Professor Stewart's Incredible Numbers

by Ian Stewart

At its heart, mathematics is about numbers, our fundamental tools for understanding the world. In Professor Stewart’s Incredible Numbers, Ian Stewart offers a delightful introduction to the numbers that surround us, from the common (Pi and 2) to the uncommon but no less consequential (1.059463 and 43,252,003,274,489,856,000). Along the way, Stewart takes us through prime numbers, cubic equations, the concept of zero, the possible positions on the Rubik’s Cube, the role of numbers in human history, and beyond! An unfailingly genial guide, Stewart brings his characteristic wit and erudition to bear on these incredible numbers, offering an engaging primer on the principles and power of math.

Genres: Mathematics, Nonfiction, Science, Physics, Stem, Education

352 pages, Paperback

First published March 19, 2015

About the author

Ian Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website

Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.

Reviews

[Brian Clegg · Rating 3 out of 5]

Ian Stewart is the most prolific writer in the field of popular maths, sometimes producing absolute crackers of a book like The Great Mathematical Problems and sometimes turning out ones that don't quite hit the mark. Intriguingly, this seems to manage to be both, in the same way as we discover that zero manages to be the same as minus zero.

The good news is that there's all kind of weird and wonderful mathematical information here. The book is divided into many sections, starting with the small integers, and making it all the way to infinity, via a plethora of different values and climaxing, appropriately enough, with 42.

The bad news is that this format means that the book is mostly a collection of facts with limited context and narrative, the part of a popular maths/science book that makes for a truly engrossing read. There are also heavy duty examples of the classic writer's error of 'If it's interesting to me, it must be to you.' So, at one point we read 'On Christmas day 1640 the brilliant mathematician Pierre de Fermat wrote to the monk Marin Mersenne, and asked an intriguing question. Which numbers can be written as a sum of two perfect squares.'

In fact there are two problems with this particular extract. One is spurious context. Unless there was some relevance to it being Christmas Day, then telling us that makes it sound like we're getting context without actually doing so. But worse is the 'intriguing question' bit - because unless you are a mathematician, there is nothing intriguing about that question.

I think a good general test of whether this book will work for you or not is how you react to magic squares - those grids of numbers that typically add up to the same value along each row, column and diagonal. It's a good example of how the book is organised, by the way, that these turn up in the section for number 9, because the smallest magic square is 3x3. If your reaction to magic squares is a mild interest that the earliest known magic square is called the Lo Shu (no date given), but then you get bored finding out about the properties of all sorts of different magic squares you will find parts of the book hard going. On the other hand, if after four pages on magic squares you think 'I wish there was more on magic squares,' rush out and buy a copy immediately.

If I am honest I am more in the first camp - but it didn't stop me reading the whole book because there are a good few genuinely interesting bits. The ones that work for me are the historically meaty ones, like the origin of zero, negative numbers and complex numbers - my suspicion is that every reader will find some parts to enjoy. So you pays your money (in real numbers) and you makes your choice.

(Note this review was for the UK edition from Profile Books - different cover)

[tara bomp]

read like 20% of it but probably won't finish it cause I don't feel like I'm actually learning anything. There's too many random mathematical facts just strung together without an explanation of what they mean and when he digs into the maths a bit it's very confusing and the explanations are very short. partially it's just that I'm dumb and haven't done maths for a while but I really don't think most of this would appeal to your average person - and if they know maths well enough to understand the explanations/wider meaning idk why they'd read the book in the first place

As an example: he talks about parities of permutations. He then says these show that the 15 puzzle is unsolvable, because the starting grid is an odd permutation of the required final grid but you can only make even permutations. But he doesn't show or explain how this is true. It's just a random fact that you learn and move on and can't actually apply.

[Liedzeit Liedzeit · Rating 2 out of 5]

Maybe, just maybe this would have been a three-stars book if not for the silly title. What is wrong with Incredible Numbers by Ian Stewart? This sounds like it was a stupid cooking book.

But even without the title this is not a very good book. Short (and sometimes very short) essays on numbers. With next to no context. And the essays are either about stuff I know (how many times have I read about the birthday paradox? Or very special or just plain boring. I really would like to know who the reading target is supposed to be. Well, I guess not everyone can be Martin Gardener.

