This page is inspired by the Curated Forms of a previous blog run by my friend, Семён. It is a mixed collection of some of the things that I find beautiful.
CORPUS HYPERCUBUS, by SALVADOR DALI
“Discovery is the privilege of the child: the child who has no fear of being once again wrong, of looking like an idiot, of not being serious, of not doing things like everyone else.”
— Grothendieck, Harvests and Sowings (translated from French)
“Starting from the individual theorems, I soon grew accustomed to piercing deeper into their relationships, and to grasp entire theories as a single entity. That is how I conceived the idea of mathematical beauty. There is a sort of mathematical beauty, just as there is an aesthetic beauty, which, however, one only comes to comprehend when, enraptured, one surveys an entire system of discoveries that follow from a single central idea and, because of their essential unity, lead to a single final result — when, that is, one sees a system of discoveries that, in their logical order, harmony, and brilliance, appear as an organic whole, like a painting before the mind’s eye.”
— Eisenstein, Curriculum Vitae (translated from German)
A PAINTING AS A DOOR, by AQUASIXIO
THE FORBIDDEN SPARK, by ADRIAN BORDA
“Should you just be an algebraist or a geometer?” is like saying “Would you rather be deaf or blind?” If you are blind, you do not see space, if you are deaf, you do not hear, and hearing takes place in time. On the whole, we prefer to have both faculties.
— Micheal Atiyah, Mathematics in the 20th century
PEACE OF MIND, by MONIQUE MUNOZ
“The efforts of most human-beings are consumed in the struggle for their daily bread, but most of those who are, either through fortune or some special gift, relieved of this struggle are largely absorbed in further improving their worldly lot. Beneath the effort directed toward the accumulation of worldly goods lies all too frequently the illusion that this is the most substantial and desirable end to be achieved; but there is, fortunately, a minority composed of those who recognize early in their lives that the most beautiful and satisfying experiences open to humankind are not derived from the outside, but are bound up with the development of the individual’s own feeling, thinking and acting. The genuine artists, investigators and thinkers have always been persons of this kind. However inconspicuously the life of these individuals runs its course, none the less the fruits of their endeavors are the most valuable contributions which one generation can make to its successors.”
— Albert Einstein on the occasion of Emmy Noether’s death
FOLIE, by JENNIFER J LEE
–––––––––––, by ZDZISŁAW BEKIŃSKI
“I wish to paint in such a manner as if I were photographing dreams.”
LIGHTHOUSE, by JOHN BRAMBLITT
“Most people, the vast majority in fact, lead the lives that circumstances have thrust upon them, and though some repine, looking upon themselves as round pegs in square holes, and think that if things had been different they might have made a much better showing, the greater part accept their lot, if not with serenity, at all events with resignation. They are like train-cars travelling forever on the selfsame rails. They go backwards and forwards, backwards and forwards, inevitably, till they can go no longer and then are sold as scrap-iron. It is not often that you find a man who has boldly taken the course of his life into his own hands. When you do, it is worth while having a good look at him.”
— William Somerset Maugham, Lotus Eater
“It is not that we have a short time to live, but that we waste a lot of it. Life is long enough, and a sufficiently generous amount has been given to us for the highest achievements if it were all well invested. But when it is wasted in heedless luxury and spent on no good activity, we are forced at last by death’s final constraint to realize that it has passed away before we knew it was passing. So it is: we are not given a short life but we make it short, and we are not ill-supplied but wasteful of it. Life is long if you know how to use it.”
— Seneca, On the Shortness of Life
THE BECOMING, by MILESTANG
“It has no survival value; rather it is one of those things which gave value to survival.”
— C.S. Lewis, The Four Loves
“The tragedy of love is not death or separation. … Oh, it is dreadfully bitter to look at a woman whom you have loved with all your heart and soul, so that you felt you could not bear to let her out of your sight, and realize that you would not mind if you never saw her again.
The tragedy of love is indifference.”
— William Somerset Maugham, Red
“The difficulty is that the elliptic curve C has no nonconstant holomorphic functions. Grojnowski and Ginzburg Kapranov-Vasserot address this problem by ignoring it.”
– Matt Ando, Power Operations in Elliptic Cohomology and Rep. of Loop Groups, pg. 29
“…this paper was written in the hope that its simple constructions, based on nothing more complicated than Landweber’s exact functor theorem, would convince its readers that homotopy theory might at least be as deep as arithmetic.”
-Jack Morava, Forms of K-theory
Why do we try to prove things, anyway? I think because we want to understand them. We also want a sense of certainty. Mathematics is a very deep field. Its results are stacked very high, and they depend on each other a lot. You build a tower of blocks but if one block is a bit wobbly, you can’t build the tower very high before it will fall over. So I think mathematicians are concerned about rigor, which gives us certainty. That’s one reason we concentrate so much more on proof than other scientists. But I also think proofs are so that we can understand. I guess I like explanations rather than step-by-step rigorous demonstrations.
– Bill Thurston