I suppose you are two fathoms deep in mathematics, and if you are, then God help you. For so am I, only with this difference: I stick fast in the mud at the bottom, and there I shall remain.
The computer is important, but not to mathematics.
The purpose of life is to conjecture and prove.
Love was even more mathematical than poetry. It was the pure mathematics of the spirit.
What cannot be known is more revealing than what can.
There has come about a general public awareness that America is not automatically, and effortlessly, and unquestionably the leader of the world in science and technology. This comes as no surprise to those of us who have watched and tried to warn against the steady deterioration in the teaching of science and mathematics in the schools for the past quarter century. It comes as no surprise to those who have known of dozens of cases of scientists who have been hounded out of jobs by silly disloyalty charges, and kept out of all professional employment by widespread blacklisting practices.
A chess problem is an exercise in pure mathematics.
Very little mathematics has direct applications - though fortunately most of it has plenty of indirect ones.
The art of doing mathematics consists in finding that special case which contains all the germs of generality
Mathematics had never had more than a secondary interest for him [her husband, George Boole]; and even logic he cared for chiefly as a means of clearing the ground of doctrines imagined to be proved, by showing that the evidence on which they were supposed to give rest had no tendency to prove them. But he had been endeavoring to give a more active and positive help than this to the cause of what he deemed pure religion.
I think the term "Kantian constructivism" as an oxymoron. Kant was a constructivist about mathematics, but not about ethics.
The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics.
Our faith in Mathematics is not likely to wane if we openly acknowledge that the personalities of even the greatest mathematicians may be as flawed as those of anyone else.
An announcement of [Christopher] Zeeman's lecture at Northwestern University in the spring of 1977 contains a quote describing catastrophe theory as the most important development in mathematics since the invention of calculus 300 years ago.
If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.
As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.
It can be argued that the mathematics behind these images [of the orbit diagram for quadratic functions and the Mandelbrot set] is even prettier than the pictures themselves.
In mathematics we find the primitive source of rationality; and to mathematics must the biologists resort for means to carry out their researches.
The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.
Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat-flour from peascods, so pages of formulae will not get a definite result out of loose data.