Atlanta, GA | Posted: April 9, 2002
John Conway, F.R.S., is the John von Neumann Professor of Mathematics at Princeton University. He is a masterful expositor of mathematics who is perhaps most widely known as the inventor of the Game of Life (popular screensaver and important example of a cellular automaton). Professor Conway is the author of numerous articles and books, including Winning Ways. He has received many prizes, including the Pólya Prize from the London Mathematical Society, the Nemmers Prize, and the Steele Prize from the American Mathematical Society.
How can you understand the shape of a knot, or prove that it really is knotted? What makes one knot different from another? I'll describe some ways in which elementary arithmetic can help. Although we're all familiar with knots, the theory of knots is a hard subject; it took more than a century before mathematicians were even able to find a guaranteed way to tell whether a string is knotted or not. However, some things are easy...