Contents
PART I
HISTORICAL TIDBITS
1 Lopping Leap Years 3
2 Is the World Coming to an End Soon? 6
3 Cozy Zurich 8
4 Daniel Bernoulli and His Difficult Family 11
PART II
UNSOLVED CONJECTURES
5 The Mathematicians’ Million Dollar Baby 17
6 A Puzzle by Any Other Name 20
7 Twins, Cousins, and Sexy Primes 24
8 Hilbert’s Elusive Problem Number 16 27
PART III
SOLVED PROBLEMS
9 The Tile Layer’s Efficiency Problem 33
10 The Catalanian Rabbi’s Problem37
11 Even Infinite Series End Sometimes40
12 Proving the Proof43
13 Has Poincaré’s Conjecture Finally Been Solved?48
PART IV
PERSONALITIES
14 Late Tribute to a Tragic Hero55
15 The Unpaid Professor59
16 Genius from a Different Planet61
17 The Resurrection of Geometry66
18 God’s Gift to Science?69
19 Vice-President of Imagineering75
20 The Demoted Pensioner 80
21 A Grand Master Becomes Permanent Visiting
Professor 85
PART V
CONCRETE AND ABSTRACT MATTERS
22 Knots and “Unknots”93
23 Knots and Tangles with Real Ropes97
24 Small Mistakes May Have Large Consequences102
25 Ignorant Gamblers106
26 Tetris Is Hard109
27 Groups, Monster Groups, and Baby Monsters112
28 Fermat’s Incorrect Conjecture116
29 The Crash of Catastrophe Theory119
30 Deceptive Simplicity122
31 The Beauty of Dissymmetry125
32 Random and Not So Random128
33 How Can One Be Sure It’s Prime?132
PART VI
INTERDISCIPLINARY POTPOURRI
34 A Mathematician Judges the Judges (Law) 137
35 Elections Aren’t Decided by the Voters Alone
(Political Science) 140
36 A Dollar Isn’t Always Worth a Dollar
(Insurance) 146
37 Compressing the Divine Comedy (Linguistics)149
38 Nature’s Fundamental Formula (Botany)155
39 Stacking Words Like Oranges and Tomatoes
(Computer Science) 158
40 The Fractal Dimension of Israel’s Security
Barrier (Geography) 161
41 Calculated in Cold Ice (Physics)164
42 Built on Sand (Physics)167
43 Buzzing Around Corners (Biology)170
44 Inexperienced Traders Make the Market Efficient
(Economics) 172
45 The Waggle Dance of Internet Servers (Computer
Science, Biology) 175
46 Turbulent Liquids and Stock Markets (Finance,
Economics) 178
47 Encrypting Messages with Candles and Hot Plates
(Cryptography) 180
48 Fighting for Survival (Evolutionary Theory,
Finance) 184
49 Insults Stink (Neurosciences, Economics)187
50 Bible Codes: The Not So Final Report
(Theology) 190
References 195
Index 199
Preface
Whenever a socialite shows off his flair at a cocktail party
by reciting a stanza from an obscure poem, he is considered
well-read and full of wit. Not much ado can be made
with the recitation of a mathematical formula, however.
At most, one may expect a few pitying glances and the
title “party’s most nerdy guest.” To the concurring nods
of the cocktail crowd, most bystanders will admit that
they are no good at math, never have been, and never
will be.
Actually, this is quite astonishing. Imagine your lawyer
telling you that he is no good at spelling, your dentist
proudly proclaiming that she speaks no foreign language,
and your financial advisor admitting with glee that he
always mixes up Voltaire and Molière. With ample reason
one would consider such people as ignorant. Not so
with mathematics. Shortcomings in this intellectual discipline
are met with understanding by everyone.
I have set myself the task of trying to remedy this
state of affairs somewhat. The present book contains articles
that I wrote on mathematics during the past three
years for the Swiss daily newspaper Neue Zürcher Zeitung
and its Sunday edition NZZ am Sonntag. It was, and is,
my wish to give readers an understanding not only of the
importance but also of the beauty and elegance of the
subject. Anecdotes and biographical details of the oftentimes
quirky actors are not neglected, but, whenever possible, I
give an idea of the theories and proofs. The complexity of
mathematics should neither be hidden nor overrated.
Neither this book nor, indeed, my career as a mathematics
journalist evolved in a linear fashion. After studies
of mathematics and physics at the Swiss Federal Institute
of Technology in Zurich and a few career changes, I
became the Jerusalem correspondent for the Neue Zürcher
Zeitung. My job was to report about the goings-on in the
Middle East. But my initial love for mathematics never
waned, and when a conference about symmetry was to be
held in Haifa, I convinced my editor to send me to this
city in northern Israel in order to cover the gathering.
It turned out to be one of the best assignments I ever did
for the paper. (It was nearly as good as the cruise on a
luxury liner down the Danube to Budapest, but that is
another story.) From then on I wrote, on and off, about
mathematical themes.
In March 2002 I had the opportunity to make use of
my mathematical interests in a more regular fashion. The
NZZ am Sonntag launched the monthly feature “George
Szpiro’s little multiplication table.” I soon found out the
hard way that the reception by the readers was better
than expected: The incorrect birth date of a mathematician
in one of the early columns led to nearly two dozen
readers’ letters ranging in tone from the ironic to the
angry. A year later I received a special honor when the
Swiss Academy of Sciences awarded the column its Media
Prize for 2003. In December 2005, at a ceremony at
the Royal Society in London, I was named a finalist for
the European Commissionís Descartes Prize for Science
Communication.
I would like to thank my editors in Zurich—Kathrin
Meier-Rust, Andreas Hirstein, Christian Speicher, and Stefan
Betschon—for their patient and knowledgeable editorial
work, my sister Eva Burke in London for diligently translating
the articles, and Jeffrey Robbins of the Joseph Henry
Press in Washington, D.C,. for turning the manuscript
into what I hope has become an enjoyable book on a
subject commonly thought of as dry as a bone.
George G. Szpiro
Jerusalem, Spring 2006
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