A Quote by Eric Temple Bell

A number of aspects of mathematics are not much talked about in contemporary histories of mathematics. We have in mind business and commerce, war, number mysticism, astrology, and religion. In some instances, writers, hoping to assert for mathematics a noble parentage and a pure scientific experience, have turned away their eyes. Histories have been eager to put the case for science, but the Handmaiden of the Sciences has lived a far more raffish and interesting life than her historians allow.
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.
Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.
If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
What is mathematics? Ask this question of person chosen at random, and you are likely to receive the answer "Mathematics is the study of number." With a bit of prodding as to what kind of study they mean, you may be able to induce them to come up with the description "the science of numbers." But that is about as far as you will get. And with that you will have obtained a description of mathematics that ceased to be accurate some two and a half thousand years ago!
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.
One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant, sharp but cold ... thus we are clearest where knowledge matters least: in mathematics, especially number theory.
Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
Statistics is, or should be, about scientific investigation and how to do it better, but many statisticians believe it is a branch of mathematics. Now I agree that the physicist, the chemist, the engineer, and the statistician can never know too much mathematics, but their objectives should be better physics, better chemistry, better engineering, and in the case of statistics, better scientific investigation. Whether in any given study this implies more or less mathematics is incidental.
...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.
Here is a quilted book about mathematical practice, each patch wonderfully prepared. Part invitation to number theory, part autobiography, part sociology of mathematical training, Mathematics without Apologies brings us into contemporary mathematics as a living, active inquiry by real people. Anyone wanting a varied, cultured, and penetrating view of today's mathematics could find no better place to engage.
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.
But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
I like science and mathematics. When I say mathematics, I don't mean algebra or math in that sense, but the mathematics of things.
We had principles in mathematics that were granted to be absolute in mathematics for over 800 years, but new science has gotten rid of those absolutism, gotten forward other different logics of looking at mathematics, and sort of turned the way we look at it as a science altogether after 800 years.
Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.
Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33, like Riemann before him. Working in total isolation from the main currents of his field, he was able to rederive 100 years' worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics.
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