# 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 Cover11
- Title iii4
- Introduction v6
- Contents ix10
- Alphabet, Application of Pyramid Height to the 112
- American Revolution, The Role of 57 in the 415
- Applied Mathematics 920
- Base for the Number System, The Best 2031
- Bitterness, Cranks' 3243
- Calculus, Celestial 3849
- Cantor's Diagonal Process 4051
- Congressional Record, Mathematics in the 4657
- Constant Society, The 5061
- Consultation, Lack of, of Cranks with Experts 5364
- Crank, Case Study of a 5566
- Crank, The Making of a 6778
- Deduction, The Joy of 7889
- Duplication of the Cube 8697
- Ellipse, Circumference of an 93104
- Encouraging Cranks, The Folly of 97108
- Equations, Solving 102113
- Fermat's Last Theorem 105116
- Fermat's Little Theorem 135146
- Fifth Postulate, Euclid's 137148
- Four-Color Theorem, The 159170
- Godel's Theorem 167178
- Goldbach Conjecture, The 171182
- Greed 179190
- Incomprehensibility of Crank's Works 182193
- Infinity, Difficulties with 184195
- Insanity 189200
- Legislating Pi 192203
- Linear Programming, Conspiracy Involving 198209
- Magic Squares 200211
- Mail, Crank 205216
- Megalomania 208219
- Money to be Made in Mathematics, Lack of 222233
- Nines, Casting Out 226237
- Nonagons, Regular 231242
- Notation, Nonstandard 235246
- Number Theory, The Lure of 239250
- Perfect Numbers 242253
- Phi 245256
- Prayer, Matrix 251262
- Primes, The Secret of the 254265
- Primes, Twin, Existence of Infinitely Many 256267
- Prolificity, Crank's 260271
- Puzzle, A 269280
- Pythagoreans, Neo- 271282
- Pythagoreans, The Mystery of the 274285
- Quadrature of the Circle 279290
- Set Theory 322333
- Signs, The Rule of 324335
- Solution to a Puzzle 330341
- Sphere, Philosophy of the 331342
- Statistics, Parameter Estimation in 334345
- Taxonomy, Mathematical 337348
- Time, Wasted 339350
- Topology, Applied 341352
- Trisection of the Angle 342353
- Van Der Pol's Equation 349360
- Notes 353364
- Index 363374
- Back Cover Back Cover1384