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E P I L O G U E Abraham Robinson: The Man and His Mathematics Playfulness is an important element in the makeup of a good mathematician. —Abraham Robinson1 He never separated the mathematical craftsman from the human being. —Jiirgen Schmidt2 ABRAHAM ROBINSON published more articles during the seven years he was at Yale than he did during any other period of his career. Yale, of course, placed a premium on research, offered reduced teaching loads and attractive leaves for concentrated study and writing. This, coupled with the constant stimulation of the brightest graduate students, prominent colleagues, and the constant stream of visitors to a renowned academic center like New Haven, all help to account for this extraordinary burst of productivity. But there is another ingredient as well—Robinson had matured as a mathematician, and his efforts peaked during the time he spent at Yale. He was always pleased to dispel the myth that the best mathematicians were under thirty and that a mathematician did her or his best work early, at the very start of one's career. As a striking counterexample , Robinson's best math- A b r a h a m R o b i n s o n > s m i l i n g . ematics was only beginning to reap the benefits of his wide experience when, suddenly, at the age of fifty-five he died—at exactly the same age as his brother—and just as Robinson had feared. It might be argued that Robinson's success as a mature mathemati1 Robinson 1973c, p. 15. 2 J. Schmidt to George Seligman, letter of May 29, 1977, RP/YUL. 492 - Epilogue The first China Symposium on Nonstandard Analysis (Xinxiang), 1978. cian was in part a function of the kind of mathematics he did. Robinson's contribution was especially significant in showing the power of model theory for mathematics, and he demonstrated clearly the benefits of bringing techniques from one area of mathematics to the service of others. In doing so he achieved startling results. Nonstandard analysis, of course, was the most prominent—and controversial —of Robinson's contributions. Whatever its merits, it was a continuing but often tangential interest at Yale. Robinson appreciated the fact that as a tool it was powerful in certain contexts, and historically far more interesting, even revolutionary, than most new discoveries . But as a tool it required finesse, and he was one of the few mathematicians who knew enough about other branches of mathematics to exploit its possibilities—at least in the early days. As he once told Gregory Cherlin, "at first it was easy to get results—now you have to do more."3 Important results have continued to come from nonstandard methods in mathematics, but perhaps of greater significance in the course of history will be Robinson's steadfast faith and promotion of mathematical logic in general, and of model theory in particular, as a subject not 3 Cherlin R-1974. The Man and His Mathematics — 493 just of local interest' to logicians, but of global interest to mathematicians . From Robinson's grave site inJerusalem, looking out from Givat Shaul to the hills surrounding the city—the city which he loved above all others —one cannot help but think of the extraordinary life he had led, and the final place to which his own personal journey had brought him to rest. But through it all, he was the consummate mathematician—a mathematician's mathematician—who lived the scientific life to its fullest . In the course of his fifty-five years, he accomplished more than most can claim to have accomplished in far longer lifetimes. Indeed, he was a man who made mathematics a thing of beauty, and equally important, he had the remarkable ability to reveal that beauty to all who wished to learn from his example. ...


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