has recited 9778 digits while juggling three balls. (p162/163).
Ramanujan, in the early twentieth centiry, developed some remarkable infinite series for pi, including the mind blowing one on page 164 (can be seen at http://en.wikipedia.org/wiki/Ramanujan) without the help of computers. In the 1980s, presumably with the help of comupters, the Chudnovsky brothers developed an even more ferocious formula (p165).
In December 2009, the record for determining the digital expansion of pi was broken, and now stands at 2.7 trillion places (p 168).
The Great Internet Mesenne Prime Search (GIMPS) links about 75,000 computers across the world in the search for higher and higher prime numbers. The highest found (at the time of publication of the book) was 2^43112609-1, which is a number almost 13 million digits long (p 271).
"Regression (to the mean) is one of the least grasped but most useful mathematical concepts you need for a rational understanding of the world" (p 378).
November 1, 2020
My brain is now filled with more number facts than I ever wanted it to be filled with. I cannot believe I was a Mathmatics major in Uni for over a year and was so unknowing of so much of what Alex talked about. Numbers are indeed fascinating, if overwhelming for most of us. The early chapters about societies use of numbers and how they did not recognise numbers over what they could see or count. Why do we have ten as the basis of our numerical system rather than 12. 12 makes sense in that we have 12 months in a year, 12 x 2 hours in a day and numerous other uses of 12 as a base for our numbers.
The exploration of other themes were often interesting (Pythagorus and other historical mathematicians) and the historical study of Pi for example. Even the math of probability in betting and the like (which bored me to tears). Alex is so much smarter and more knowlegible than I am that I found this book mesmirising, yet ofter boring as it was so far over my head.
Only for the keen mathematician.
The exploration of other themes were often interesting (Pythagorus and other historical mathematicians) and the historical study of Pi for example. Even the math of probability in betting and the like (which bored me to tears). Alex is so much smarter and more knowlegible than I am that I found this book mesmirising, yet ofter boring as it was so far over my head.
Only for the keen mathematician.
July 17, 2020
'Alex's Adventures in Numberland' is a book that I would want everyone to read. Part history, part sociology, and part philosophy, it traces the origins of man's desire to introduce numbers and counting into his life and how that choice has led to the growth of Mathematics today.
While it may sound strange to us, the desire to question the need for math, Alex sets the ball rolling right from the first chapter(the zeroth, in the book) where he introduces a tribal community in the Amazon who don't have the vocabulary for numbers beyond 5 because they have no need for counting the things they own. It is at that point he makes you realize how much about the math around us we take for granted - why do we have a base 10 for counting, how did the names for the numbers come about, how did humans over the world establish math as a globally standard way of communicating, and where did the ideas for concepts like probability, statistics, and infinity come from?
He also explores what he terms 'ethnomathematics' - the approach of different cultures towards Mathematics; how Indians(Hindus) have made Vedic math as a symbol of past glory and how Japanese have made mental arithmetic and the abacus a mark of intelligence. He's also traced the link of innovations and ideas over time - how one idea led to another and it snowballed into fads and theories. There are sprinkles of neat mathematical tricks and patterns to amuse the reader - curious little observations and theorems. There are references to religion and how many people associated the exploration of math to getting closer to divinity.
Although it runs nearly 450 pages, it is a book one can breeze through. The writing is easy to follow and so are the mathematical explanations(for the most part). In any case, the point isn't to grasp the math but the philosophy behind it. If you'd like to spend some time being impressed with the ingenuity of brilliant minds who lived before us and had the ability to invent these concepts, then this book would be a field day for you.
While it may sound strange to us, the desire to question the need for math, Alex sets the ball rolling right from the first chapter(the zeroth, in the book) where he introduces a tribal community in the Amazon who don't have the vocabulary for numbers beyond 5 because they have no need for counting the things they own. It is at that point he makes you realize how much about the math around us we take for granted - why do we have a base 10 for counting, how did the names for the numbers come about, how did humans over the world establish math as a globally standard way of communicating, and where did the ideas for concepts like probability, statistics, and infinity come from?
He also explores what he terms 'ethnomathematics' - the approach of different cultures towards Mathematics; how Indians(Hindus) have made Vedic math as a symbol of past glory and how Japanese have made mental arithmetic and the abacus a mark of intelligence. He's also traced the link of innovations and ideas over time - how one idea led to another and it snowballed into fads and theories. There are sprinkles of neat mathematical tricks and patterns to amuse the reader - curious little observations and theorems. There are references to religion and how many people associated the exploration of math to getting closer to divinity.
