Is Mathematics Inevitable?

by Dudley, Underwood

• ISBN13: 9780883855669
• ISBN10: 0883855666
• Format: Hardcover
• Copyright: 2008-01-09
• Publisher: Mathematical Assn of Amer

Summary

This is a collection of gems from the literature of mathematics that shine as brightly today as when they first appeared in print - they deserve to be seen and admired. The selections include two opposing views on the purpose of mathematics, the strong law of small numbers, the treatment of calculus in the 1771 Encyclopaedia Britannica, several proofs that the number of legs on a horse is infinite, a deserved refutation of the ridiculous Euler-Diderot anecdote, the real story of and the Indiana legislature, the reason why Theodorus stopped proving that square roots were irrational when he got to the square root of 17, an excerpt from Mathematics Made Difficult, a glimpse into the mind of a calculating prodigy, and much more. There will be something here for anyone interested in mathematics.

Author Biography

Underwood Dudley was born in New York City in 1937. He attended the Carnegie Institute of Technology and had a Ph.D. from the University of Michigan. He is the author of Mathematical Cranks, Numerology, and The Trisectors. He has been a P°lya Lecturer for the MAA, has edited the College Mathematics Journal and the Pi Mu Epsilon Journal, has received a Trevor Evans Award, and has an Erd÷s number of 1. He has been a member of the MAA for longer than half of the organizations existence.

Table of Contents

Dieudonne on Mathematics	p. 1
Mathematics and Mathematicians	p. 1
Why Is Mathematics?	p. 15
Mathematics and the Physical World	p. 16
Is Mathematics Inevitable?	p. 31
Mathematics in Fun and in Earnest	p. 32
A Defense of Quadratic Equations	p. 41
Quadratic Equations	p. 43
Obtuse Triangles	p. 55
There Are Three Times as Many Obtuse-Angled Triangles as There Are Acute-Angled Ones	p. 57
A Small Paradox	p. 63
Why Your Classes Are Larger than "Average"	p. 63
Why is a Restaurant's Business Worse in the Owner's Eyes Than in the Customers'?	p. 66
Applied Mathematics	p. 69
Assigning Driver's License Numbers	p. 69
The Law of Small Numbers	p. 83
The Strong Law of Small Numbers	p. 83
The Parallel Postulate	p. 103
The Problem With Postulate 5	p. 105
Arithmetic in the United States	p. 119
A Calculating People	p. 120
The Moore Method	p. 141
I Want to be a Mathematician	p. 141
Early Calculus	p. 157
Problems	p. 173
On the Origin of Certain Typical Problems	p. 175
A Tangled Tale	p. 181
A Tangled Tale	p. 182
A Brief Life	p. 189
Brief Lives	p. 190
Cardano	p. 197
The Book of My Life	p. 199
Boole and Finite Differences	p. 217
George Boole and the Calculus of Finite Differences	p. 218
Calculating Prodigies	p. 231
The Great Mental Calculators	p. 232
James Smith, Circle-Squarer	p. 247
The Quadrature of the Circle	p. 249
Legislating [pi]	p. 261
Indiana's Squared Circle	p. 261
Mathematics and Music	p. 271
Emblems of Mind	p. 272
Mathematics Books	p. 285
On the Value of Mathematics (Books)	p. 285
Irrational Square Roots	p. 293
Theodorus' Irrationality Proofs	p. 295
The Euler-Diderot Anecdote	p. 299
The So-called Euler-Diderot Incident	p. 300
Mathematics Made Difficult	p. 305
Mathematics Made Difficult	p. 306
Mathematical Humor	p. 319
On the Set of Legs of a Horse	p. 319
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