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" "The black hole solution of Einstein's equations is also a work of art. The black hole is not as majestic as Godel's proof, but it has the essential features of a work of art: uniqueness, beauty, and unexpectedness. Oppenheimer and Snyder built out of Einstein's equations a structure that Einstein had never imagined. The idea of matter in permanent free fall was hidden in the equations, but nobody saw it until it was revealed in the Oppenheimer-Snyder solution. On a much more humble level, my own activities as a theoretical physicist have a similar quality. When I am working, I feel myself to be practicing a craft rather than following a method. When I did my most important piece of work as a young man, putting together the ideas of Sin-Itiro Tomonaga, Julian Schwinger, and Richard Feynman to obtain a simplified version of quantum electrodynamics, I had consciously in mind a metaphor to describe what I was doing. The metaphor was bridge-building. Tomonaga and Schwinger had built solid foundations on the other side, and my job was to design and build the cantilevers reaching out over the water until they met in the middle. The metaphor was a good one. The bridge that I built is still serviceable and still carrying traffic forty years later. The same metaphor describes well the greater work of unification achieved by Stephen Weinberg and Abdus Salam when they bridged the gap between electrodynamics and the weak interactions. In each case, after the work of unification is done, the whole stands higher than the parts.
Freeman John Dyson (15 December 1923 – 28 February 2020) was an English-born American physicist, mathematician, and futurist, famous for his work in quantum mechanics, nuclear weapons design and policy, and the search for extraterrestrial intelligence. He was the winner of the Templeton Prize in the year 2000.
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Fifty years ago Kurt Gödel... proved that the world of pure mathematics is inexhaustible. … I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all mathematics. If it should turn out that the whole of physical reality can be described by a finite set of equations, I would be disappointed, I would feel that the Creator had been uncharacteristically lacking in imagination.
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Gödel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas.