By Peter Freund
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Extra info for A Passion for Discovery
Qxd 6/5/2007 2:37 PM Page 38 FA 38 A Passion for Discovery We have seen how, on rare occasions, physicists can create rich new mathematics. Most physicists, however, go and raid the shelves of the mathematicians and show how existing mathematical structures are custom-made to describe nature. Think of Einstein who, in constructing his General Relativity, used the already existing geometry of spaces in which the concepts of distance and curvature are defined — a geometry discovered by Riemann in the nineteenth century.
At the 1900 International Congress of Mathematicians in Paris, Hilbert set the tone for twentieth– century mathematics by listing twenty-three problems, the solution of which he found central to its progress. qxd 6/29/2007 9:41 AM Page 44 FA 44 A Passion for Discovery nothing short of miraculous how clearly Hilbert saw what the mathematics of the dawning century would be about. In 1915 Hilbert wrote one of the fundamental papers in general relativity, and this led him to a certain problem in invariant theory.
Yet, can one even imagine how quantum mechanics would have been discovered a full century later, had Lagrange, Hamilton, and Jacobi not invented these powerful approaches? Sure, quantum mechanics can also be arrived at by starting directly from Newton’s equations, but it is more something you do “for completeness’ sake” than something that forces itself upon you. Maybe what is now being done in string theory is the latter day version of what Lagrange, Hamilton, and Jacobi did for mechanics, the true impact of which will not be felt for quite some time.