Although it runs nearly 450 pages, it is a book one can breeze through. The writing is easy to follow and so are the mathematical explanations(for the most part). In any case, the point isn't to grasp the math but the philosophy behind it. If you'd like to spend some time being impressed with the ingenuity of brilliant minds who lived before us and had the ability to invent these concepts, then this book would be a field day for you.
September 27, 2011
The world of maths can seem mind-boggling, irrelevant and, let's face it, boring. This groundbreaking book reclaims maths from the geeks.
This is how the blurb on the back cover starts. Alex's Adventures in Numberland isn't quite as awful as that suggests, but it's very apparent Bellos is a journalist, not a mathematician. He shares with most of his colleagues a subconscious but profound contempt of experts (to his credit, at least it is subconscious), an inability to distinguish substance and legitimacy from woo and crankery, or at least a belief that woo and crankery are interesting (he talks to ``Puff Daddy'''s numerologist (whom he calls a ``modern-day Pythagorean''), representatives from the cult behind Vedic maths, and economists), an unwillingness to let truth or nuance get in the way of a ``good story'', and a preference for expensive and pointless trips abroad to interview people he barely knows anything about over genuine research.
The things he covers are the usual pedestrian party tricks and low-level trivia not even worth enumerating. The whole thing is analogous to someone who has just discovered the Flemish Primitives drawing a whole bunch of stick figures in an attempt to convey his new-found enthusiasm for painting; it's nice that you're enthusiastic (and I do believe he genuinely is), but dude, lurk before you post.
I would say that this book would have been better if it had been written by a mathematician, but of course it has been, a thousand times over.
April 3, 2012
If you read just one book about math this year, it should totally be this one and I am right about everything.
June 19, 2011
Surprising, indeed! This book (and my puchase of it) is proof that a great title can sell a book. I'd never heard of the author. I'm not particularly interested in math, and have certainly never intentionally read over 300 pages about it. A month ago it would have been difficult for me to conceive of something so seemingly dull as a book about math.
But I loved this book!
Part of the appeal of the book is its author. I am convinced that Alex Bellos could make anything interesting. He is a gifted writer, who just happens also to be a gifted mathematician; the perfect left/right-brained combination to make something like this work.
The book is ordered into twelve chapters (numbered 0-11; Chapter Zero is, fittingly, about the concept of zero and how it's invention changed the world). Each chapter can be read individually, which, as Bellos says, means you can skip any chapters that you find boring... but I can pretty much guarantee that won't happen. For a book about numbers, the content is largely narrative, as opposed to being arranged in lists, tables, and other mathematical ways. The author uses his skills as a journalist to track down some remarkable people from all parts of the world, and engages readers in their fascinating stories.
The "World of Math" truly is astonishing. From ancient philosophy and counting monkeys to sudoku puzzles and how to beat the odds in the casino, my mind was consistently blown on every page (but in a good way!). If I start listing individual facts that amazed me, I wouldn't be able to stop, so you're going to just have to read this book for yourself.
You don't have to know advanced math to enjoy this book. Honestly, you probably don't need to know much at all about math, or be particularly good at it. Bellos never assumes too much about his audience. You merely need to love a good story, and be prepared to be thoroughly entertained.
P.S. — This book has opened my eyes to an entire genre that I never knew existed: "Recreational Math Books". I'll definitely be returning to this well!
But I loved this book!
Part of the appeal of the book is its author. I am convinced that Alex Bellos could make anything interesting. He is a gifted writer, who just happens also to be a gifted mathematician; the perfect left/right-brained combination to make something like this work.
The book is ordered into twelve chapters (numbered 0-11; Chapter Zero is, fittingly, about the concept of zero and how it's invention changed the world). Each chapter can be read individually, which, as Bellos says, means you can skip any chapters that you find boring... but I can pretty much guarantee that won't happen. For a book about numbers, the content is largely narrative, as opposed to being arranged in lists, tables, and other mathematical ways. The author uses his skills as a journalist to track down some remarkable people from all parts of the world, and engages readers in their fascinating stories.
