Dr. Crypton

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 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.… (more)

I'm planning a trip around the world in Erdos' style --- showing up, working hard on a project with someone, and then peaceing out. Most books about mathematicians I hate because they spend too much time discussing their personal lives, and not enough talking about their mathematical contributions. Unfortunately, this is the one book contrary to that style. It's a book with a few fun Erdos anecdotes, but mostly a description of somewhat-related mathematics and mathematicians for the layperson. Cantor's diagonalization argument is great and all, but I know it, and it doesn't help answer any questions I have about Erdos' lifestyle.

All of that being said, this is a fun book that's worth reading. It just didn't answer what I was hoping it would.… (more)