JOHN STILLWELL, DEPARTMENT OF MATHEMATICS, UNIVERSITY OF SAN FRANCISCO
Many of the most important concepts in mathematics were once thought to be impossible; for example, irrational and imaginary numbers, infinitesimals, points at infinity, the fourth dimension, and curved space. Thus it seems that yearning for the impossible can be fruitful, but why? Kolmogorov once wrote (in his diary, 14 September, 1943): "At a given moment there is only a fine layer between the 'trivial' and the impossible. Mathematical discoveries are made in this layer." This talk will review some of the close encounters with the impossible on which mathematics thrives, with illustrations of the impossible in the art of Escher, Magritte, and others
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Posted by bayleyw at September 12, 2007 09:22 AM