David Acheson - 1089 and All That: A Journey Into Mathematics

1089 and All That is an instant classic an inspiring little masterpiece.

Mathematical Association of America

Possibly the nicest maths book ever written.

Kjartan Poskitt, author of Murderous Maths

Every so often an author presents scientific ideas in a new way Starting from such minimalist material, David Acheson works his way up to chaos and catastrophe theory. Not a page passes without at least one intriguing insight Anyone who is baffled by mathematics should buy it. And all mathematicians should buy at least a dozen copies to hand out to people they meet at parties. My enthusiasm for it knows no bounds.

Ian Stewart in New Scientist

Who would like this book? Absolutely anyone. It is so nicely written, so charming, and so entertainingly lighthearted, that it is an absolute little gem.

PLUS online magazine, Cambridge

A lovely little book.

Simon Singh, author of Fermats Last Theorem

A little gem.

SIAM News

Great fun.

Mathematics Today

Delightful.

Mathematical Digest

Inspired.

Niall Ferguson, historian, in The Sunday Times

Highly accessible and entertaining.

The Mathematical Association

The tone of this little gem of a book is set by the allusion in its title to the W.C. Sellar and R.J. Yeatman classic 1066 and All That, and the outrageous Steve Bell cartoon on its cover The book is such an easy and entertaining read (my non-mathematical family members agree) There are few mathematicians who succeed in writing popular accounts of their craft without being superficial or condescending. With this book David Acheson has joined the best of them.

Times Higher Education Supplement

My ten-year-old daughter read the book with my guidance and loved it. Even mathematicians will find fresh perspectives on old themes in this playful and inventive book.

John Mighton in The Mathematical Intelligencer

The reader is left with a sense of the magic of mathematics An earlier reviewer has advised everyone to go out and buy a dozen copies, and I heartily agree, and hope that our embattled schoolteachers (and university lecturers!) take up the cry.

UK Nonlinear News

On the surface this book is another of those lets look at the funny things about numbers books. But no, this one was far more than that. It treated subjects briefly but in depth and breadth, linked them together, didnt make assumptions Truly inspiring, and a great read over a weekend.

Mathematics Teaching

Every teenage mathematician should have a copy.

Symmetry Plus Magazine

An ideal present for friends and relatives who are not mathematicians.

London Mathematical Society
Newsletter

A Journey into Mathematics

David Acheson
Jesus College, Oxford

Great Clarendon Street, Oxford ox2 6dp

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David Acheson, 2002

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First published 2002

First published in paperback 2010

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Think of a three-figure number.

Any three-figure number will do, so long as the first and last figures differ by 2 or more.

Now reverse it, and subtract the smaller number from the larger. So, for example,

782 287 = 495.

Finally, reverse the new three-figure number, and add:

495 + 594 = 1089.

At the end of this procedure, then, we have a final answer of 1089, though we have to expect, surely, that this final answer will depend on which three-figure number we start with.

But it doesnt.

The final answer always turns out to be 1089.

As I remember, the 1089 trick was the first piece of mathematics that really impressed me, and I came across it at the age of ten, in the I-SPY Annual for 1956.

This was a book for children, published by a well-known British newspaper of the time, and it contained a mixture of adventure stories and more educational articles with titles like Pond Life.

But my favourite bit, by a long way, was

There were other conjuring tricks as well, including The Vanishing Glass of Water and Reading the Mind, but somehow it was 1089 that really caught my attention.

It was the element of mystery and surprise, I think, that put this result into a different league from some of the work we were doing in school.

Now, Im not saying that I didnt enjoy sums, and other bits of elementary mathematics, for I most certainly did. But if I tell you, for instance, that a typical homework problem at the time went something like this: