Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.
As a graduate student I studied mathematics fairly broadly, and I was fortunate enough, besides developing the idea which led to 'Non-Cooperative Games,' also to make a nice discovery relating to manifolds and real algebraic varieties.
Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.
Well, if you were the American public, you saw a catastrophe. In general, you would say, "The biggest institutions of America - Washington, broadly, and Wall Street, broadly - they're to blame." And, broadly, they're right.
Prosperity isn't defined by money alone; it encompasses time, love, success, joy, comfort, beauty, and wisdom.
I really do fervently believe that every child deserves to have the kind of access to educational opportunities, broadly defined, including music and sports, that I enjoyed. So, I'm trying to do my part, and I believe that all of us with a privileged background who are fortunate enough to have had that kind of access have a responsibility to try to pass it on.
The piano's world encompasses glass-nerved virtuos and stomping barrel-housers in fedoras; it is a world of pasture and storm, of perfumed smoke, of liquid mathematics.
Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating.
Nothing in life is more liberating than to fight for a cause larger than yourself, something that encompasses you but is not defined by your existence alone.
Politics is not an exact science. That's why in school I loved mathematics. Everything in mathematics was clear to me.
Other paths would include making nuclear fission cheap enough and safe enough that people broadly embrace it, so that could be scaled up.
The BBC has tended over the years to be broadly liberal as opposed to broadly conservative for all sorts of perfectly understandable reasons. The sort of people we've recruited - the best and the brightest - tended to come from universities and backgrounds where they're more likely to hold broadly liberal views than conservative.
Mathematics catalogues everything that is not self-contradictory; within that vast inventory, physics is an island of structures rich enough to contain their own beholders.
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers.