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Publisher:

Chapman & Hall/CRC

Publication Date:

2013

Number of Pages:

215

Format:

Paperback

Price:

29.95

ISBN:

9781466564916

Category:

General

[Reviewed by , on ]

P. N. Ruane

10/10/2013

‘What does it mean, “to do mathematics”?’ asks the author in the opening sentence of this very readable book. The response to this rhetorical question is spread over 200 pages and 10 chapters, in which there is very little use of mathematical symbolism and only one diagram.

The dearth of illustrations naturally means that geometrical ideas do not feature prominently in these ‘stories from mathematics’. Conversely, for the purposes of engaging non-specialist readers in the art of *doing* mathematics, much of the narrative is based upon elementary number theory — or rather, simply stated problems that lead to complex areas of mathematics.

The imagination is stirred by the introduction of ‘interesting numbers’, such as 6 (a perfect number), 7 (a Mersenne prime), 8 and 9 in relation to the Catalan Conjecture, 17 (the Gauss polygon), 1729 (Hardy’s taxi), and so on. But which numbers are uninteresting? What is the smallest uninteresting number? Such is the degree of fun and latent humour in Ziegler’s pedagogical style.

Use and abuse of numerical data is discussed in one short chapter, and the use and misuse of equations in communicating ideas in another. We know that scientific activity is mainly located university research labs or in industrial establishments. But where is mathematics created? Almost anywhere according to chapter 6, but often in the most informal of circumstances.

Who creates mathematics? This question accounts for the significant amount of biographical and historical observations contained in the last three chapters. Mathematicians are seen as being all too human, and often quite idiosyncratic. For instance, we read of the nomadic Paul Erdős, the disappearance of Grothendieck and the asocial Perelman. Not just their strange worldly ways, but their wonderful achievements also.

This very enjoyable book is informative on so many levels for specialists and non-specialists alike.

Peter Ruane is not nomadic, has not (yet) disappeared, and he thinks he is not asocial. Indeed, he can be contacted at ruane.hp@blueyonder.co.uk.

**On the Number Line**

3—Can Bees Count?

5—Can Chickens Compute?

10—And the Name of the Rose

13—Bad Luck?

42—The Answer to Everything?

91—The Numbers on the Bone

1729—Hardy’s Taxi

119/100—High Percentages

π—As Beautiful as the Mona Lisa?

√−1—Victim of a Character Assassination

χ_{0}—The End of the Number Line?

**The Never-Ending Story of Prime Numbers**

Euclid Is Still Right

How Many Prime Numbers Are There?

Fermat Made a Mistake

The "Mozart of Mathematics" Makes Use of an Error

Another Search for Errors

**The Mathematical Perspective**

Estimates

Random Numbers

Everything Far Above Average

Integers

**Caution: Equations**

Equations for Everything?

The Body Mass Index

The Huntington Affair

Pythagoras Lives

Equations as Art

**The Small Puzzles**

Sudokus

3*x *+ 1

The Perfect Monster

The Great Puzzles

**Where Mathematics Is Created**

At the Desk

At the Coffee Machine

At the Café

In the Computer

In Bed

In Captivity

In an Attic Room in Princeton

On a Beach

In a Paradise with a Library

Knowledge in the ArXiv

Research in the Internet?

**The Book of Proofs**

About Proofs

Concerning Errors

About Computer Proofs

Concerning Precision

Concerning Surprises

**Three Legends**

Mathematician vs. Mathematician

Was It Kovalevskaya's Fault?

The Disappearance of Alexander Grothendieck

**What Kinds of People Are These?**

Paul Erdős: Traveler

Gian-Carlo Rota: Provocateur

Persi Diaconis: Magician

Daniel Biss: Politician

Caroline Lasser: Colleague

**What Mathematicians Can Do**

Self-Confidence and Visions

"Unfortunately Difficult" vs. "The Right Stuff"

Record Races

You Know More Math Than You Think

"Mathematics Is …"

**Read More**

**Index**

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