Mathematical Quotes

500+ Sourced quotes

He was a man of immense intellectual capabilities and most of us were marvelling at his doctorate thesis which focused on the mathematical solutions using digit zero. As a politician he was a man who choose his words carefully. As a personal and trusted friend whom I had assigned key responsibilities, the loss of Saitoti has been a painful experience to me,

Mathematical Reasoning is not only exact; it has its own criteria of reality

Paul Feyerabend

Mathematics as a science commenced when first someone, probably a Greek, proved propositions about any things or about some things, without specification of definite particular things. These propositions were first enunciated by the Greeks for geometry; and, accordingly, geometry was the great Greek mathematical science.

Alfred North Whitehead

Seurat and Signac mixed paintings with the dry and abstract laws of science. This approach, in my opinion, usually strays from the purpose of art in general. Because it means that one cannot expect from an artifact, that is created with mathematical laws, to establish an improbable and irrational relationship between the work and the viewer.

What we call objective reality is, in the last analysis, what is common to many thinking beings, and could be common to all; this common part, we shall see, can only be the harmony expressed by mathematical laws. It is this harmony then which is the sole objective reality, the only truth we can attain; and when I add that the universal harmony of the world is the source of all beauty, it will be understood what price we should attach to the slow and difficult progress which little by little enables us to know it better.

Henri Poincaré

Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?

The reason is not to glorify "bit chasing"; a more fundamental issue is at stake here: Numerical subroutines should deliver results that satisfy simple, useful mathematical laws whenever possible. [...] Without any underlying symmetry properties, the job of proving interesting results becomes extremely unpleasant. The enjoyment of one's tools is an essential ingredient of successful work.

It is a remarkable fact in the history of geometry, that the Elements of Euclid, written two thousand years ago, are still regarded by many as the best introduction to the mathematical sciences.

The invention of logarithms and the calculation of the earlier tables form a very striking episode in the history of exact science, and, with the exception of the Principia of Newton, there is no mathematical work published in the country which has produced such important consequences, or to which so much interest attaches as to Napier's Descriptio.

James Whitbread Lee Glaisher

Modern man lacks a unified conception of the world. He lives in a dual world: in his environment, which is naturally given to him, and, at the same time, in the world which since the beginning of the modern era has been created for him by sciences founded upon the principle that the laws of nature are, in essence, mathematical. The non-unity which has thus come to penetrate our entire life is the true source of the spiritual crisis we are going through today.

Pure mathematics is on the whole distinctly more useful than applied. [...] For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

At each stage of in the advance of mathematical thought the outstanding characteristics are novelty and originality. That is why mathematics is such a delight to study, such a challenge to practise and such a puzzle to define.

George Frederick James Temple

[The mathematical character of Descartes' physics lies in its methodological nature, namely, the] axiomatic structure of the whole system, in the establishment of indubitable foundations and the deduction of the phenomena.

Eduard Jan Dijksterhuis

I am fully assured, that no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognize, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.

When asked to comment on the mathematical properties of space:

Nonsense. Space is blue and birds fly through it.

Werner Heisenberg

Journalism attracts people with exceptional linguistic talent, but I have found that very few have the mathematical sophistication to appreciate the difference between skill and luck.

William J. Bernstein

Money, having freed itself from the physical universe, has become number itself, and finance a strange form of mathematical alchemy.

It is a mathematical fact that the casting of this pebble from my hand alters the centre of gravity of the universe.

Mass psychology is not simply a summation of individual psychologies; that is a prime theorem of social psychodynamics—not just my opinion; no exception has ever been found to this theorem. It is the social mass-action rule, the mob-hysteria law, known and used by military, political, and religious leaders, by advertising men and prophets and propagandists, by rabble rousers and actors and gang leaders, for generations before it was formulated in mathematical symbols. It works.

Robert A. Heinlein

I started with a kind of artistic approach... I visualized the best-looking shapes and sizes. I worked with the variables until it got to the point where, if I changed one of them, it didn't get any better... [only then I] figure out the mathematical formula to produce that effect.

Arthur H. Robinson

If all consciousness is subject to essential laws in a manner similar to that in which spatial reality is subject to mathematical laws, then these essential laws will be of most fertile significance in investigating facts of the conscious life of human and brute animals.

There is a history of mathematical models of oligopolistic competition dating from Cournot to the theory of games. There is also a literature generated by institutional economists, lawyers, and administrators interested in formulating and implementing public policy. It has been the tendency of these groups to work almost as though the other did not exist.

In the realm of ideas, of mental objects, those ideas whose properties are reproducible are called mathematical objects, and the study of mental objects with reproducible properties is called mathematics.

Philip J. Davis

Page after page of professional economic journals are filled with mathematical formulas leading the reader from sets of more or less plausible but entirely arbitrary assumptions to precisely stated but irrelevant theoretical conclusions.

Wassily Leontief

She knew only that if she did or said thus-and-so, men would unerringly respond with the complimentary thus-and-so. It was like a mathematical formula and no more difficult, for mathematics was the one subject that had come easy to Scarlett in her schooldays.

Margaret Mitchell