The "World of Math" truly is astonishing. From ancient philosophy and counting monkeys to sudoku puzzles and how to beat the odds in the casino, my mind was consistently blown on every page (but in a good way!). If I start listing individual facts that amazed me, I wouldn't be able to stop, so you're going to just have to read this book for yourself.
You don't have to know advanced math to enjoy this book. Honestly, you probably don't need to know much at all about math, or be particularly good at it. Bellos never assumes too much about his audience. You merely need to love a good story, and be prepared to be thoroughly entertained.
P.S. — This book has opened my eyes to an entire genre that I never knew existed: "Recreational Math Books". I'll definitely be returning to this well!
October 9, 2016
Didn't believe I'll read an entire book just about math. But this one is just weirdly engaging.
October 20, 2022
Deserves a 5 for the title, but the content is excellent as well. One student of mine asked one question about math history and so I checked this book out and asked my math mom (hi mom) for help, and ended up giving my class way more math history they asked for. I'm unapologetic.
I learned a lot. Bellos breaks down complex math concepts for the math-curious layman to comprehend relatively easily (after 2-3 re-readings of sentences sometimes). It's entertaining and wet, as in not dry... seriously.
I look forward to revisiting this book in the future.
I learned a lot. Bellos breaks down complex math concepts for the math-curious layman to comprehend relatively easily (after 2-3 re-readings of sentences sometimes). It's entertaining and wet, as in not dry... seriously.
I look forward to revisiting this book in the future.
January 11, 2026
Numbers are fun
December 16, 2022
Solid pop-maths book, wanted to see some topics in more detail but that probably wouldn't suit the target audience
November 30, 2016
Is this a great book, or did I read it at the right time? I am tutoring high-school math and found much inspiration in these pages. While there is little that is completely new for me, most of what is there is well explained. He provides a lot of historical background, starting with tribes using a number system of one, two, many. The author is not afraid of philosophy, as can be seen in this meditation on the number zero:
“Indian philosophy embraced the concept of nothingness just as Indian math embraced the concept of zero. The conceptual leap that led to the invention of zero happened in a culture that accepted the void as the essence of the universe. The symbol that emerged to represent zero, the circle, encapsulated the message that mathematics cannot be separated from spirituality. Zero means nothing, and it means eternity.”
He later informs us that when math prodigy Jedediah Buxton was taken to see Shakespeare's Richard III, his reaction was that the actors had taken 5,202 steps and spoken 14,445 words. Before one generalizes about crazy mathematicians, note that a prodigy means an ability to do complex mental arithmetic, such as multiplying two six-digit numbers. Other than that, the guy was barely literate. To me, the story reveals why they are able to do seemingly impossible tasks - they spend their entire lives doing nothing but arithmetic, and by practice get very good at it. In contrast, mathematicians deal with abstractions, so maybe they are slightly crazy in different ways.
As for the math, the book ends with what I think is the best explanation of multiple levels of infinity I have seen. Or was I just at the right state of knowledge for his explanation? Still, I highly recommend this book for those interested in mathematics at the high school level.
“Indian philosophy embraced the concept of nothingness just as Indian math embraced the concept of zero. The conceptual leap that led to the invention of zero happened in a culture that accepted the void as the essence of the universe. The symbol that emerged to represent zero, the circle, encapsulated the message that mathematics cannot be separated from spirituality. Zero means nothing, and it means eternity.”
He later informs us that when math prodigy Jedediah Buxton was taken to see Shakespeare's Richard III, his reaction was that the actors had taken 5,202 steps and spoken 14,445 words. Before one generalizes about crazy mathematicians, note that a prodigy means an ability to do complex mental arithmetic, such as multiplying two six-digit numbers. Other than that, the guy was barely literate. To me, the story reveals why they are able to do seemingly impossible tasks - they spend their entire lives doing nothing but arithmetic, and by practice get very good at it. In contrast, mathematicians deal with abstractions, so maybe they are slightly crazy in different ways.
As for the math, the book ends with what I think is the best explanation of multiple levels of infinity I have seen. Or was I just at the right state of knowledge for his explanation? Still, I highly recommend this book for those interested in mathematics at the high school level.
July 24, 2012
This strays so far from my normal read, but I found it very interesting, and Bellos' writing was engaging.
