Dr. Crypton

the best math book for nonmathematicians I have ever read. a perfect mix of explanations of theorems, history, and hysterical anecdotes (which I read aloud to anyone who would listen).

There seems to be a thin line between being an eccentric genius and an incandescent excretory orifice; Paul Hoffman’s biography of Paul Erdős, The Man Who Loved Only Numbers, sometimes puts Erdős straddling the line. I think some of this is sour grapes; there’s a temptation for the ordinary to find lapses in the genius – hence all the stories about Einstein forgetting to wear socks.


Nevertheless, Erdős was definitely at least a quarter bubble off level. His typical routine consisted show more of showing up – often unannounced – at a colleague’s house and expecting to be fed and maintained for a couple of weeks. His initial greeting would be something like “Hello. Let n be an integer…” He would fiddle with the air conditioning, try to feed the dogs breakfast cereal, make disastrous attempts at cooking for himself, and generally act like Sheridan Whiteside in The Man Who Came to Dinner – except the host would get several academic papers out of the encounter. This led to the invention of the Erdős number: if you were Paul Erdős, your Erdős number was zero. If you had published a paper with Paul Erdős, your Erdős number is 1. If you published a paper with someone who had, in turn, published a paper with Erdős, your Erdős number is 2, and so on. Hoffman is not a mathematician and is thus sometimes at a loss for things to say about Erdős; thus he relates that when Henry Aaron was trying to break Babe Ruth’s home run record, Emory mathematician Carl Pomerance noted that 714 X 715 (Ruth’s number and Aaron’s target) was the product of the first seven primes, and that the sum of the prime factors of 714 was also the sum of the prime factors of 715, leading to the discovery of “Ruth-Aaron Numbers”, consecutive integers with these properties (the next pair is 18490 and 18491). Erdős had never heard of Pomerance but called him, leading to the publication of 21 papers. Pomerance persuaded Erdős to come to Emory and get an honorary degree; by coincidence Henry Aaron received an honorary degree at the same convocation and Pomerance persuaded them to sign a baseball – leading to Hoffman’s point in the anecdote: Henry Aaron has an Erdős number of 1, if you count baseballs.


There are lots of amusing little anecdotes like this – I suppose this is the only way a casual reader is likely to read the book. My favorite is the account of René Descartes encountering a ruffian while escorting a lady of the evening, quickly whipping out his rapier and disarming the thug, then commenting that he wouldn’t kill him because “…he was too ugly to die before such a beautiful lady”. I never realized Descartes was a swordsman. It would take the mind of a sadist to expand on the anecdote and speculate what might have happened if he had stepped to the front to defend an entire troop of harlots this way – but that would be putting Descartes before the whores.


It is somewhat gratifying to find that Erdős was stumped by Marilyn vos Savant’s “Monty Hall” problem; Erdős, like a substantial fraction of the world’s mathematicians, assumed that no advantage would be gained by switching doors (if you’re not familiar with the problem I suggest googling, it’s too long to explain it here). Hoffman correctly points out that this is actually a case of Bayesian probability – but unfortunately doesn’t explain why. Interestingly enough for a book on a mathematician whose main interest was number theory, when I tried to look up the details I found that the book’s index is incorrect. Apparently a 16-page photo section was added without re-indexing; thus every index entry after page 148 is incorrect. I was pleased to find that I still have a sufficient grasp of mathematics to b e able to add 16 to everything. Although I tried subtracting 16 first.


Good light reading for the slightly mathematically inclined. show less

I wish there were more people like Paul Erdös. I was only ever decent at math in high school, and terrible at math after that, so his exploits make me jealous in a good way. I think for many people, and certainly frequently for me, math beyond a certain point is a dense, lightless thicket of symbols. Maybe everyone is born with a certain amount of math facility, and once you learn up to the point where your returns have diminished to uselessness, you have no choice but to forget about it show more and move on to something else. I made it through calculus and still remember some of what I learned, but I wouldn't want to bet anyone's life on me being able to integrate anything more complicated than a sine function very quickly. That's why it's so cool to read an account of a genuine math genius at work - even though I know that this guy who published over 1,500 papers in his lifetime is on another plane entirely when it comes to mathematics, he's so dedicated to the wonders of the subject that it gradually infected me through the pages and I came away wishing I had stuck with my math classes.

I often wonder to what extent being good at math is simply an innate quality, a gift that you either have or you don't. One of the things that struck me when I was reading Gödel Escher Bach is that Douglas Hofstader's explanations of complicated mathematical issues were much more comprehensible than that same explanation from a textbook (or even Wikipedia), and a large part of it was due to the fact that he gave a lot of history and narrative behind the various problems instead of just laying out symbols and variables. Humans naturally learn through narratives and stories, and it takes a rare kind of person to be able to strip away all of the scene-setting and background and get straight to the abstract symbol-manipulation. Probably some people are just born with the potential to understand things like Russell's paradox and some aren't, but I would really like to know exactly why that is, what separates the neurology of an Erdös from that of a mere mortal. I like that the book doesn't make Erdös - a fairly weird guy even by the relaxed standards of mathematicians - out to be some kind of freak, which I've frequently seen done to some of the more singular characters in science history like Newton.

Instead it's filled with plenty of testimonials about his kindness, his many friendships, and of course his unbelievable gift for probing the relationships between numbers. Explaining higher-level mathematics to a lay audience is one of the toughest tasks a writer can undertake, and Hoffman does a good job of giving the reader a brief tour of some of the many areas of math that Erdös influenced or revolutionized in some way. It's almost comforting to realize that even many professional mathematicians were baffled by what he was doing, and really the way he was able to find patterns in numbers is one of those things that just got more and more impressive with each page. I don't know what kind of mental circuitry lies behind mathematical talent, but I wish I had it, because many of the problems Erdös struggled with are extremely interesting in their own right, if you're curious at all at the mysterious relationships behind the world that we see. There are just so many weird things about prime numbers that you can forgive Erdös' monastic devotion to the subject. I wish I had read this when I was struggling with differential equations, it might have given me some inspiration and fortitude to remember that mathematics is an infinite field. No one can know everything, and that leaves plenty of room for even the most meager contributor to make a mark. show less

By the time I got around to reading this book, I'll admit that I was wondering if it was a redundant exercise in the wake of seeing the PBS documentary based on Hoffman's work. Such is not the case. While the TV program plays up the technological successes in Santo-Dumont's career the book is more of a life, and deals quite forthrightly with the issues relating to the man's life-style, sexuality, and the question of just when Santos-Dumont's "madness" began to assert itself. Hoffman also show more goes further in the book in terms of placing the achievements of Santos-Dumont in the context of the technological fervor of the time, and the activities of his fellow aviation pioneers. show less