# Hanc marginis…

## 15/3/02 for four voices

hanc.mp3 (3'16, 3.0Mb)

#### Composer's note

Hanc marginis… is a setting of Pierre de Fermat's notorious 1670 claim, made in a gloss to Diophantus' Arithmetica;

'Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere: cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.

'It is impossible for a cube to be written as a sum of two cubes or a fourth power to be written as the sum of two fourth powers or, in general, for any number which is a power greater than the second to be written as a sum of two like powers. I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.

For the next three hundred and twenty-five years mathematicians tried and failed to reconstruct the 'marvellous' proof which Fermat had teasingly withheld. Fermat's Last Theorem, as it became known, was eventually proved in 1995 under extraordinary circumstances by the English mathematician Andrew Wiles. The proof cost him six years of solitary effort to achieve, and runs to well over a hundred pages. In the course of proving FLT, Wiles also managed to go a long way towards proving a much more important result, the Taniyama-Shimura Conjecture, which concerns a deep link between two otherwise unrelated areas of mathematics.

### Notes

First performed 3/8/02 by Orlando Consort at the Dartington International Summer School, in the absence of the bloody composer.

Duration ~3'30