Mathematics and the Real World (74 page)

perfect solids (a.k.a. Platonic bodies),
74
,
103
,
169
,
360

photoelectric effect,
158
,
161

photons,
188

Planck's constant,
161

Platonism,
75

Plimpton 322 (potsherd),
43

Poggendorff illusion,
65

Poincaré's conjecture,
351
,
353
,
357

polynomial rate,
295

positron,
166

principle of least action,
122
,
149
,
174

probabilistic algorithms,
299

probability function,
211

proton,
160

public-key cryptology,
303

purpose,
69
,
81

Pythagoras's theorem,
37
,
44
,
51

Pythagoreans,
51
,
71
,
78
,
92

Pythagorean triplets,
44

quantum computers,
311

quantum theory,
164

quarks,
170

randomness,
164
,
181
,
186

rational expectations,
229

reduction ad absurdum,
53
,
144

relativity

general,
155

special,
151
,
153

theory of,
142

Renaissance,
91

revealed preferences,
258

RGB (color system),
134

Rhind papyrus (a.k.a. Ahmes papyrus),
47

rigor,
39

RSA (encryption method),
304

Russell's paradox,
333

St. Petersburg paradox,
200
,
257

sample space,
211

Schrödinger's equation,
162
,
170

self-similarity,
176

sieve of Eratosthenes,
85
,
291

slide rule,
282

social choice,
239

spin,
166

squaring the circle,
56

stable marriage (a.k.a. stable matching),
233

statistical mechanics,
134

statistics,
195
,
197

strategies in equilibrium,
246

strategy,
245
,
248

dominant,
246

mixed,
251

string,
71
,
124
,
125
,
137

string equation,
124
,
163

string theory,
171

SU(3) group,
168

sudoku,
293
,
302

sunspots,
231

syllogisms,
59

syllogistic fallacies,
61

tali,
185

Talmud,
187
,
263

tangent,
318

teleology,
69
,
81

thinking,
343

by comparison,
344

creative,
344

mathematical,
383

tidal waves,
95
,
118
,
230
,
288

trigonometry,
87
,
275

trisecting an angle,
56

Turing machine,
291

Turing's test,
306

types, theory of,
334

uncertainty,
181
,
220
,
252
,
257

uncertainty principle,
165

utility,
255

expected,
255

von Neumann–Morgenstern,
257

value of a game,
251

Watt regulator,
365

wave equation,
124

Weizac (computer),
287

Zermelo-Fraenkel axioms,
335
,
339
,
340

Photo by Raanan Michael

ZVI ARTSTEIN is the Hettie H. Heineman Professor of Mathematics at The Weizmann Institute of Science, where he has worked for over thirty-eight years as a scientist, a teacher, and an administrator. He is the author of more than 120 scientific articles published in peer-reviewed journals.

Table of Contents

Cover

Title Page

Copyright Page

Dedication Page

Contents

Preface

Chapter I. Evolution, Mathematics, and the Evolution of Mathematics

1. Evolution

2. Mathematical Ability in the Animal World

3. Mathematical Ability in Humans

4. Mathematics that Yields Evolutionary Advantage

5. Mathematics with no Evolutionary Advantage

6. Mathematics in Early Civilizations

7. And then Came the Greeks

8. What Motivated the Greeks?

Chapter II. Mathematics and the Greeks’ View of the World

9. The Origin of Basic Science: Asking Questions

10. The First Mathematical Models

11. Platonism versus Formalism

12. Models of the Heavenly Bodies

13. On the Greek Perception of Science

14. Models of the Heavenly Bodies (Cont.)

Chapter III. Mathematics and the View of the World in Early Modern Times

15. The Sun Reverts to the Center

16. Giants’ Shoulders

17. Ellipses versus Circles

18. And then Came Newton

19. Everything you Wanted to know about Infinitesimal Calculus and Differential Equations

20. Newton's Laws

21. Purpose: The Principle of Least Action

22. The Wave Equation

23. On the Perception of Science in Modern Times

Chapter IV. Mathematics and the Modern View of the World

24. Electricity and Magnetism

25. And then Came Maxwell

26. Discrepancy between Maxwell's Theory and Newton's Theory

27. The Geometry of the World

28. And then Came Einstein

29. The Discovery of the Quantum State of Nature

30. The Wonder Equation

31. Groups of Particles