THE PUBLIC perception of a research mathematician is that of an introvert working with pencil and paper. Daniel Gorenstein was the prime counterexample, a man who elevated his subject to the pages of the New York Times.
Finite group theorists, Graham Higman once commented, are the natural successors to the classical geometers, their work arising out of the study of symmetry. Gorenstein did not see group theory that way. To him, it was a deeply technical subject at the heart of modern algebra, and the Holy Grail was the classification of the finite simple groups, building-blocks whose role is somewhat akin to that of prime numbers in arithmetic, where every number is the product of primes.
John Thompson's thesis, and its application of methods developed by Philip Hall and Graham Higman, revolutionised group theory in the late 1950s. An attack on the general classification problem for finite simple groups seemed possible, and in 1960 Gorenstein began his fruitful collaboration with John Walter. By the end of that decade, they had proved theorems which suggested that a generic simple group might enjoy some fairly specific properties.
Much of Gorenstein's thinking had been influenced by study of Thompson's work on N-groups, as he remarked in his book Finite Groups (1968) - indispensable reading for those moving into the subject. In 1972, in lectures at a symposium in Chicago, he set out a formal 16-point plan for the classification, which he refined in lectures given in London and at the Weizmann Institute in Rehovot, Israel, the following year.
Gorenstein was not an elegant lecturer, but what he lacked in traditional style he made up by sheer drive and enthusiasm. To him no problem was unsolvable. He was a short, stocky man who applied the same muscular technique to his mathematics as to his tennis; if one approach failed, then one just had to make adjustments, and often a member of his audience would find that he was expected to alter his own work to fit into Gorenstein's game-plan. As a result of Gorenstein's leadership, the venture became perhaps the only time that a piece of mathematical research has adopted the shape of a scientific project in terms of team effort; parts of the task were subcontracted, to use his own words.
Some referred to Gorenstein as the Godfather - not misplaced, given his inspiration of a generation of younger group theorists. Others described his role as being somewhere between that of coach and quarterback - he called both the plays and the audibles.
By 1980 his programme had been completed. But some were dubious. Could 20,000 pages of mathematics be correct? And in any case, not all was yet published. With a small group of collaborators, Gorenstein set himself the target of convincing the mathematical community by revising the classification, seeking a shorter proof as well as carrying out any correction or completion. Although it was to prove a slower and more difficult task than perhaps he initially envisaged, this work was well in hand at the time of his untimely death.
Gorenstein was not always a group theorist. After graduating from Harvard College, he became a student of Zariski, writing a thesis in algebraic geometry. He once commented that he found this subject rather hard, though as a result of his work others have introduced the idea of a Gorenstein ring. Later, with Zierler, he was to find the first algorithm for decoding general BCH-codes, particular examples of which are now used in recording digital compact discs, and it was while he was working at the Institute for Defense Analysis in Princeton in the late 1950s that he met Herstein, who introduced him to group theory.
After holding positions at Clark University and at Northeastern University, he moved to Rutgers in 1969. Soon he was department chairman. He never held high office, though his advice was often sought and he served his university with a number of special assignments. Perhaps his greatest was his last; he was a prime mover for the establishment in 1988 of DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), funded by the National Science Foundation and by the State of New Jersey, and he became its first Director.
Gorenstein both worked hard and played hard. A house-guest could rise to find that many of the day's lemmas had already been proved. Research was over by lunchtime. Living in Portland Place in 1972-73 must have been ideal, for he could then devote the rest of the day to seminars, and to visits to art galleries, museums, restaurants and the theatre. He collected modern art, with a good eye for artists yet to be recognised, and for the value of the works of those who were. He enjoyed good food and was an excellent dinner companion. Many dinners he attended are part of the folklore - indeed, the only problem ever known to defeat him was a large Maine lobster which had to be returned to the kitchen, from which could then be heard sounds of a mallet.
Life, as work, had its game- plan; for those who knew him well and anticipated little change in his activities upon retirement, the mail message 'Danny Gorenstein died this morning' was certainly not part of the script.