AMS / MAA SPECTRUM VOL 44 Steven G. Krantz MATHEMATICAL More Stories & Anecdotes of Mathematicians & the Mathematical 10.1090/spec/044 Mathematical Apocrypha Redux Originally published by The Mathematical Association of America, 2005. ISBN: 978-1-4704-5172-1 LCCN: 2005932231 Copyright © 2005, held by the American Mathematical Society Printed in the United States of America. Reprinted by the American Mathematical Society, 2019 The American Mathematical Society retains all rights except those granted to the United States Government. ⃝1 The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at https://www.ams.org/ 10 9 8 7 6 5 4 3 2 24 23 22 21 20 19 AMS/MAA SPECTRUM VOL 44 Mathematical Apocrypoha Redux More Stories and Anecdotes of Mathematicians and the Mathematical Steven G. Krantz SPECTRUM SERIES Published by THE MATHEMATICAL ASSOCIATION OF AMERICA Council on Publications Roger Nelsen, Chair Spectrum Editorial Board Gerald L. Alexanderson, Editor Robert Beezer Ellen Maycock William Dunham JeffreyL. Nunemacher Michael Filaseta Jean Pedersen Erica Flapan J. D. Phillips, Jr. Michael A. Jones Kenneth Ross Eleanor Lang Kendrick Marvin Schaefer Keith Kendig Sanford Segal Franklin Sheehan The Spectrum Series of the Mathematical Association of America was so named to reflect its purpose: to publish a broad range of books including biographies, acces­ sible expositions of old or new mathematical ideas, reprints and revisions of excel­ lent out-of-print books, popular works, and other monographs of high interest that will appeal to a broad range of readers, including students and teachers of mathe­ matics, mathematical amateurs, and researchers. 777 Mathematical Conversation Starters, by John dePillis All the Math Thats Fit to Print, by Keith Devlin Carl Friedrich Gauss: Titan ofScience, by G. Waldo Dunnington, with additional material by Jeremy Gray and Fritz-Egbert Dohse The Changing Space ofGeometry, edited by Chris Pritchard Circles: A Mathematical View, by Dan Pedoe Complex Numbers and Geometry, by Liang-shin Hahn Cryptology, by Albrecht Beutelspacher Five Hundred Mathematical Challenges, Edward J. Barbeau, Murray S. Klamkin, and William 0. J. Moser From Zeroto Infinity, by Constance Reid The Golden Section, by Hans Walser. Translated fromthe original German by Peter Hilton, with the assistance of Jean Pedersen. I Want to Be a Mathematician, by Paul R. Halmos Journey into Geometries, by Marta Sved JULIA: a lifein mathematics, by Constance Reid R. L. Moore: Mathematician and Teacher, by John Parker The lighter Side ofMathematics: Proceedings ofthe Eugene Strens Memorial Coriference on Recreational Mathematics & Its History, edited by Richard K. Guy and Robert E. Woodrow lure of the Integers, by Joe Roberts Magic Tricks, Card Shujjling, and Dynamic Computer Memories: The Mathematics ofthe PerfectShuffle, by S. Brent Morris The Math Chat Book, by Frank Morgan Mathematical Adventures for Students and Amateurs, edited by David Hayes and Tatiana Shubin. With the assistance of Gerald L. Alexanderson and Peter Ross Mathematical Apocrypha, by Steven G. Krantz Mathematical Apocrypha Redux, by Steven G. Krantz Mathematical Carnival, by Martin Gardner Mathematical Circles Vol I: In Mathematical Circles Quadrants I, II, III, IV, by Howard W. Eves Mathematical Circles Vol II: Mathematical Circles Revisited and Mathematical Circles Squared, by Howard W. Eves Mathematical Circles Vol III: Mathematical Circles Adieu and Return to Mathematical Circles, by Howard W. Eves Mathematical Circus, by Martin Gardner Mathematical Cranks, by Underwood Dudley Mathematical Evolutions, edited by Abe Shenitzer and John Stillwell Mathematical Fallacies, Flaws, and Flimflam, by Edward J. Barbeau Mathematical Magic Show, by Martin Gardner Mathematical Reminiscences, by Howard Eves Mathematical Treks: From Surreal Numbers to Magic Circles, by lvars Peterson Mathematics: Queen and Servant of Science, by E.T. Bell Memorabilia Mathematica, by Robert Edouard Moritz Musings of the Masters: An Anthology of Mathematical Reflections, edited by Raymond G Ayoub New Mathematical Diversions, by Martin Gardner Non-Euclidean Geometry, by H. S. M. Coxeter Numerical Methods That Work, by Forman Acton Numerologyor What Pythagoras Wrought, by Underwood Dudley Out of the Mouths of Mathematicians, by Rosemary Schmalz Penrose Tiles to Trapdoor Ciphers ... and the Return of Dr. Matrix, by Martin Gardner Polyominoes, by George Martin Power Play, by Edward J. Barbeau R. L. Moore: Mathematician and Teacher, by John Parker The Random Walks of George Po/ya, by Gerald L. Alexanderson Reality Conditions: Short Mathematical Fiction, by Alex Kasman Remarkable Mathematicians, from Euler to von Neumann, by loan James The Search for E. T