Chapter 13.
of a 300 Year Old Problem
Jurg
¨
Kramer 175
1. Introduction 175
2. How did Fermat come to his Conjecture? 175
3. The period between 1637 and 1980 177
4. The three worlds 178
5. The bridges between the three worlds 181
6. The anti-Fermat world does not exist 182
References 183
Chapter 14. A Short History of the Nash Equilibrium
Karl Sigmund 185
Does Sherlock Holmes have a chance? 185
The art of the bluff 186
Maximin solutions 188
The Nash equilibrium 189
Ideas from evolution theory 190
The prisoners’ dilemma 191
Tit for Tat 192
Altruism versus self-interest 193
Chapter 15. Mathematics in the Climate of Global Change
Rupert Klein 197
Why climate and climate impact research? 197
Complexities 199
“Story exercises” 202
Multiple scales 204
Approximate solutions and missing lattice points 206
Multiscale asymptotics for the oscillator with small mass and damping 208
Hurricanes: an example in multiscale phenomena 212
Conclusion 214
References 215
Part 4. The Central Theme 217
Chapter 16.
and the Boundaries of Computability
Martin Aigner 219
1. Prime numbers 219
2. Secret codes 221
3. Boundaries of computability 224
References 226
Chapter 17. The Mathematics of Knots
Elmar Vogt 227
History 227
Wild and tame knots and the search
for the right mathematical concept 231
viii CONTENTS
Fermat’s Last Theorem—the Solution
Prime Numbers, Secret Codes
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