# Mathematical Cranks

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*Underwood Dudley*

MAA Press: An Imprint of the American Mathematical Society

A delightful collection of articles about people who claim they have achieved the mathematically impossible (squaring the circle, duplicating the cube); people who think they have done something they have not (proving Fermat's Last Theorem); people who pray in matrices; people who find the American Revolution ruled by the number 57; people who have in common eccentric mathematical views, some mild (thinking we should count by 12s instead of 10s), some bizarre (thinking that second-order differential equations will solve all problems of economics, politics and philosophy). This is a truly unique book. It is written with wit and style and is a part of folk mathematics.

#### Reviews & Endorsements

Dudley Underwood extracts insights from an astonishing variety of examples.

-- Robert Matthews, New Scientist

A delightful collection of true accounts of individuals who claim to have achieved the mathematically impossible ...It is hard to put down and provides topics for an unending series of interesting discussions. The organization and breadth of the book are impressive, supported by a helpful index and a list of resources that encourage further explorations. A classic.

-- Choice

# Table of Contents

## Mathematical Cranks

- Cover 11
- Title 44
- Introduction 66
- Contents 1010
- Alphabet, Application of Pyramid Height to the 1212
- American Revolution, The Role of 57 in the 1515
- Applied Mathematics 2020
- Base for the Number System, The Best 3131
- Bitterness, Cranks' 4343
- Calculus, Celestial 4949
- Cantor's Diagonal Process 5151
- Congressional Record, Mathematics in the 5757
- Constant Society, The 6161
- Consultation, Lack of, of Cranks with Experts 6464
- Crank, Case Study of a 6666
- Crank, The Making of a 7878
- Deduction, The Joy of 8989
- Duplication of the Cube 9797
- Ellipse, Circumference of an 104104
- Encouraging Cranks, The Folly of 108108
- Equations, Solving 113113
- Fermat's Last Theorem 116116
- Fermat's Little Theorem 146146
- Fifth Postulate, Euclid's 148148
- Four-Color Theorem, The 170170
- Godel's Theorem 178178
- Goldbach Conjecture, The 182182
- Greed 190190
- Incomprehensibility of Crank's Works 193193
- Infinity, Difficulties with 195195
- Insanity 200200
- Legislating Pi 203203
- Linear Programming, Conspiracy Involving 209209
- Magic Squares 211211
- Mail, Crank 216216
- Megalomania 219219
- Money to be Made in Mathematics, Lack of 233233
- Nines, Casting Out 237237
- Nonagons, Regular 242242
- Notation, Nonstandard 246246
- Number Theory, The Lure of 250250
- Perfect Numbers 253253
- Phi 256256
- Prayer, Matrix 262262
- Primes, The Secret of the 265265
- Primes, Twin, Existence of Infinitely Many 267267
- Prolificity, Crank's 271271
- Puzzle, A 280280
- Pythagoreans, Neo- 282282
- Pythagoreans, The Mystery of the 285285
- Quadrature of the Circle 290290
- Set Theory 333333
- Signs, The Rule of 335335
- Solution to a Puzzle 341341
- Sphere, Philosophy of the 342342
- Statistics, Parameter Estimation in 345345
- Taxonomy, Mathematical 348348
- Time, Wasted 350350
- Topology, Applied 352352
- Trisection of the Angle 353353
- Van Der Pol's Equation 360360
- Notes 364364
- Index 374374
- Back Cover 384384