Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly-yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.
We decided that 'trivial' means 'proved'. So we joked with the mathematicians: We have a new theorem- that mathematicians can prove only trivial theorems, because every theorem that's proved is trivial.
It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.
It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.
Democracy can't work. Mathematicians, peasants, and animals, that's all there is - so democracy, a theory based on the assumption that mathematicians and peasants are equal, can never work. Wisdom is not additive; its maximum is that of the wisest man in a given group.
Mathematicians do not write for the circulating library.
Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.
Some things that satisfy the rules of algebra can be interesting to mathematicians even though they don't always represent a real situation.
Mathematicians tend to prefer a worst-case analysis, a kind of paranoia that is especially understandable if you live in Israel!
All musicians are subconsciously mathematicians.
Mathematics is written for mathematicians.
Mathematicians are a bit like the laconic Vermonter who, when asked if he's lived in the state his whole life, replies, "Not yet. "
It is obvious that mathematics needs both sorts of mathematicians, theory-builders and problem-solvers.
The computers are not replacing mathematicians; they are breeding them.
In fact, the answer to the question "What is mathematics?" has changed several times during the course of history. . . It was only in the last twenty years or so that a definition of mathematics emerged on which most mathematicians agree: mathematics is the science of patterns.
It has been a fortunate fact in the modern history of physical science that the scientist constructing a new theoretical system has nearly always found that the mathematics. . . required. . . had already been worked out by pure mathematicians for their own amusement. . . . The moral for statesmen would seem to be that, for proper scientific "planning", pure mathematics should be endowed fifty years ahead of scientists.
The mathematicians know a great deal about very little and the physicists very little about a great deal.
Only professional mathematicians learn anything from proofs. Other people learn from explanations.
There are two kind of mathematicians, smart ones, and dumb ones. I am one of the dumb ones.
When I told my son that I had to give a talk about my work to non-mathematicians, he warned me that regular people don't think like mathematicians.
