From Zero to Infinity

by Constance Bowman Reid

From Zero to Infinity is a combination of number lore, number history, and sparkling descriptions of the simply stated but exceedingly difficult problems posed by the most ordinary numbers that first appeared in 1955 and has been kept in print continuously ever since. With the fifth edition this classic has been updated to report on advances in number theory over the last 50 years, including the proof of Fermat's Last Theorem. Deceptively simple in style and structure, it is a book to which the reader will return again and again, gaining greater understanding and satisfaction with each reading.

Genres: Mathematics, Nonfiction, Science, History, Number Theory

208 pages, Paperback

First published January 1, 1955

Reviews

[ياسر · Rating 3 out of 5]

- An interesting journey with numbers..
- "Zero", as usual, was the most interesting one..

- Good book, simple language..

[Mishehu · Rating 5 out of 5]

A gem of pop math exposition, harking back to the days when the notion of a broadly literate lay readership was taken seriously (I guess it still is, but more narrowly). I can understand why this one has been published and republished in successive editions. Reid, though not a mathematician herself, is a terrific expositor. She has an eye for the interesting detail and a gift for explaining it. For the budding young mathematician, this book's a delight. For anyone who thinks math's a bore, I challenge them not to find something at which to marvel in it.

[Paul Speck · Rating 5 out of 5]

"Complex ideas presented in simple terms." That should be a goal of all books on science or math written for serious students or a broadly-educated general audience. Few authors do it this well. Constance Bowman Reid does. Her book is not a textbook or a history but a series of essays (chapters) that build a bit on each other but could be read in any order. The chapter titles (zero to infinity) are mostly starting points that she uses to introduce a related topic. [Wikipedia lists her topics chapter by chapter.]

Most chapters follow a similar pattern. Implicitly or explicitly, someone (classical, medieval or modern) is intrigued by a number or a pattern of numbers that he cannot figure out. Later (sometimes much later), another person takes up the challenge. The incomplete puzzle. Then another. Then another. And finally a breakthrough. An insight. A proof. Closure. But resolution often leads to revolution and new questions, new insights, a new world, a new branch of mathematics. This is how math progresses. And science.

The book's current subtitle was its original title: "What makes numbers interesting." Men are naturally curious. Endlessly looking to make sense of things. Yes, Reid does present complex ideas in simple terms (no small achievement) but her bigger goal (and bigger achievement) is to share the collective ingenuity and effort of past generations in such a way that they entice and inspire a new generation of math lovers. As attested by many reviews, especially those of teachers, Reid's book has done that for almost seventy years. And still does.

Although From Zero to Infinity was first published in 1955, Reid expanded and updated it. The current edition (2006) is not outdated. Without being a textbook, it provides a broad introduction to Number Theory. And without being a history of math, it demonstrates that all modern ideas have a history.

[Jef · Rating 5 out of 5]

Ik had een editie van 1965. Het taalgebruik doet archaïsch aan, maar het stoort niet, integendeel, zeker in de passage waar beschreven wordt hoe een wiskundige die een jaar van zijn leven besteedde om uit te vissen of een bepaald getal een priemgetal was of niet, aanwezig was toen een 'elektronische rekenmachine' dit vraagstuk op een minuutje oploste, lijkt het alsof je terug geworpen wordt in de tijd. Verder kwam ik een passage tegen waarin verteld wordt hoe Euler een voortbrengende functie vond om te bepalen op hoeveel manieren een getal geschreven kan worden als de som van natuurlijke getallen: een vraagstuk dat in de lijst van https://projecteuler.net voorkomt, waarop ik mijn tanden stuk beet. Een vlot geschreven boekje dat ik aan iedereen die een beetje interesse in wiskunde heeft, kan aanbevelen.

[Matt · Rating 4 out of 5]

This is an interesting little book. The content at the beginning is a little simplistic and I was worried that nothing in the book would be challenging or new to me. However, as the chapters progress the mathematics discussed gets more complex and more interesting. And the final chapter on infinity is excellent.
One complaint I have about the book is that the organization is strange. The book is organized by chapters on each digit starting 0, 1, 2, etc. before ending with e and infinity (aleph sub zero). However, each chapter is not really about the digit. The chapter on '2' is actually about binary, '3' is about primes, '6' is about Mersenne numbers, '7' Fermat numbers, '9' congruence (modular arithmetic), etc.

