Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever

by Hal Hellman

Praise for Hal Hellman

Great Feuds in Mathematics

""Those who think that mathematicians are cold, mechanical proving machines will do well to read Hellman's book on conflicts in mathematics. The main characters are as excitable and touchy as the next man. But Hellman's stories also show how scientific fights bring out sharper formulations and better arguments.""
-Professor Dirk van Dalen, Philosophy Department, Utrecht University

Great Feuds in Technology

""There's nothing like a good feud to grab your attention. And when it comes to describing the battle, Hal Hellman is a master.""
-New Scientist

Great Feuds in Science

""Unusual insight into the development of science . . . I was excited by this book and enthusiastically recommend it to general as well as scientific audiences.""
-American Scientist

""Hellman has assembled a series of entertaining tales . . . many fine examples of heady invective without parallel in our time.""
-Nature

Great Feuds in Medicine

""This engaging book documents [the] reactions in ten of the most heated controversies and rivalries in medical history. . . . The disputes detailed are . . . fascinating. . . . It is delicious stuff here.""
-The New York Times

""Stimulating.""
-Journal of the American Medical Association

Genres: Mathematics, Nonfiction, History

256 pages, Hardcover

First published September 1, 2006

Reviews

[Sean Farhat · Rating 3 out of 5]

I wonder how all these fragile-ego mathematicians would react to academic twitter

[Ra7thsign · Rating 4 out of 5]

Warning: If you don't like math, this book is not for you.

This book will be interesting to mathematicians who have experienced a broad range of college mathematics courses (the author assumes that the reader has a familiarity with many important theorems and definitions from various branches), but there is not much in the way of actual "feuds," so this book isn't one of those "popular math" books; don't read this if that's what you're looking for.

The only real feuds to speak of are the differing viewpoints about mathematics as a philosophy, and that doesn't really start until chapter 6. The author's personal opinions on certain matters are subtle, but clear. It was a good read overall, but there are better books out there about the history of mathematics and/or the popularization of mathematics.

Ch. 1: Tartaglia vs. Cardano
Two unknowns engaged in a "feud" of sorts that time has shown to be insignificant either way. If you remember some algebra 2 this chapter may interest you.

Ch. 2: Decartes vs. Fermat
Interesting insight into the personal life of Decartes. Not so much a feud as a disagreement over a minor result in the field of optics. Fermat's response was revealing, though...

Ch. 3: Newton v. Liebniz
The one true mathematics feud of the book. It's difficult to choose a side here, but as Hellman states, history shows that Newton won the battle, but Liebniz won the war.

Ch. 4: Bernoulli vs. Bernoulli
Again, not so much a "feud" as a harmless sibling rivalry/jealously, perhaps inflamed by Johann's inferiority complex.

Ch. 5: Sylvester vs. Huxley
No feud to speak of as Huxley never responded to Sylvester. Interesting viewpoint from a supposed scientist, though.

Ch. 6: Kronecker vs. Cantor
Here's where the book really starts getting good, as we are now starting to see the differing viewpoints about what mathematics really is. Cantor is awesome. Kronecker is a retard (dude didn't believe in fractions! Let alone irrationals, transcendentals, et alia).

Ch. 7: Borel vs. Zermelo
This chapter picks up where the last chapter left off, discussing Zermelo's attempt to prove the axiom of choice, inspired by Cantor. Borel sucks.

Ch. 9: Poincare vs. Russell
Russell's attempt to formalize EVERYTHING is at odds with Poincare's simplistic and realistic view of mathematics. I side with Poincare if only for his sarcastic comments towards Russell (i.e.: do we really need no less than 25 equations to understand what the number 1 is?)

Ch. 9: Hilbert vs. Brouwer
More of the same. The lines begin to blur here, but I can't help but to side with Brouwer for some reason. Hilbert rubs me the wrong way; always has.

Ch. 10: Absolutists/Platonists vs. Fallibilists/Constructivists
Possibly the best chapter in the whole book. (Score one for the Absolutists!)

[Paul Quick · Rating 4 out of 5]

Many years ago I earned a degree in Mathematics so in this book recognize many names in this book ie.g. Hilbert, Weierstrauss, Poincare, Cardano, Tartaglia, Peano, Brouwer ... but only from names on theorems, postulates, conjectures .... However, I learned little about their personalities, conflicts, families so this book filled that huge gap. The story of the gambler-medical doctor cardano who stole a valued solution from Tartaglia who in turn had stole the solution from an earlier mathematician. What a mess and yet if it had not been stolen then the solution might never have been published since during those times secrecy could earn them big money. However, the story ended in tragedy for Cardano whose three children were losers - one promiscuous women, another murdered his wife and was executed, the second son was a gambler and alcoholic breaking into Cardano house and then arrested. However, eventually that same son teamed up with tartaglia and turned Cardano into the Inquisition and was arrested.

