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.
:-)

Madmen and mathematicians

This is my latest reading pile. These two novels on the left caught my eye at different times at the local bookstore (the Foer book and the Doctorow book). But the other two were lent to me by my friend Judy, who taught mathematics before she retired. They have been sitting in a pile waiting for me to read them. While the novels were interesting, each in its own way, they will not stay with me the way the other two are likely to. I can hardly wait to find out what sparked Judy's interest in math. I already knew that she loves words as much as me.

The Professor and the Madman is a very interesting biography by Simon Winchester, who has written quite a few different types of books. The subtitle is "A Tale of Murder, Insanity, and the Making of the Oxford English Dictionary." What is amazing to me was what an absorbing tale it is! Professor James Murray was the first editor of the incredibly massive undertaking of the first complete dictionary of the English Language, which took seventy years to finish, beginning in 1857. One person he got a great deal of assistance from was Dr. William Chester Minor, who was one of the thousands of contributors who submitted illustrative quotes showing the different nuances of a particular word's usage.

It turns out that Minor was in an insane asylum in Crowthorne, fifty miles from Oxford. The book tells of the relationship that developed over thirty years between the two men, and how for such a long time Murray didn't know that his colleague was mad. Minor was afflicted with what now is labeled paranoid schizophrenia, killed a man, and the only treatment at the time was to lock up the patient behind bars. One thing that I was struck with, over and over, was that if the treatment that exists today had been available then, Minor would most likely never have completed all that he did for the OED (Oxford English Dictionary). The task gave him a focus for his entire incarcerated life, and I wonder whether other geniuses might lay hidden under the lithium-induced state of present-day victims of schizophrenia. The author raises that very question toward the end of the book. The picture on the cover (at right) was taken of William Minor, which surprised me when I finally figured it out from the contents of the book. At first, I was sure this was a picture of the professor. The link at the beginning of these two paragraphs goes to the Amazon website where I found several copies of this 1998 book still available for very reasonable prices. It was a truly absorbing read.

And now onto the book that I'm reading right now: The Man Who Loved Only Numbers, the story of Paul Erdős, a Hungarian mathematician who died in 1996 at the age of 83. Paul Hoffman's biography of Erdős tells the story of a man who traveled constantly, never had a home to speak of, lived out of a plastic bag, and never cared about anything except, well, numbers. (That first link takes you to Amazon in order to find out how to order it, and the second takes you to the Wikipedia link about Erdős himself.) I am not finished with this book, but my mind has already been opened in many ways to the mystery of numbers. I knew a little about prime numbers, not very much, but they never seemed all that interesting to me in the first place. I didn't realize that there are perfectly sane people who spend their entire lives thinking about them. (Okay, maybe not perfectly sane, but they are not locked up.) (smile)

For those of you who don't know what makes a number a prime number, integers like 2, 3, 5, 7, 11, 13, and 17 are numbers that are evenly divisible only by themselves and the number 1. Except for 2, all prime numbers are odd. They don't follow any particular order, and there is no known useful formula that yields all the prime numbers and no composites. At first, I wondered why anybody would even CARE, but then, while pondering their attraction, I suddenly remembered how incredibly fascinated I was years ago when I first learned about the Golden Mean or, more correctly, the Golden Ratio. I have been amazed at how many times I have seen this same pattern in nature:

From Wikipedia

Okay, maybe there is a reason why so many mathematicians throughout the ages have been fascinated with the mystery of numbers. Last night when I went to bed, after starting this book, I could hardly wait to ask Smart Guy about prime numbers. This started a conversation that went on for at least an hour, and I went to sleep with numbers dancing around in my head. Although I am only on page 73 of the 268-page book, I am definitely hooked. More later.
:-)