I've been spending the summer feeling like one of the teachers from Pink Floyd's The Wall, forcing my 12 year old to study Algebra in preparation for next school year. It's been shear hell for both of us. Neither of us likes math, but I'm a really stubborn woman & I've been seeking sources that will make math & algebra more accessible, more understandable, maybe even interesting. Who knew? There's a lot out there! YouTube is rich with cool math tricks, etc., and there are some how-to books that explain it well.
This is not a book of practical applications, and I won't make my 12 year old read it - there are some tough spots for sure. Maybe if I forbid him from reading it he will. This is more an exploration of math throughout history and around the world, different ways things have evolved, what mathematicians do for fun - such as adding digits to Pi - and why they do it. It's just a whole lot of interesting!
One of the big take-aways was that plenty of great mathematicians weren't very good at "math". Wish I could deliver that message to a few students who've been turned off by math and their teachers.
I've been spending the summer feeling like one of the teachers from Pink Floyd's The Wall, forcing my 12 year old to study Algebra in preparation for next school year. It's been shear hell for both of us. Neither of us likes math, but I'm a really stubborn woman & I've been seeking sources that will make math & algebra more accessible, more understandable, maybe even interesting. Who knew? There's a lot out there! YouTube is rich with cool math tricks, etc., and there are some how-to books that explain it well.
This is not a book of practical applications, and I won't make my 12 year old read it - there are some tough spots for sure. Maybe if I forbid him from reading it he will. This is more an exploration of math throughout history and around the world, different ways things have evolved, what mathematicians do for fun - such as adding digits to Pi - and why they do it. It's just a whole lot of interesting!
One of the big take-aways was that plenty of great mathematicians weren't very good at "math". Wish I could deliver that message to a few students who've been turned off by math and their teachers.
May 28, 2011
This is a great book that delves into the fascinating history of math. Stops along the way include the advent of zero, the use of the abacus and the sliderule, the search for the trillionth decimal in pi, the Fibonacci sequence, the golden ratio, fractals, varying levels of infiniti, counting cards in blackjack, the definition of what's "normal", and straight lines that aren't straight.
Unlike some books that try to cover so many topics, Bellos goes into enough depth in each chapter to educate, entertain, and satisfy even a well-versed mathematician. As the subtitle states, this is truly "A Surprising Excursion through the Astonishing World of Math."
Unlike some books that try to cover so many topics, Bellos goes into enough depth in each chapter to educate, entertain, and satisfy even a well-versed mathematician. As the subtitle states, this is truly "A Surprising Excursion through the Astonishing World of Math."
February 7, 2021
This book was recommended by many math lovers and enthusiasts. I was expecting to explore a layout of math and it's beauty, yet the topics were math-related and not mathimatical concepts. It was quite a fun read, but not as compelling as I was expecting.
August 13, 2019
Pretty good pop-sci but strangely unsatisfying. Possibly I just wasn't in the right mood, but I think it's something to do with his authorial voice...
May 23, 2020
What an amazing adventure through the world of math.
Read
September 4, 2023safe to say i am now out of my reading slump
August 11, 2021
Da leggere è sicuramente a tratti piacevole e ricco di spunti interessanti.
Credo però, ed è per questo che la mia votazione non è in definitva positiva, che si tratti del classico libro clickbait. Come prima cosa, gli esempi di indagine matematica del risvolto di copertina, basati sull'etologia di popoli esotici o di personaggi eccezionali che portano ad avvicinarsi al libro come ad un bel saggio divulgativo, sono tutti tratti dal solo primo capitolo, quello introduttivo. La qual cosa non è di per sè un male, ed indica solo un editore forse un pò pigro nella lettura. Il vero problema è però che, nelle parti in cui si parla di matematica, a mio avviso la spiegazione dei fenomeni matematici e la descrizione dei procedimenti sono veramente carenti e confusionarie. I ragionamenti e le dimostrazioni, per come sono presentate, sono davvero spesso incomprensibili per un non addetto ai lavori (la qual cosa la trovo sicuramente negativa in un libro che si vanta di aver fatto amare la matematica anche a chi l'ha odiata a scuola), e non credo che senza un minimo di infarinatura di calcolo infinitesimale e logaritmi avrei alla fine capito fino in fondo dove l'autore andasse a parare.
