Word: mathematician
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...unwise.'" We're by now with the notion that and unwisdom generate scientific progress. But it is one thing to say that one scientist's mistakes send another in the right direction, and quite another that unwisdom in a wayward scientist presents no contradiction to his greatness. The English mathematician G. H. Hardy said the first of Ramanujan, the Indian genius: "Ramanujan's false statement was one of the most fruitful he ever made, since it ended by leading us to all our joint work on partitions...
...done much better on the few occasions when he treats his subjects at length. His favorite sort of topic is covered by two major articles in the first volume, one on Einstein and the other (by far the longest piece in the set) on the nineteenth-century mathematician William Kingdon Clifford. Scientific American readers will recognize neither of these: the Clifford piece was the introduction to a 1946 edition of Clifford's The Common Sense of The Exact Sciences, and the excellent survey of Einstein's more important work came out as a separate article three years...
...long section on Clifford: biography, as detailed as I'd want to read; a fascinating treatment of Clifford's work; and glimpses of the twentieth-century relevance of his visions. These are carefully partitioned, hence Newman's touch is convincing here as nowhere else. Clifford emerges as a superb mathematician even in the company of the nineteenth-century geniuses. He was one of the last to work with equal success on several mathematical fronts, Poincare being perhaps the last who managed it. Clifford spun out the consequences of the new non-Euclidean geometries and of Abelian function theory; he also...
...theorems are found in a queer branch of top mathematics called "topology." A French mathematician, Jordan, gave the fundamental theorem of this study: every simple curve has an inside and an outside. That is, ever simple curve divides the plane into two regions, one inside the curve, and one outside...
...formulae (1.10)--(1.13) are on a different level and obviously both difficult and deep ... (1.10)--(1.12) defeated me completely; I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written down by a mathematician of the highest class. They must be true because, if they were not true, no one would have had the imagination to invent them...