So what do I try to remember? 42 is both a pronic number. And the sixth Catalan number.

[jaroiva · Rating 5 out of 5]

Jízda na roller-coasteru:
150 stránek nudy... zívačka...
Pro koho to je vlastně určené? Základy teorie čísel, přirozená, malá čísla, pfff..., nuda, nuda, šeď, šeď...
To je totiž cesta nahoru, kdy je potřeba vozíček namáhavě vytáhnout vzhůru po dráze.
Nahoře už dobré, trochu záživnější; π, φ, e...
A hele, začalo mě to bavit! Fraktaly, ty jsem nikdy komplexně popsané neviděla, ... paráda, užívám si už jízdu.
Ale pozor..., strana 225, nějak se to začíná svažovat z kopce, chytám si klobouk, teorie strun... Jé, narozeninový paradox! ... Jůů - kryptografie! ... To si to krásně užívám...
Šmarjá, už se to řítí dolů samospádem! Faktoriály, velká prvočísla, nekonečna větší než jiná nekonečna... ÁÁÁÁÁ....
Buch, jsme dole, hustý! Stálo to za to!

[Paul · Rating 3 out of 5]

Think of a number, any number...

Multiply it by 2

Add 10

Then divide by 2

Subtract your original number

And I will tell you your answer later on.

Stewart has a knack of making complicated and difficult mathematical concepts easy to comprehend and understand. In this book he introduces us to the numbers that we come across day in and day out. Some will be familiar, zero, one and Pi for example. Other are less familiar, from logs (not trees) to that strange areas of mathematics that encompass imaginary numbers and the vastness of infinity.

In this journey we venture through the primes, peers back into the history of mathematicians, informs us what is a rational number, traverses the circular numbers, plumbs the depths of fractals and explains the birthday paradox. There is a brief sojourn to the really small, before seeing the really really large numbers stretching away in the distance, and reaching the restaurant at the end of the universe with a reservation at table 42.

Occasionally complex, most of this is written with the layman in mind. Stewart writes with clarity on a subject that he knows and loves, and what really comes across is his enthusiasm to get other to love, or at the very least like maths once again.

Oh, and the answer is 5.

[Víctor Cid · Rating 4 out of 5]

Entretenido libro de divulgación matemática, que trata sobre curiosidades y anécdotas divertidas centradas en números concretos. Está estructurado en capítulos muy cortitos, tremendamente concisos y muy amenos en su lectura: números irracionales, pentominós, la escala musical... incluso un capítulo dedicado por completo al número 42 y el sentido de la vida. Simplemente genial!

[Maksym Valevatyi · Rating 5 out of 5]

Наскільки ж неймовірно нудними можуть бути числа і взагалі математика в школі. Щоправда, у мене була гарна вчителька, математику любив, але скільки ж я не знав про числа, чи не розумів.
Ця книга точно відповідає своїй назві - автор розділ за розділом розглядає різні числа, і чим вони цікаві: 0, 1, 2, пі, безкінечність, 42 та багато інших. Тут і історія математики, і визначні математики, і актуальні математичні проблеми.
Я дізнався багато нового, навіщо уявні числа, наприклад, і що воно взагалі таке. Чи як багатокутники замощують площину. Або ж як виглядає чотиривимірний куб. Принаймні в проекції на 3 та 2 виміри.
На жаль, не все мені в книзі зрозуміло. Ну, двадцять років після школи далися взнаки. Хоча, гадаю, автор міг би щось розтлумачити ясніше. Десь у симетріях я, наприклад, заблукав. З іншого боку, він спирався не на нашу традицію викладання математики в школі. Та й не всім дано так, поза іншим, з першого разу збагнути.
До речі, ще з'ясувалося, що автор разом з Террі Пратчеттом написав книгу про математику Дискосвіту...
Тож п'ять зірок і буду купувати інші книги з математики. Так просто, без практичного застосунку, а для радості розуміння.

[Andriy Kvasnytsya · Rating 3 out of 5]

Непогано, але складність книжки плаває вверх-вниз дуже сильно — від пояснення на пальцях факторіалу, і до інтегрального означення гамма-функції на наступній.