I was somewhat familiar with Fermat and his annoying statement 'here is a new theorem' but its proof I have but there is no space to write it here and then he died. Took three hundreds more to reproduce his proof if indeed he actually had one. Furthermore, his controversy with Descartes was a classic battle with Descartes unable to take criticism from 'The Prince of The Amateurs'.

So many other juicy stories very human and the Author gives a very lively perspective on a subject often thought to be dry. Good book!

[Chris · Rating 5 out of 5]

It's pretty good if you are interested in the schools in mathematics. Sort of like a guide book for undergrad like me to get some background on stuff that I'm learning.

[Emilio Minichiello · Rating 4 out of 5]

An interesting history of the main feuds in mathematical history. I learned a few new interesting tidbits about the Bernoullis, Descartes and Fermat. The writing was good, and it kept me interested til the last chapter or so. The only issue I had with it is that much of the book is well-trodden ground, kind of the same couple of stories told in every pop math book, but in a good deal more detail. Overall good though.

[Evanston Public Library]

My two middle-school kids are learning algebra and geometry, which I discovered I mostly remember. But they’re heading toward calculus, which I discovered I had mostly forgotten. So I started re-educating myself. While getting re-educated I learned the remarkable story behind calculus.

But first: What is calculus? In simple terms, it’s the mathematics of changing values. In less simple terms, it’s the set of tools for calculating “momentary” values like acceleration, deceleration, or slopes of curves (that’s differential calculus), and the related set of tools for calculating “cumulative” values like area, volume, or work (that’s integral calculus).

In metaphorical terms, it’s the song of the universe. I think of algebra as the words, and geometry as the music. Combine them and you get the song: the song of motion, engineering, physics, medicine, statistics, business, computers, even sports—any field in which problems can be mathematically modeled, and in which optimal solutions are desired.

So it matters who invented calculus. Was it the Englishman, Sir Isaac Newton (1642-1727)? Or the German, Gottfried Leibniz (1646-1716)? Probably the best answer is that it was both.

Newton came up with the basics first (building on predecessors’ work, of course—that’s another story). But Leibniz published first, independently, and did more to advance understanding. Neither saw it this way: each felt threatened by the other, perhaps even plagiarized by the other, and they battled bitterly. Their battle held back mathematical progress for decades, separating the English-speaking scientific world from the scientific world of continental Europe.

Ackroyd’s book highlights Newton’s personality, connecting it to his amazing insights not only into calculus, but also into gravitation and optics. It is a delight to read. Each sentence is a springboard for the next, and you gain keen insight into the character of the man voted by many the “scientist of the millennium.” Bardi writes more amateurishly, but explains the calculus battle in rich detail, exploring both Newton’s and Leibniz’s characters and linking them to the complex politics of their era. But if you don’t have the time (or the interest) to spend on a whole book, zero in on chapter three of Hellman—just twenty pages, almost as well-written as Ackroyd. (Jeff B., Reader's Services)

[dejah_thoris · Rating 2 out of 5]

Kind of split on this one. For someone who hasn't read the history of these debates, the overviews are good recaps of the highlights with some mathematical language that can be hard to follow for the layperson. Unfortunately, a few of the ten "feuds" mentioned weren't actually direct quarrels, but more like struggles between differing viewpoints on the same conundrum. Some got pretty heated though with careers in shambles after the more prominent person acted against the underdog, so it's interesting to see how science and mathematics developments are based on human interactions.

[Al Capwned · Rating 3 out of 5]

I had high expectations for this one. As a student of Mathematics I couldn't wait to read about the conflict between Newton and Leibniz or fallibilists versus constructivists etc. I was a bit disappointed, though. Some of the fueds discussed here are about purely mathematical ideas but some others are totally personal. I'm not saying that the latter is not interesting but I get the feeling this work is a bit unbalanced. It can also be a little tricky for those who are not associated with the exact siences at all.

[Chelsea M · Rating 3 out of 5]

It started out quite slow. I was expecting the disputes to be between mathematical ideas, but at first it was mostly just personal conflicts. This improved from about chapter 6, though, and I liked that ideas and people introduced in one chapter were often elaborated upon in the next.