Mathematician Quotes

Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languanges of the world than to master all mathematics at present known.

Walter Warwick Sawyer

Yes, but when I discovered it, it stayed discovered.

One thing at least they have not forgotten, that geometry is nothing if it be not rigorous, and that the whole educational value of the study is lost, if strictness of demonstration be trifled with. The methods of Euclid are, by almost universal consent, unexceptionable in point of rigor. Opening Address by the President, Section A

Henry John Stephen Smith

Functions, just like living beings are characterized by their singularities.

Misinforming people by use of statistical material might be called statistical manipulation; in a word (though not a very good one), statisticulation.

But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they had better lead to something interesting.

Julian Coolidge

If you want to be a reference librarian, you must learn to overcome not only your shyness but also the shyness of others!

S. R. Ranganathan

With the exception of the geometric series, there does not exist in all of mathematics a single infinite series whose sum has been determined rigorously.

Niels Henrik Abel

Proofs really aren't there to convince you that something is true — they're there to show why it is true.

Andrew M. Gleason

It is not so much whether a theorem is useful that matters, but how elegant it is.

The conclusion seems inescapable: that formal logic has to be taken over by the mathematicians. The fact is that there does not exist an adequate logic at the present time, and unless the mathematicians create one, no one else is likely to do so.

Mathematics is not constrained by mundane reality. It can build castles in the air and concepts in the mind whose beauty, magnificence, and intrigue are as boundless as the ideas themselves.

Michael Starbird

I am always surprised when a young man tells me he wants to work at cosmology; I think of cosmology as something that happens to one, not something one can choose.

William McCrea (astronomer)

Even in the realm of things which do not claim actuality, and do not even claim possibility, there exist beyond dispute sets which are infinite.

Bernard Bolzano

Proof, being the highest level of reproduction activity, has an important interiorization aspect: as Yuri Manin stresses in his book Provable and Unprovable, a proof becomes such only after it is accepted (as the result of a highly rigorous process)... Manin describes the act of acceptance as a social act; however, the importance of its personal, psychological component can hardly be overestimated.

Alexandre Borovik

If we arrive at an equation containing on each side the same term but with different coefficients, we must take equals from equals until we get one term equal to another term. But, if there are on one or on both sides negative terms, the deficiencies must be added on both bides until all the terms on both sides are positive. Then we must take equals from equals until one term is left on each side.

Mathematics deals mainly with realities and stern facts, and it arms those whose life work is beset with physical difficulties. Hence it appeals especially to the leaders of the common people, and it performs a fundamental function in the education of those who aim to excel in overcoming material difficulties.

George Abram Miller

Mathematics... is a bit like discovering oil... But mathematics has one great advantage over oil, in that no one has yet... found a way that you can keep using the same oil forever.

Very belatedly in 1947, Darwin [Sir Charles Darwin, great-grandson of the famous Charles Darwin] agreed to set up a very small electronics group [...] It was not easy to have the imagination to foresee that computers were to become one of the most important developments of the century.

James H. Wilkinson

Whether any other Mathematician will appear, possessing sufficient leisure, patience, and facility of computation, to calculate the value of [pi] to a still greater extent, remains to be seen: all that the Author can say is, he takes leave of the subject for the present...

Given a conjecture, the best thing is to prove it. The second best thing is to disprove it. The third best thing is to prove that it is not possible to disprove it, since it will tell you not to waste your time trying to disprove it. That's what Godel did for the Continuum Hypothesis.

Relativity without mathematics may be compared with "Painless Dentistry," or "Skiing without Falling," or "Reading without Tears."

We use Reason for improving the Sciences; whereas we ought to use the Sciences for improving our Reason.

Antoine Arnauld

The triplet of specifications - the product-market scope, the growth vector and the competitive advantage - describes the firm's product-market path in the external environment.

By slow degrees, the minds of men were cut adrift from their old scholastic moorings and sent forth on the wide sea of scientific inquiry, to discover new islands and continents of truth.