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Wednesday, January 16, 2008

Donald E. Knuth

Last week, Thursday, January 10th, was Donald E. Knuth's birthday. I cannot believe I missed it.

I first learned about him in university. Someone mentioned The Art of Computer Programming. They talked about it as if EVERYONE knew about it. Coming from a trade school background I had no idea who Donald E. Knuth was or any of his publications. Since my background was graphic arts and typesetting I was first intrigued by TeX and started using it to typeset my math homework. As time went on I switched from a Mathematics major to a Computer Science major, in part due to Donald E. Knuth.

When I started reading The Art of Computer Programming I noted in the preface the information about questions and how he ranked them. If it had [1] it would be a question that takes a second to answer. Something like [10] might take a few seconds to a minute, [20] might take a day, etc. (I might have these estimate wrong). The one which stuck in my head was questions ranked [50]. Remember, I had no idea who Donald E. Knuth was nor how brilliant he was. He gave as an example the following question:

If an integer n is greater than 2, then the equation an + bn = cn has no solutions in non-zero integers a, b, and c.

He then proceeded to say, "If anyone finds an answer to these questions I'd appreciate you letting me know."

I figured this question didn't look too hard so I'd give it a try. I spent 3 months on it and figured out that if I could prove it for an integer n as a prime number then I could prove it for any integer n. Try as I might that was the closest thing I could come up with. I'd figured out a lot of algebra and log/exp theory but I was stumped. After Christmas (I spent from mid September to Christmas working on this), I was defeated. It was the first time I couldn't answer a math puzzle. I went to my professor and asked him for the solution; I feel so stupid for not being able to figure it out myself. My professor laughed out loud when I asked for the solution. I felt so humiliated and a little angry; I was thinking he was laughing at me because of how stupid I must be. He quickly realized I actually expected an answer and thought he was laughing at my stupidity. He told me no one knows the answer to this puzzle and the most brilliant minds have been trying to prove it since Fermat wrote it over 350 years ago (this was 2 years before Andrew Wiles published his proof).

The funniest thing is a year later I was watching an episode of Star Trek NG and Picard is reading a book. The book is about Fermat's Last Theorem; he says something like, "There are things man was never meant to understand, like Fermat's Last Theorem." The writers of Star Trek NG assumed no one was going to solution this thing.

Donald E. Knuth, he always seemed to write in a very unassuming way. I have never had the pleasure of meeting the man. I would guess he just truly loves math and computers. Maybe some day.

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