Gödel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not… - Freeman Dyson

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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.

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About Freeman Dyson

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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Birth Name: Freeman John Dyson
Alternative Names: Freeman J. Dyson
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In the history of science it happens not infrequently that a reductionist approach leads to a spectacular success. Frequently the understanding of a complicated system as a whole is impossible without an understanding of its component parts. And sometimes the understanding of a whole field of science is suddenly advanced by the discover of a single basic equation. Thus it happened that the Schrodinger equation in 1926 and the Dirac equation in 1927 brought a miraculous order into the previously mysterious processes of atomic physics. The equations of Erwin Schrodinger and Paul Dirac were triumphs of reductionism. Bewildering complexities of chemistry and physics were reduced to two lines of algebraic symbols. These triumphs were in Oppenheimer's mind when he belittled his own discovery of black holes. Compared with the abstract beauty and simplicity of the Dirac equation, the black hole solution seemed to him ugly, complicated, and lacking in fundamental significance.

The gospel of St. Matthew told of the angry Jesus driving the merchants and money-changers out of the temple, knocking over the tables of the money-changers and spilling their coins on the floor. Jesus was not opposed to capitalism and the profit motive, so long as economic activities were carried on outside the temple. In the parable of the talents, he praises the servant who used his master's money to make a profitable investment, and condemns the servant who was too timid to invest. But he draws a clear line at the temple door. Inside the temple, the ground belongs to God and profit-making must stop.

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There is an enormous variety of things that we never dreamed of, like... black holes, s, quasars, all these unbelievably active goings-on in the universe... [I]n Aristotle's time the universe... was supposed to be quiescent, it was supposed to be perfect and peaceful, and nothing ever happened in the ; and that remained true... throughout all of the revolutions... It remained the general view of astronomers... through Copernicus, and Galileo, and Newton, and everybody else... until just the last 30 years, and now we know it's not like that at all. In fact the universe is full of violent events, and fantastic strong gravitational fields, and collapsed objects, and huge outpourings of energy. ...The things we understand least are the quasars... the most violent and... energetic objects in the universe, and they're totally... mysterious... and... they're rather frequent; and nobody ever dreamed that they existed... [E]ven after they were found it took a long time before people took them seriously. Nature's imagination is always richer than ours.

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