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Mathematician David Joyce knows that the study of geometry has a lot to offer students who will never become mathematicians. He has used the internet to make available to a wide audience a new translation of the classic text on geometry, Euclid's Elements. |
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Meet the researchers:
Interested in lots of things
Interview with Professor David Joyce
In a recent interview, mathematics professor David Joyce discussed his research interests, especially his web page that features a new translation of Euclid's Elements. Joyce's pages on the Clark web site were recently selected for Scientific American's Sci/Tech Web Awards 2001.
Tell me how you came to be involved in mathematics.
I was interested in lots of different things, chemistry, logic, philosophy. Sometime when I was in college I narrowed down my study to mathematics and computer science. Then I went to graduate school and there I had to choose one particular subject and I chose mathematics. Since coming to Clark I've been able to broaden out into other fields again, including computer science, history of mathematics, and the history of science.
What would you consider your main research areas now?
Right now I'm finishing up some things that I did with English professor Charles Blinderman on Aldous Huxley. Huxley was a 19th century British scientist, not a mathematician at all. He was interested in lots of different things. (Professor Blinderman's field was 19th and 20th century British scientific literature.) We also worked on the 20th century Piltdown Man investigation. Right now I'm working on inversive geometry-a traditional mathematical subject. I expect to publish something on that very soon.
What's inversive geometry?
It's about inverting things in circles. You have a circle-everything that is outside the circle comes inside, everything inside the circle goes outside-that's what inversion means-it's the geometric study of circles and lines without regard to things like distance. Geometry is the study of distance--imagine geometry without distance!
You've also completed for the web your translation of the Elements by the Greek mathematician Euclid. How did that come about?
I've always been interested in the history of mathematics, but I had no intention of doing Euclid's Elements. Then, in the mid-1990s, a time when I was interested in computer programming, Java came out. By using Java, you can write a program on your own computer that can be viewed by anyone in the world with a browser. Something like that had not existed before and I wanted to experiment with it.
I thought that trying to illustrate geometry would be a good place to start. I tried using Java applets to illustrate two or three of the figures from Euclid's Elements and thought it worked great. So I proceeded to illustrate the rest of Euclid's first book. At that point I realized that more was needed in addition to the applets.
When British mathematician Thomas Heath wrote his translation and commentary on the Elements from 1908 to about 1923, it was, naturally, 19th century British mathematics that he was connecting it to. I thought it was time to do a new translation and commentary. So I learned to read Greek. Mathematical Greek is not like spoken Greek. It's a very limited language with simple forms. So it's quite easy to translate technical books like Euclid's Elements compared to translating something like Homer, which would be very difficult. In addition, I added my own commentary connecting the Elements to modern mathematics.
So then you placed your new translation and commentary on the web, illustrating the Elements with Java applets.
Yes, this set of pages encompasses about three volumes of work.
Did Euclid invent geometry?
No. He pulled together a lot of things and reorganized what was known. Probably everything he mentioned had been invented, distributed and published before, although we can't be certain, because a lot of the original publications no longer exist. We know from later commentary that many of his books were created by his predecessors.
I know he studied and worked in Alexandria, Egypt. I assume that he worked in the famous library there?
Yes. He was one of the first librarians. The work of many of his contemporaries was probably lost in the great fire that destroyed the library. But Euclid's works had been copied and distributed already.
What is the difference between Euclidean and non-Euclidean geometry?
The first non-Euclidean geometries were worked on probably in the 19th century. In Euclidean geometry, given a straight line and a point, there is only one other straight line that passes through the point and is parallel to the first line. But even in ancient times, mathematicians wondered if this was indeed true. In the 19th century the mathematicians Bolyai, Lobachevsky, and Gauss thought there might be many parallel lines that pass through that point, even in two dimensions. In Euclidean space they might look curved, but in non-Euclidean space they would look straight. Euclidean and non-Euclidean geometry are two different theories. They have differing axioms. Physicists have concluded that space is probably non-Euclidean.
In addition to information on courses you teach, I noticed other mathematical topics on the your web site. For example you post the 23 unsolved mathematical problems of David Hilbert.
Yes. Hilbert was one of the premier mathematicians at the beginning of the 20th century. He put together the most famous collection of problems in mathematics in the world. In 1900 there was a Centennial International Congress of Mathematicians and these 23 problems were designated as problems to be solved in the coming century. It really affected all mathematics at that time. A great many were solved at the beginning of the 20th century, some at the end of the 20th century, and some have not been solved yet.
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Additional Resources
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Professor David Joyce
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