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Do I Count? Stories from Mathematics

Chapman & Hall/CRC
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‘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

Date Received: 
Friday, August 9, 2013
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Gunter M. Ziegler
Publication Date: 
P. N. Ruane
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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
χ0—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
Random Numbers
Everything Far Above Average

Caution: Equations
Equations for Everything?
The Body Mass Index
The Huntington Affair
Pythagoras Lives
Equations as Art

The Small Puzzles
3x + 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 …"

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Friday, August 9, 2013