[Maurizio Codogno · Rating 5 out of 5]

Avete presente il libro di Piergiorgio Odifreddi Il museo dei numeri? Ecco, Ian Stewart ha scritto esattamente lo stesso libro ma in modo completamente diverso. Anche in questo caso si parla di numeri, piccoli e grandi: ma non necessariamente interi, a differenza del libro di Odifreddi, né necessariamente reali o se per questo finiti. Ma anziché trattarli per mezzo di fattoidi e opere d'arte, Stewart sceglie di limitarsi a qualche proprietà matematica e spiegarla - non "dimostrarla", non è mica un manuale scolastico! - ricordando tra l'altro che quando i matematici trovano qualcosa di impossibile ma che pare loro interessante trovano sempre il modo di farla diventare possibile. Non so se la differenza sia dovuta alla diversa percezione degli interessi del pubblico italiano rispetto a quello anglofono; però ritengo che sarebbe molto più bello che anche da noi la divulgazione entrasse più nel merito dei temi e non si limitasse a stupire con effetti speciali. Ah, l'ultimo capitolo è dedicato a un numero molto importante, come vedrete: il 42.

[Mario Bustamante Reyes · Rating 1 out of 5]

Creí que el libro se parecería a los de Martin Gardner, es decir con acertijos o historias interesantes acerca de números.
Pero de eso encontré muy poco. Cada capítulo está dedicado a allgún tipo de número en general (imaginarios, reales, irracionales) o a números en particular, pi. e. 0, etc. Pero el nivel de profundidad que se requiere para seguir la mayor parte del libro solo la tienen los mátemáticos de profesión o los verdaderos fanáticos de los números.
A mí solo me gustan las curiosidades y al no ser verdadero FAN del tema, no saqué más jugo que unas cuantas anécdotas interesantes.
No es un libro de divulgación, es un libro para expertos. Es un libro difícil para el lector promedio diría yo, a pesar de que le gusten las matemáticas.
A pesar de todo lo terminé, pero es demasiado duro para mí.

[Jennifer · Rating 4 out of 5]

I docked it a star because I wasn't quite sure who his intended audience is - the math is rather technical and complex to be accessible to a non-specialist, even one who enjoys math and isn't scared of numbers, yet I'm not sure a mathematician would need a book like this, as I suspect most of the information is covered somewhere along the way in a math degree. Still, it did give a sense of the wide range of questions mathematicians play with, and I found myself wanting to read on even when I didn't quite follow the technical explanations.

[Adrian Goh · Rating 3 out of 5]

Not for those without mathematical background. While some of it is easily understood with basic mathematical knowledge learnt in school. At least a good half of the book requires knowledge of much more advanced mathematics. That being said, I think a reader with adequate mathematical background would enjoy at least half of the book.

[Laira · Rating 4 out of 5]

me siento matematica

[Roger · Rating 3 out of 5]

Professor Ian Stewart is a prolific author of popular maths books, with at least 28 to his name according to the list in the front, although this is the first one that I've read. It's a fast moving book, with each chapter devoted to a variety of largely unrelated facts concerning a particular number or topic. He starts off with integers from 1 to 10 and then zero, -1, and i, before moving on to discussing a selection of rational and irrational numbers that have particular mathematical significance, such as √2, π and e (and others I had never come across before). Then the latter part of the book branches out to explore a range of disparate topics, such as string theory, pentominoes, the birthday paradox, the Rubik cube, sudoku, and infinity, to list just a few. The final chapter considers 42, which is the answer to "the great question of life, the universe, and everything" in Douglas Adams' book, The Hitchhiker's Guide to the Galaxy. In total, there are forty chapters, and possibly therein lies the problem - I think the author is trying to cover too much ground. While the title, Professor Stewart's Incredible Numbers, gives the impression that this is lightweight book, and Stewart's occasional dry humour feeds into that notion, nonetheless it is a heavy going tome, which includes a vast amount of information, much of which I felt is not well enough explained unless the reader has a solid grounding in maths. In an effort to cover so much, many of the explanations seemed rushed or else assume more existing knowledge than the average mathematically-minded lay person is likely to possess. 

