Constance Reid on Paul Gordan

In her famous book Hilbert (Springer-Verlag, New York, 1970), Constance Reid describes Paul Gordan. We give below part of her description of Gordan from pages 30-31.

Paul Gordan

Paul Gordan was an impressive personality among the mathematicians of the day. ... he had come to science rather late. His merchant father, while recognizing the son's unusual computational ability, had refused for a long time to concede his mathematical ability. A one-sided, impulsive man, Gordan was to leave a curiously negative mark upon the history of mathematics; but he had a sharp wit, a deep capacity for friendship, and a kinship with youth. Walks were a necessity of life to him. When he walked by himself, he did long computations in his head, muttering aloud. In company he talked all the time. He liked to "turn in" frequently. Then, sitting in some cafe in front of a foaming stein of the famous Erlangen beer, surrounded by young people, a cigar always in his hand, he talked on, loudly, with violent gestures, completely oblivious of his surroundings. Almost all of the time he talked about the theory of algebraic invariants. It had been Gordan's good fortune to enter this theory just as it moved onto a new level. The first years of development had been devoted to determining the laws which govern the structure of invariants; the next concern had been the orderly production and enumeration of the invariants, and this was Gordan's meat. Sometimes a piece of his work would contain nothing but formulas for 20 pages. "Formulas were the indispensable supports for the formation of his thoughts, his conclusions and his mode of expression," a friend later wrote of him. Gordan's strength, however, in the invention and execution of the formal algebraic processes was considerable. At the beginning of his career, he had made the first break-through in a famous invariant problem. For this he had been awarded his title as king of the invariants. The general problem, which was still unsolved and now the most famous problem in the theory, was called in his honor "Gordan's Problem."

JOC/EFR February 2017

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