Born in 1938, American computing pioneer Donald Knuth is known for his greatly influential multi-volume work, 'The Art of Computer Programming', his novel 'Surreal Numbers', his invention of TeX and METAFONT electronic publishing tools and his quirky sense of humor.
This is… is a unique event in my life. It took place in early 70s. I was… I had… I had met John Conway – probably one of the… certainly one of the greatest living mathematicians. I had… I had met him on a trip to… to University of Calgary, in '71, and we had lunch, and he scribbled on a napkin a new theory that he… that he came up with, which… which I thought was… was really terrific. And… and well, it's… it’s a purely mathematical theory about a new way to define numbers, not only the integer numbers and the fractional numbers, but also infinite numbers and square root of infinity, and infinity to the infinity, and… and infinity to the square root of infinity, and one over infinity, and makes sense of all these numbers. So a… a year later I was on sabbatical in… in Norway, and a thought came to me in the middle of the night. Wow, this theory is so beautiful it would be interesting to tell the story, to… to write a… a book that… where the characters in the book discover Conway's theory. They… they find… they find his rules, on a… on a stone tablet, and they… and they decipher the tablet, and they… and they develop all the consequences of this tablet, so that they can prove things about infinity, and… and so on, by themselves. And, the point being that this would be a way to teach how to do research, that the… that the students could, you know… not only learning what other people had done, but how to do new things in mathematics themselves. And it could be taught in… it could be presented in the form of a story, with characters discovering these things, by themselves. And so I thought, this would really be a cool book to have, and it would supplement… it could be used as a supplement. I was thinking of it as actually high school teachers could… could recommend it to some of their students, so that students could see the way… the way mathematics is discovered.
So, I got the idea of calling these numbers surreal numbers. You have to know that real numbers had… is what we called our numbers that have infinitely many decimal places, and so surreal numbers are even more so, because they… there are surreal numbers between the real numbers. And this was Conway's system, and I thought… so I had this title, Surreal Numbers, and I had the idea that the… a theory could be developed by characters in a book. And… and I woke Jill up, and said, ‘Jill, you know how I've been working on The Art of Computer Programming for many years, and… and I'm still not anywhere near being done with it? Well, I just thought of another book that has to be written, what do you think?’ And I said, ‘I thought I could write this one in a week, and really a week, because it would be short’. And… and so, you know, she said, ‘Okay, Don, go for it. This is your year on sabbatical, we're in… we’re in Norway, why not actually take your week, and go do this project, you know, concentrate on that, and… and then, you know, then you'll be happy, and we'll live happily ever after.’
Trained as a journalist, Dikran Karagueuzian is the
director of CSLI Publications, publisher of seven
books by Donald Knuth. He has known Knuth since the
late seventies when Knuth was developing TeX and
Metafont, the typesetting and type designing computer programs, respectively.
Norway, Surreal Numbers, The Art of Computer Programming, John Conway, Jill Knuth