By the end I didn't feel I'd learnt much. But there were areas where I was left wanting to know more. For instance, several times Stewart mentioned that all mathematical concepts are considered to be mental models of reality, not reality itself. He didn't attempt to explain this, which I found regrettable, as I have long thought that if we get close to defining the nature of reality it will be in terms of mathematics.

The book is also missing an index so if you want to recall some obscure fact at a later date it is necessary to remember which chapter it was in. For instance, if I wanted to remind myself about quaternions I would need to remember they were in the chapter entitled "4 - Square". Or for the Riemann Hypothesis, I have to turn to "½ - Dividing the Indivisible". This is not very convenient.

Stewart wrote this book with the best of intentions but I was left feeling that he may have misunderstood his audience. Nevertheless, those with an in-depth knowledge of maths might find this a good book to dip into in spare moments because it doesn't need to be read in any particular order.

[Adam84 · Rating 3 out of 5]

Ian Stewart se řídí heslem: Neexistuje nudné a nebo nezajímavé číslo. A v této knize se tímto přístupem snaží popularizovat matematiku a strhnout tak bariéry, které často u lidí k vůli nudnému výkladu vzniknou již na základních a středních školách.

Od samotného vzniku čísel, až po složité výpočty fyziky teorie strun, je kniha ilustrována, ovzorečkována a doplněna hravými výpočty tak, že se čte často až s komiksovou lehkostí. Samozřejmě je autor doslova nabitý vědomostmi o číslech, které si nehodlá nechat pro sebe, takže čtenář narazí i na složité kapitoly (či spíše části kapitol), laikovi téměř nepřístupné. Přesto si myslím, že je kniha vhodná i pro čtenáře matematikou téměř nepolíbeného, protože informacemi v ní autor zůstává na povrchu, zahltí spíš jejich počtem než hloubkou. A to je dle mého i úskalí knihy, doslova každá kapitola si zaslouží knihu vlastní (a většina i svou knihu samozřejmě má), takže hloubaví čtenář by ocenil spíše podrobný výklad konkrétního matematického pojmu, než sumář všech.

[Sanjay Banerjee · Rating 4 out of 5]

The author explores the astonishing properties of numbers from zero to infinity, narrates the insights of the ancient mathematicians and also shows how numbers evolved through time. He also dwells upon the mathematical secret of codes, Sudoku, Rubik’s cubes and musical scales, how we live in eleven-dimension space as well as how one kind of infinity is greater than another.

Highly recommended reading for readers interested in numerals and mathematics. It also clarified (at least to me) some basic concepts better. However, it often got into somewhat intricate mathematics and concepts of finite geometry etc which may be hard for a lay reader. It took me almost a month to finish (~1-2 chapters a day) for the concepts to sink in.

[Katheryn Thompson · Rating 3 out of 5]

After reading Percival Everett’s Dr. No, I fancied reading a book about maths, so I picked this one up. Professor Stewart’s Incredible Numbers contains lots of interesting and elucidating information about maths and numbers, and I especially enjoyed the sections that made me think differently about apparently self-evident things. However, the lack of narrative structure, as the book is essentially just comprised of different sections on different numbers, meant it wasn’t always clear what the point was. I’m not sure I’ll be reading any more of Ian Stewart’s books, but I enjoyed the experience of reading this one.

[Bruno Laschet · Rating 3 out of 5]

Viel Mathematik mit dem Versuch es 'locker' zu beschreiben. Das gelingt auch bei den Themen wo man (ich) noch mitkommt. Aber bei den ganz komplizierten Themen nützt das dann auch nichts mehr. Eine schöne Wiederholung von Themen, die ich vor 35 im Studium lernte, einige neue interessante Kapitel und vieles was zu kompliziert ist...

Aber für ein rein mathematisches Buch ist der Ansatz gut gewählt. Besonders gelungen das Kapitel über die Antwort aller Fragen. Die Zahl 42.

Vielleser wissen was ich meine...

[Book Grocer · Rating 5 out of 5]

Purchase Professor Stewart's Incredible Numbers here for just $8!

A prolific writer in the field of popular maths. There's all kind of weird and wonderful mathematical information here. Along the way, Stewart takes the reader through prime numbers, cubic equations, the concept of zero, the possible positions on the Rubik’s Cube, the role of numbers in human history, and beyond.

