Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Mordell's finite basis theorem revisited

J. W. S. Casselsa1

a1 D.P.M.M.S., 16 Mill Lane, Cambridge CB2 1SB

0. Mordell proved his ‘Finite Basis Theorem’ in the paper [31] ‘On the rational solutions of the indeterminate equations of the third and fourth degrees’ which appeared in 1922 in Volume 21 of these Proceedings. It had been assumed, rather than conjectured, by Poincaré some 20 years previously, but it was not what he had set out to prove. The theorem and its generalizations are at the heart of many of the most interesting achievements and problems of the theory of numbers and also of algebraic geometry. Mordell himself had virtually no part in these developments: his great work was to lie elsewhere ([5]).

(Received January 06 1986)