Bell, also known as John Taine, by Constance Reid Shaping Space, edited by Marjorie Senechal and George Fleck Sherlock Holmes in Babylon and Other Tales of Mathematical History, edited by Marlow Anderson, Victor Katz, and Robin Wilson Student Research Projects in Calculus, by Marcus Cohen, Arthur Knoebel, Edward D. Gaughan, Douglas S. Kurtz, and David Pengelley Symmetry, by Hans Walser. Translated from the original German by Peter Hilton, with the assistance of Jean Pedersen. The Trisectors, by Underwood Dudley Twenty Years Before the Blackboard, by Michael Stueben with Diane Sandford The Words of Mathematics, by Steven Schwartzman Preface Jt has been a pleasure to experience the warm reception that the first vol­ ume of these stories has received. The reader may understand, therefore, that I have been thereby motivated to collect more stories. This has turnedout to be easier than one might have imagined. The hard­ bitten skeptic may suppose that all the best stories went into the original Mathematical Apocrypha. l am happy to say that that is not the case. More people have come forward with new stories, and my memory has shifted into overdrive forreviving old and forgotten stories. For this new edition, Michael B. Henry did a marvelous job of unearthing dates and details about the subjects of various stories. His efforts add a lot to the credibility and verisimilitude of these anecdotes, and I owe him my hearty thanks. The MAA reviewers gave my manuscript a careful read and offered many constructive suggestions and criticisms. I was frequently impressed and amazed by their knowledge of mathematical culture. Don Albers has been an enthusiastic and proactive publisher. He did a great job of collecting photographs for this volume. Jerry Alexanderson, serving as editorial advisor for the project, was a marvel. He read many drafts of the manuscript and contributed much detail and wisdom. I am most grateful to him. Elaine Pedreira oversaw the entire editorial process forthis book, and Beverly Joy Reudi supervised the typesetting and produc­ tion. I am gratefulto them both. It is, as always, a pleasure to record these bits of our cultural folklore. I seek feedback and corrections from readers so that future editions may be more complete and more accurate. SGK St. Louis, MO vii In memory of Halsey Roy den ( 1928-1993 ), an inspiring storyteller. And for Paul Erdos ( 1913-1996), who lived the mathematical lifeto its fullest. eontents Chapter 1 Utter Frivolity .................................... I Chapter 2 Utter Helplessness ................................ 31 Chapter 3 Utter Utterances ................................. 59 Chapter 4 Utter Sagacity ................................... 89 Chapter 5 Utter Sanguinity ................................ 117 Chapter 6 Utter Seriousness ............................... 145 Chapter 7 Utter Credulity ................................. 183 Chapter 8 Utter Confusion ................................. 217 Chapter 9 Utter Solipsism ................................. 233 Further Reading .......................................... 277 Index ................................................... 281 lurtlterKeading [BEL] E.T. Bell, Men ofMathematics, Simon & Schuster, New York, 1965. [BLO] S. Bloch, Review of £tale Cohomology by J. S. Milne, Bulletin of the AMS, new series, 4(1981), 235-239. [COD] B. Beckman, Codebreakers: Arne Beurling and the Swedish Crypto Program During World War II, translated by Kjell-Ove Widman, American Mathematical Society, Providence, RI, 2002. [BOA] R. P. Boas, Jr., Lion Hunting and Other Mathematical Pursuits,. A Collection ofMathematics, Verse and Stories, Gerald L. Alexanderson and Dale H. Mugler, eds., The Dolciani Mathematical Expositions 15, Mathematical Association of America, Washington, DC, 1995. [CAH] Campbell and Higgins, Mathematics: People, Problems, Results, Wadsworth, Belmont, CA, 1984. [DUR] P. Duren, A Centuryof Mathematics in America, with the assistance of Richard Askey and Uta Merzbach, American Mathematical Society, Providence, 1988-1989. [ERO] P. Erdos, On the fundamentalproblem of mathematics, Amer. Math. Monthly 79(1972), 149-150. [EVE] H. Eves, Mathematical Circles 3 Volume Set, The Mathematical Association of America, Washington, DC, 2004. [EXO] G. Exoo, A Euclidean Ramsey problem, Disc. Comput. Geom. 29(2003), 223-227. [FAD] C. Fadiman, The Mathematical Magpie, Simon and Schuster, New York, 1962. [GOF] C. Goffman,And what is your Erdos number?, Amer. Math. Monthly 76(1969), 791. 277 278 [GRA] J. Gray, Did Poincare say "Set theory is a disease."?, Math. Intelligencer 13( 1991), 19-22. [HAL] P. Halmos, / Want to Be a Mathematician, Springer-Verlag, New York, 1985. [HAR] G. H. Hardy, A Mathematician's