Paul - The Book Grocer

[Andrew Brassington · Rating 3 out of 5]

Some really intriguing insights into number theory (and many other areas of mathematics) but I think the idea of spawning discussions about various mathematical topics rooted from the numbers themselves can get quite messy. Jumping between various concepts all because they are linked to the number 6, for an example, just doesn't make the book flow easily like it could if it had a slightly tweaked structure. But then maybe that would undermine the whole purpose of the book itself...

[Robert · Rating 3 out of 5]

A decent collection of mathematical facts, but that's all it is. No particular logical structure, and in fact many of the same concepts are repeated in different parts of the book.

I think Professor Stewart made a lot more use of wikipedia than he would like to admit.

Nevertheless, 3/5 because I learnt new things

[LeoRuslan · Rating 2 out of 5]

Розділи книги побудовані якогось геть нелогічно, після елементарних речей йдуть розділи із далеко непростою математикою. Не зрозуміло для кого ця книга призначена. Я сумніваюся, що пересічна людина цікавиться циклічними група чи групами симетрій або що таке алеф-нуль.

Також, склалося таке враження, що редактор цю книжку в очі не бачив/ла, а до перекладу не залучався жодний математик.

[Warren Bridle · Rating 4 out of 5]

Enjoyed it mostly. There is plenty of content that will be way over the head of most lay people. I did several years of advanced mathematics at university, and still found some content very difficult, with very limited explanation.

[Elazar · Rating 2 out of 5]

Too much information for me. I used to understand some of this stuff...

[Fábio Ferreira · Rating 3 out of 5]

Foi interessante relembrar alguns conceitos básicos da matemática que só vemos no fundamental. Porém, por tentar abordar muitos tópicos, alguns deles deixaram a desejar, prejudicando o entendimento.

[PTSD · Rating 1 out of 5]

Sin hilo conductor. Habla más de otras cosas que de matemáticas. No lo terminé

[Mike Peleah · Rating 4 out of 5]

What is special in number 1? 42? What about pi? and √2? The book "Professor Stewart's Incredible Numbers" offers a great introduction into the world of numbers, providing all kind of weird and wonderful mathematical information (as well as some historical accounts around the numbers). The book is divided into many sections, starting with the small integers, passing zero and negative numbers, complex number, all way to big numbers and infinities. The book is ending, appropriately enough, with 42.

However, this format makes the books quite uneven. In fact, it is mostly a collection of facts with limited context and narrative. Some numbers are described in details with some profound discussion and some are just skimmed through. (Which resembles me an old joke "take out two pages of proofs and write instead 'obviously'").

Overall the book is a good read for those interested in math, as it offers many entry points and references for further exploration.

[Yaroslav Skorokhid · Rating 3 out of 5]

Почали за здравіє, закінчили за упокій

Книжка не наук-поп.

Починається начеб легко - вавилоняни, системи числення. А потім в такі дебрі заходить, що треба точно вчитися на мехматі щоб це все зрозуміти - не пояснено нічого, ніяк. Автор хіба скомпілював статті з вікі + те що сам вчився в університеті, але чи пояснив що це і звідки взялося для пересічної людини - ні.


Не рекомендую якщо у вас немає мінімум бакалавра з прикладної, мехмату чи фізики. А як що він у вас є - то навіщо вам ця книжка?

[Sebastian Fiedler · Rating 4 out of 5]

I really enjoyed this book but... as a physicist I kind of have a basic backgound in maths and... even then, he lost me at times. Especially in the latter parts of the book. It's goood to not only appeal to the lay person but here it seems Professor Stewart at times forgot how complicated mathematics can be. I whole-hearteld recommend it to anyone who knows a bit about maths and wants to know more but people who are not academics might get lost rather fast and hard at times. Quite a shame.

[Casper H · Rating 4 out of 5]

I read this when it came out, and reread it now. Really nice overview of various interesting numbers (in a way, they are all interesting) - and why they are particularly interesting. The math is not too advanced, but certainly not low level. Contains relatively obscure stuff like the sausage conjecture (for the number 56), and doesn't shy away from things like 24 dimensions and geometry in the complex plane. But really, read it.