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

It has always puzzled me that so many religious people have taken it for granted that God favors those who believe in him. Isn't it possible that the actual God is a scientific God who has little patience with beliefs founded on faith rather than evidence?

Raymond Smullyan

I cannot tell you the efforts to which I was condemned to understand something of the diagrams of Descriptive Geometry, which I detest.

Charles Hermite

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

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

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

Not only the laws of nature, but also the events occurring in nature, the world itself, must appear the same to all observers, wherever they may be.

Edward Arthur Milne

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.

With the extremely small or the extremely large, with inconceivably brief or extended phenomena, science has a difficult time. It is by no means clear that our present concepts or even our existing language is suitable for these ranges.

Mathematics, that giant pincers of scientific logic.

Mathematics is the product of real flesh-and-blood human beings whose lives may reflect the inspiration, the tragic, or the bizarre.

William Dunham (mathematician)

The fixed stars appear to be of different bignesses, not because they really are so, but because they are not all equally distant from us; those that are nearest will excel in Luster and Bigness; the more remote stars will give a fainter Light, and appear smaller to the Eye.

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.

The importance of infinite processes for the practical exigencies of technical life can hardly be overemphasized. Practically all applications of arithmetic to geometry, mechanics, physics and even statistics involve these processes directly and indirectly.

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

Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today.

Stephen Wolfram

The theory of probability as mathematical discipline can and should be developed from axioms in exactly the same way as Geometry and Algebra.

Andrey Kolmogorov

If we have a certain class of objects and a certain class of relations and if the only questions which we investigate are whether ordered groups of these objects do or do not satisfy the relations, the results of the investigations are called mathematics.

It is indeed wonderful that so simple a figure as the triangle is so inexhaustible in properties. How many as yet unknown properties of other figures may there not be?"

August Leopold Crelle

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.