A Quote by Hermann Weyl
Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or achievements of mathematics in the last 50 years. [Said in 1950]
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Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.
The way we eat has changed more in the last 50 years than in the previous 10,000.
There is no greater fallacy than the belief that aims and purposes are one thing, while methods and tactics are another ... All human experience teaches that methods and means cannot be separated from the ultimate aim.
When we talk about the impact inside mathematics, and applications in the sciences, [Mandelbrot] is one of the most important figures of the last 50 years.
In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, "this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere." He immediately protested: "No, no. These concepts were not dreamed up. They were natural and real."
If succeeding generations of Americans don't understand the concepts of justice, individual rights, free enterprise, capitalism, sovereignty or national security, there can be no guarantee that those concepts - or others like them - will continue.
The scoreboard said I lost today, but what the scoreboard doesn't say is what it is I have found. Over the last 21 years, I have found loyalty. You have pulled for me on the court and also in life. I found inspiration. You have willed me to succeed, sometimes even in my lowest moments, and I've found generosity. You have given me your shoulders to stand on to reach for my dreams, dreams I could never have reached without you.
I say, of the Congress, then, this - that its aims are mistaken, that the spirit in which it proceeds towards their accomplishment is not a spirit of sincerity and whole-heartedness, and that the methods it has chosen are not the right methods, and the leaders in whom it trusts, not the right sort of men to be leaders; - in brief, that we are at present the blind led, if not by the blind, at any rate by the one-eyed.
In fact, the answer to the question "What is mathematics?" has changed several times during the course of history... It was only in the last twenty years or so that a definition of mathematics emerged on which most mathematicians agree: mathematics is the science of patterns.
There is a thing called clean coal. Coal will last for 1,000 years in America. Now we have natural gas and so many other things because of technology. We have unbelievable - we have found over the last seven years, we have found tremendous wealth right under our feet. So good. Especially when you have $20 trillion in debt.
It could be that the methods needed to take the next step may simply be beyond present day mathematics. Perhaps the methods I needed to complete the proof would not be invented for a hundred years.
Probably the smartest president we've had in terms of I.Q. in the last 50 years was Jimmy Carter, and I think he is the worst president of the last 50 years.
I had invited 50 or 60 peers and friends, most of whom were parents, to see the film [Trust], and I asked about the last scene. It was interesting because it was split right down the middle, 50/50. About half the audience wanted it to end with the very emotional scene between Clive and Liana, and that feeling of realization and catharsis. And, the other half were adamant about keeping that last scene.
It is indubitable that a 50-year-old mathematician knows the mathematics he learned at 20 or 30, but has only notions, often rather vague, of the mathematics of his epoch, i.e. the period of time when he is 50.
Whenever you have a possibility of going in two ways, either for peace or for war, for peaceful methods of for military methods, in the present age there is a strong prejudice for the peaceful ones. War seldom ever leads to good results.
Orthodoxy, or right opinion, is, at best, a very slender part of religion. Though right tempers cannot subsist without right opinions, yet right opinions may subsist without right tempers. There may be a right opinion of God without either love or one right temper toward Him. Satan is a proof of this.
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