[Adrian Doan · Rating 5 out of 5]

The wonders of mathematics are awesome and boundless, and yet we do an incredible job quashing the interest of children and teenagers in the subject at a young age. Perhaps we take for granted the knowledge and techniques that have been hard won over the millennia of human investigation. Things that are basic to a middle or high schooler would’ve amazed the Ancient Greek Mathematical giants, even kids at that age would probably enjoy knowing that. There is a whole world of treasures and hidden truths in the integers 0,...,9. Not everyone needs to be a mathematician, but it’s beauty can be appreciated by anyone.

[Patrick · Rating 5 out of 5]

Excellent 'pop' exposition of numbers 0 through 9, infinity, and e - along with related theorems and historical snippets. Intriguing, engaging, and a fun read. Recommended, particularly if you have any interest at all in mathematics and number theory.

[Marco · Rating 2 out of 5]

Ciascun capitolo è pretestuosamente "dedicato" ad un numero, chiarendo ben poco del contenuto.

[Tom Richards · Rating 5 out of 5]

A little gem of a book

[Maurizio Codogno · Rating 4 out of 5]

Carramba che sorpresa! Io mica lo sapevo che Constance Reid fosse la sorella di Julia Robinson... (ovviamente nessuno dei due era il loro vero cognome. Erano entrambe nate Bowman, ma negli USA ancora adesso la moglie diventa proprietà cognominale nel marito).
L'edizione che ho letto è quella "del cinquantenario", nel senso che il libro è stato scritto da una Reid trentottenne e rivisto poi da una Reid ottantottenne.

Constance Reid non era una matematica, anche se naturalmente in caso di dubbi poteva sempre chiedere a sua sorella; era una scrittrice che si è specializzata in libri di divulgazione sulla matematica e sui matematici. Questo libro nacque per caso, dopo che scrisse un articolo sullo Scientific American a proposito della scoperta di due nuovi numeri perfetti (da parte di suo cognato... e la storia è molto divertente). Il libro ha dodici capitoli, sui numeri naturali da 0 a 9 oltre che al numero di Nepero e che come tutti sanno è alla base dei numeri naturali e all'infinito che è la fine di tutti i numeri naturali. Già da qui dovrebbe essere chiaro che i numeri sono solo un pretesto per raccontare varie storie matematiche, spesso già note per altre vie ma sicuramente raccontate molto bene grazie anche alla traduzione fresca di Domenico Minunni. Credo insomma che il testo sia molto adatto per avvicinare non tanto alla matematica come materia quanto come modo di pensare i lettori: caldamente consigliato.

[Sean Maguire · Rating 4 out of 5]

Even better than Hodges' 'From One to Nine'. First published in 1955, and updated to keep track of developments in math in the intervening 50 years, Reid does a masterful job of journeying through the fascinating intricacies of the digits. She also offers up my new favourite quote: "It would be difficult for anyone to be more profoundly interested in anything than I am in the theory of primes" (G.H. Hardy).

[Andrew Robertson · Rating 5 out of 5]

An intriguing book that delves deep into zero, the single-digit numbers, infinity, and "e." Some of the chapters deal specifically with that number and what makes it interesting. However, other chapters will veer away from the number itself and discuss prime numbers or other broad mathematical concepts that apply to that number.

[Todd Spicer · Rating 3 out of 5]

Read it five and a half years ago. Got it out again seven weeks ago. Working through it now and really letting the big questions sink in more.

Great place to start for concepts dealing with "the shadowy history and philosophy of the modern digits."

[Melissa · Rating 3 out of 5]

So far it's been really good

[Darren Kirby · Rating 4 out of 5]

Interesting book. Fascinating at times even. Not overly heavy on math drudgery, easy for non-math nerds to understand.