The music of the primes Millennium （质数的音乐）.pdf

The music of the primes © 1997−2009, Millennium Mathematics Project, University of Cambridge. Permission is granted to print and copy this page on paper for non−commercial use. For other uses, including electronic redistribution, please contact us. January 2004 Features The music of the primes by Marcus du Sautoy Many people have commented over the ages on the similarities between mathematics and music. Leibniz once said that music is the pleasure the human mind experiences from counting without being aware that it is counting. But the similarity is more than mere numerical. The aesthetics of a musical composition have much in common with the best pieces of mathematics, where themes are established, then mutate and interweave until we find ourselves transformed at the end of the piece to a new place. Just as we listen to a piece of music over and over, finding resonances we missed on first listening, mathematicians often get the same pleasure in rereading proofs, noticing the subtle nuances that make the piece hang together so effortlessly. The one advantage that music has over mathematics is the physical connection that our body has with the The music of the primes 1 The music of the primes sound of a composition. The hairs on the back of my neck never fail to stand on end when I hear Schuberts Death and the Maiden Quartet . The tingle factor stimulated by some pieces of music is something mathematics is rarely able to match. This is why those without any musical training can respond to a concert performance, whereas only after years of mathematical training does one eventually have the ears to listen to the great mathematical compositions. Listen to Schuberts Death and the Maiden It is one of the failings of our mathematical education that few even realise that there is such wonderful mathematical music out