A Quote by Nicolaus Copernicus
When, therefore, I had long considered this uncertainty of traditional mathematics, it began to weary me that no more definite explanation of the movement of the world-machine established in our behalf by the best and most systematic builder of all, existed among the philosophers who had studied so exactly in other respects the minutest details in regard to the sphere.
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We had to depend on other institutions to do research on our behalf. We had to use the information that already existed to craft the best practices to distribute throughout the country. And we had to do all of that in ten months.
When I came back from Munich, it was September, and I was Professor of Mathematics at the Eindhoven University of Technology. Later I learned that I had been the Department's third choice, after two numerical analysts had turned the invitation down; the decision to invite me had not been an easy one, on the one hand because I had not really studied mathematics, and on the other hand because of my sandals, my beard and my "arrogance" (whatever that may be).
Do you suppose that I should have lived as long as I have if I had moved in the sphere of public life, and conducting myself in that sphere like an honorable man, had always upheld the cause of right, and conscientiously set this end above all other things? Not by a very long way, gentlemen; neither would any other man.
Hope is in some respects a thing more brilliant, more vivifying, than fruition. What we have looked forward to with eager and earnest aspiration is never in all respects equal to the picture we had formed of it. The very uncertainty enhances the enjoyment.
While I think in principle people should not have irrational beliefs, I should say that as a matter of fact, it is people who hold what I regard as completely irrational beliefs who are among the most effective moral actors in the world, in many respects. They're among the worst, but also among the best, even though the moral beliefs are ostensibly the same.
At the age of eleven, I began Euclid, with my brother as my tutor. ... I had not imagined that there was anything so delicious in the world. After I had learned the fifth proposition, my brother told me that it was generally considered difficult, but I had found no difficulty whatsoever. This was the first time it had dawned on me that I might have some intelligence.
I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn.
We find sects and parties in most branches of science; and disputes which are carried on from age to age, without being brought to an issue. Sophistry has been more effectually excluded from mathematics and natural philosophy than from other sciences. In mathematics it had no place from the beginning; mathematicians having had the wisdom to define accurately the terms they use, and to lay down, as axioms, the first principles on which their reasoning is grounded. Accordingly, we find no parties among mathematicians, and hardly any disputes.
This doctrine, that of the ghost in the machine, strictly separates the mind or soul from the body. And by doing so it takes the soul outside the sphere of mechanical or scientific explanation. It splits the world of the mind from the world of science. It is often supposed to protect our cherished free will.
When I became a Sigma Chi it was great, because they were the pople I enjoyed being with and I was very proud of the association. It was kind of an instant confidence builder for me--that what I considered the best fraternity on campus had actually wanted me. And I had always been very shy and without a lot of confidence. So it was a really good social experience and for me it was also a social maturation. It was a great benefit.
The women's movement appeared at a very crucial moment in my life. There was a whole political movement asking such questions and others I had never asked. I began to feel heard in that movement. But it was because my voice was resonating with other voices.
She felt a board indifference toward the immediate world around her toward other children and adults alike. She took it as a regrettable accident to be borne patiently for a while, that she happened to be imprisoned among people who were dull. She had caught a glimpse of another world and she knew it existed somewhere, the world that had created trains, bridges, telegraph wires and signal lights winking in the night. She had to wait she thought, and grow up to that world. - Dagny Taggart
Here, where we reach the sphere of mathematics, we are among processes which seem to some the most inhuman of all human activities and the most remote from poetry. Yet it is here that the artist has the fullest scope of his imagination.
Because there was just one thing that I had to believe to be able to live - I had to know that he existed. That was all. Everything else I could endure. So long as he existed.
When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as Bertrand Russell says, "one at least of our nobler impulses can best escape from the dreary exile of the actual world."
I had innumerable analysts who came to me in apology that the world that we were finding was not the world that they had thought existed and that they had estimated. Reality on the ground differed in advance.
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