Se volete leggere un libro con spunti carini che diano la sensazione che forse la matematica può avere qualcosa di nascosto e piacevole, allora è il libro che fa per voi. Se cercate un saggio divulgativo per capire cosa siano queste cose piacevoli e misteriose che non vi hanno insegnato sulla matematica, passatre oltre.
Credo però, ed è per questo che la mia votazione non è in definitva positiva, che si tratti del classico libro clickbait. Come prima cosa, gli esempi di indagine matematica del risvolto di copertina, basati sull'etologia di popoli esotici o di personaggi eccezionali che portano ad avvicinarsi al libro come ad un bel saggio divulgativo, sono tutti tratti dal solo primo capitolo, quello introduttivo. La qual cosa non è di per sè un male, ed indica solo un editore forse un pò pigro nella lettura. Il vero problema è però che, nelle parti in cui si parla di matematica, a mio avviso la spiegazione dei fenomeni matematici e la descrizione dei procedimenti sono veramente carenti e confusionarie. I ragionamenti e le dimostrazioni, per come sono presentate, sono davvero spesso incomprensibili per un non addetto ai lavori (la qual cosa la trovo sicuramente negativa in un libro che si vanta di aver fatto amare la matematica anche a chi l'ha odiata a scuola), e non credo che senza un minimo di infarinatura di calcolo infinitesimale e logaritmi avrei alla fine capito fino in fondo dove l'autore andasse a parare.
Se volete leggere un libro con spunti carini che diano la sensazione che forse la matematica può avere qualcosa di nascosto e piacevole, allora è il libro che fa per voi. Se cercate un saggio divulgativo per capire cosa siano queste cose piacevoli e misteriose che non vi hanno insegnato sulla matematica, passatre oltre.
June 19, 2022
7/10
Mathematics has always been there but it requires a human understanding to become seen. Bellos focuses primarily on these subjects from an anthropological perspective which is uniquely interesting. I'm coming at this from the position of a pretty heavy maths background at this point so a lot of the theory wasn't new. I found particularly interesting the development of numeral systems, the sometimes hilarious professional feuds, probability relating to gambling and the finale which delves into hyperbolic geometry (a bizarre area I'm not overly comfortable with) and Cantor's theories. Mathematics can be dry, tough and frustrating but it's ultimately a human science for better or worse.
Mathematics has always been there but it requires a human understanding to become seen. Bellos focuses primarily on these subjects from an anthropological perspective which is uniquely interesting. I'm coming at this from the position of a pretty heavy maths background at this point so a lot of the theory wasn't new. I found particularly interesting the development of numeral systems, the sometimes hilarious professional feuds, probability relating to gambling and the finale which delves into hyperbolic geometry (a bizarre area I'm not overly comfortable with) and Cantor's theories. Mathematics can be dry, tough and frustrating but it's ultimately a human science for better or worse.
January 22, 2022
2.5
Good book however Alex lost me / my interest many times while explaining theories and going on about details of history of maths. I really hoped this book would have explained the world around me better but instead there were waaay too many distracting details. I won't lie that some chapters really dragged. Still, I learnt quite a bit from it :)
Definitely not a maths noob book but a book for someone who already has a clue and an existing interest in maths + its history.
Good book however Alex lost me / my interest many times while explaining theories and going on about details of history of maths. I really hoped this book would have explained the world around me better but instead there were waaay too many distracting details. I won't lie that some chapters really dragged. Still, I learnt quite a bit from it :)
Definitely not a maths noob book but a book for someone who already has a clue and an existing interest in maths + its history.
March 1, 2023
No fears if you are not a mathematician. This book examines the wonders of mathematical concepts in language plain enough for someone who never made it past algebra (e.g., moi). It is written by a journalist with a degree in mathematics who understands the drawing power of human interest stories.
I still don't understand infinity.
I still don't understand infinity.
February 23, 2025
3.5 stars, rounded up. I usually think of math as something that must be studied in a very stuffy, formal way, so it was fun to read about more playful mathematical discoveries involving origami, Sudoku, and crochet. Some chapters definitely dragged. My favorites were chapters 0, 1, 4, 7, and 11.
August 3, 2022
A cute little book which touches upon many of the curious quirks of mathematics. Definitely got me more fascinated with the subject
December 26, 2022
Absolutely delightful. The best kind of popular science, since it covers actual concepts but also introduces a huge number of bonkers characters both historical and current.
January 24, 2026
Didn't understand most of it, but delighted nonetheless.
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