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