More than a little crazy

I finished Paul Hoffman's book about Paul Erdős, The Man Who Loved Only Numbers, last week and wanted to give a little more complete book review about what I learned, not only about Erdős, but about mathematicians in general. Hoffman discusses many famous thinkers, along with mathematics in general and why he thinks it's important.

Permission granted by Fan Chung Graham 11/9/07

Can you guess which one of these mathematicians is Erdős? I thought so. The picture was taken in 1986 at a conference in Japan. The other two are a couple who basically created a permanent room in their home for him: Ron and Fan Graham. Both collaborated with him extensively and have stories in Hoffman's book about how difficult he could be. He was very childlike in many ways; he couldn't even tie his own shoes by himself. He only needed a few hours of sleep every night and whoever he was staying with would be worn out within a week or two at most. Erdős traveled constantly and went from one mathematician's home to another. He really did love only numbers and came up with some astounding mathematical theories. He also developed the probabilistic method, which helped others create computers.

Hoffman shows that many mathematicians are a little bit crazy. In fact, the last chapter in the book is titled, "We Mathematicians Are All a Little Bit Crazy." I remember the movie "A Beautiful Mind,"about John Forbes Nash, a Nobel laureate, who suffered from schizophrenia. Apparently paranoid schizophrenia often comes with a highly creative mind, which makes me wonder why. I learned about several paranoid but brilliant mathematicians who managed to continue their work with this debilitating affliction. The fact that Erdős was so eccentric is not as surprising once you read Hoffman's book and read about some really odd fellows.

I also learned to appreciate math and numbers in a way I never had before. It was very interesting to read about how the concept of zero came into being. Roman numerals were the only game in town throughout the Dark Ages. Fibonnaci was born in Pisa in the twelfth century and studied Euclid and other Greek mathematicians. He wrote a book that became the most influential work in getting the West to convert to Hindu-Arabic numerals. He helped to show how superior they were, and it seems hard to imagine a world today without the concept of zero or negative numbers. The Greeks had no trouble subtracting three cows from six cows, for example, but they didn't take seriously the concept of minus three cows. From pp. 212-213 in the book:

As Martin Gardner put it, "A cow from a cow leaves nothing, but adding a negative cow to a positive cow, causing both to vanish like a particle meeting its antiparticle, seems as ridiculous as the old joke about the individual whose personality was so negative that when he walked into a party, the guests would look around and ask, 'Who left?' "

The concept of prime numbers also fascinates me now, after finishing the book and understanding their importance. I can't actually SEE a prime like many mathematicians can, but it makes sense to me now that so many mathematicians have spent their entire careers with those magical numbers. Just as an aside, as I was reading the book I realized that the first day of the upcoming new year will be 1/1/11 (eleven is a prime number). So I guess you could say a little of the religion has rubbed off on me. A very little.
:-)