“one of the most striking applications of model theory to date” in order to prove in a direct way the Ax-Kochen theorem.

Back at Yale one of the first courses Robinson taught was “Chapters in the History of Mathematics,” offered in the spring of 1968. Subsequently, in a Festschrift to honor Arend Heyting he chose to consider in partly historical terms the “ultimate foundation” for mathematics. Just as non-Euclidean geometry destroyed faith in Euclidean geometry as the one true geometry of space, so too, Robinson held, did the results of Gödel and Cohen destroy any faith one might have had in the existence of a single, absolutely true set theory. Thus both standard and nonstandard versions of arithmetic and analysis were possible, which served to reinforce the reasonableness of a formalist foundation for all of mathematics.

The following summer, 1969, Robinson was back in Heidelberg, to work again with Peter Roquette on nonstandard number theory. By now the two had been collaborating for some five or six years and had found that they could greatly simplify parts of Siegel’s work, which the nonstandard approach made “manageable” (G.D.Mostow, quoted in Dauben, 1995, p. 419).

In the spring of 1970 while on leave from Yale, Robinson was invited to give three Shearman lectures back at his alma mater, the University of London. These he devoted to “Logic as the Science of Mathematical Reasoning.” He also gave a second series of lectures for the mathematics department on nonstandard analysis. At this time the Mathematical Association of America released a film it had made with Robinson, an hour’s introductory lecture on nonstandard analysis. Following a straightforward account of formal languages and mathematical logic, whereby he introduced the nonstandard, non-Archimedean continuum R* of nonstand-