If you ever find yourself drawing one of those meaningless diagrams with arrows connecting different areas of mathematics, it's a good sign that you're going senile. —Richard Borcherds
One cannot invent the structure of an object. The most we can do is patiently bring it to the light of day, with humility. —Alexander Grothendieck
To myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. —Isaac Newton
The essence of mathematics lies in its freedom. —Georg Cantor
I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense. —Charles Darwin
Nothing that is really good can be got without labour and hardship, for so the gods have ordained. —W. H. D. Rouse
Study hard what interests you the most in the most undisciplined, irreverent and original manner possible. —Richard Feynman
I have been reading Chevalley's new book on class field theory; I am not really doing research, just trying to cultivate myself.
—Grothendieck
"What can you prove with exterior algebra that you cannot prove without it?" Whenever you hear this question raised about some new piece of mathematics, be assured that you are likely to be in the presence of something important. In my time, I have heard it repeated for random variables, Laurent Schwartz' theory of distributions, ideles and Grothendieck's schemes, to mention only a few. A proper retort might be: "You are right. There is nothing in yesterday's mathematics that could not also be proved without it. Exterior algebra is not meant to prove old facts, it is meant to disclose a new world. Disclosing new worlds is as worthwhile a mathematical enterprise as proving old conjectures. —Gian-Carlo Rota
The mathematical aristocracy at the creative level is... the most restrictive of all possible aristocracies. —Alain Badiou
All problems in mathematics are psychological.
—Pierre Deligne
A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas... The mathematician's patterns, like the painter's or the poet's, must be beautiful. The ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics. —G. H. Hardy
What determines how well you're going to solve a problem is how well you can think about math. —Eric Larson
It's fine to work on any problem, so long as it generates interesting mathematics along the way even if you don't solve it at the end of the day. —Andrew Wiles
God exists since mathematics is consistent, and the Devil exists since we cannot prove it. —Andre Weil
If you can't solve a problem, then there is an easier problem you can solve: find it. —George Polya
The typical working mathematician is a Platonist on weekdays and a formalist on Sundays. —Reuben Hersch
He had marvelous intuition, and so far as I know, all of the results he claimed in algebraic geometry have now been proved. When I was a graduate student at Princeton, it was frequently said that "Lefschetz never stated a false theorem nor gave a correct proof." —Phillip Griffith
A thing is symmetrical if there is something you can do to it so that after you have finished doing it, it looks the same as before. —Hermann Weyl
In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics. —Weyl
It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments. —Alfred N. Whitehead
By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race. —Whitehead
The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it. —Whitehead
The lesson from childhood, then, is that if you want to win the war for attention, don't try to say "no" to the trivial distractions you find on the information smorgasbord; try to say "yes" to the subject that arouses a terrifying longing, and let the terrifying longing crowd out everything else.—David Brooks
The introduction of the digit 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps.—Grothendieck
What about those donuts, when do they show up?—sister
