A Quote by Benoit Mandelbrot
Most were beginning to feel they had learned enough to last for the rest of their lives. They remained mathematicians, but largely went their own way.
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The enduring realization that when a great challenge comes, the most ordinary people can show that they value something more than they value their own lives. When the last of the veterans had gone, and the sorrows and bitterness which the war created had at last worn away, this memory remained.
Had the followers of Jesus remained an obscure Jewish sect, most of you would not have learned to read, and the rest of you would be reading from hand-copied scrolls.
Silicon Valley, "the largest legal creation of wealth in history," was built largely by unprofessional amateurs using math, sand, and the institutions of freedom. The Soviet Union had the greatest mathematicians on earth, and plenty of sand, but without the institutions of freedom their brilliant mathematicians were not empowered to create those devices that are changing the world.
As for me: I loyally remained right where I was, remembering the very first I had ever seen the boy and then just now, the very last time-and all the times in between. The deep aching grief I knew I would feel would come soon enough, but at that moment mostly what I felt was peace, secure in the knowledge that by living my life the way I had, everything had come down to this moment. I had fulfilled my purpose.
Women, I learned, adapted.
At first..they seemed so fragile, so dependent on fathers and husbands and brothers and lovers. Gradually, though, I noticed how supple their lives were beneath the surface. Then I realized it was this flexibility that enabled them to survive...that sooner or later, by choice or by chance, most women faced the task of adapting to a future on their own. When at my most optimistic, I thought of it as independence; in darker moods, as survival. Either way women had to do it.
Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.
There was a commonality in a lot of the private school experiences that I had of children whose lives were not their own. They thought they were their own, but they were essentially gifted this life by their parents. So they were spending money; they were going on trips - I guess, in a way, it is their life, but they didn't earn it.
I'm not skilled enough to explain properly how we feel. Not only me, but I'm sure Tony and Tim and Pop feel the same way. Last year was a tough one for all of us. We felt like we had the trophy, that we were touching it, and it slipped away. We all felt guilty. We got to this spot, and we didn't let it go.
Try a little harder, and meditation comes. You do not feel the body or anything else. When you come out of it after the hour, you have had the most beautiful rest you ever had in your life. That is the only way you ever give rest to your system. Not even the deepest sleep will give you such a rest as that.
There are a lot of people who had past lives where they were monks and nuns and all their needs were provided for them. I feel like most people in the new age had this as their most recent lifetime experience, that kind of communal living.
"All right", said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone.
Today I am amazed at the things our children have done and their wide range of interests. They are all living their lives and not the ones I would have planned for them. But I have learned that their lives are theirs, not mine, and in living their own lives they have given me experiences and an education I would never have had if I'd been fool enough to make them do what I thought they should do.
These early Saints were indeed homeless, but they were not hopeless. Their hearts were broken, but their spirits were strong. They had learned a profound and important lesson. They had learned that hope, with its attendant blessings of peace and joy, does not depend upon circumstance. They had discovered that the true source of hope is faith—faith in the Lord Jesus Christ and in His infinite Atonement, the one sure foundation upon which to build our lives.
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."
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.
If we were always, indeed, getting our living, and regulating our lives according to the last and best mode we had learned, we should never be troubled with ennui.
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