Mathematical Quotes

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What would geometry be without Gauss, mathematical logic without Boole, algebra without Hamilton, analysis without Cauchy?

George Frederick James Temple

Computer science research is different from these more traditional disciplines. Philosophically it differs from the physical sciences because it seeks not to discover, explain, or exploit the natural world, but instead to study the properties of machines of human creation. In this it as analogous to mathematics, and indeed the "science" part of computer science is, for the most part mathematical in spirit. But an inevitable aspect of computer science is the creation of computer programs: objects that, though intangible, are subject to commercial exchange.

Our first objective in undertaking the experimental program described here has been to gain some understanding of what goes on in long sequences of plays of Prisoner's Dilemma. We have attempted to gain this understanding by postulating a system going through a sequence of states and by attempting to formulate some mathematical models from which the dynamics of the system could be deduced. Once such a model is found, its parameters, properly interpreted, become the key terms in the emerging psychological theory. This strategy can be deemed successful, if the parameters so discovered are independent of the process itself, if they suggest further investigation, and if the further investigations, in turn, lead to a more inclusive theory.

Anatol Rapoport

What a mathematical proof actually does is show that certain conclusions, such as the irrationality of, follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.

Boyle was among the first who recognized that the withdrawal of sympathy licenses conduct that would not be permissible within an animistic vision of nature.... The vision that he and his scientific colleagues were creating was fast becoming a mathematical abstraction lacking color, odor, texture, and personality.... The task of the natural philosopher, we are told, is to "probe," "penetrate," and "pierce" nature in all her "mysterious," secret," and "intimate recesses."

Theodore Roszak

An accurate charting of American women's progress through history might look more like a corkscrew tilted slightly to one side, its loops inching closer to the line of freedom with the passage of time-but, like a mathematical curve approaching infinity, never touching its goal.

Mathematical sciences require theories, molecular biology facts.

David Berlinski

No mathematical exactness without explicit proof from assumed principles — such is the motto of the modern geometer.

Symbolic Logic has been disowned by many logicians on the plea that its interest is mathematical, and by many mathematicians on the plea that its interest is logical.

Alfred North Whitehead

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

The concatenations of mathematical ideas are not divorced from life, far from it, but they are less influenced than other scientific ideas by accidents, and it is perhaps more possible, and more permissible, for a mathematician than for any other man to secrete himself in a tower of ivory.

In the most general mathematical sense, a space is a set of elements which conform to certain postulates.

James Grier Miller

Theoretical physicists accept the need for mathematical beauty as an act of faith...For example, the main reason why the theory of relativity is so universally accepted is its mathematical beauty.

The bewildered novice in chess moves cautiously, recalling individual rules, whereas the experienced player absorbs a complicated situation at a glance and is unable to account rationally for his intuition. In like manner mathematical intuition grows with experience, and it is possible to develop a natural feeling for concepts such as four dimensional space.

Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future. A good many people are working on the mathematical basis of quantum theory, trying to understand the theory better and to make it more powerful and more beautiful. If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them.

The further we analyse the manner in which such an engine performs its processes and attains its results, the more we perceive how distinctly it places in a true and just light the mutual relations and connexion of the various steps of mathematical analysis; how clearly it separates those things which are in reality distinct and independent, and unites those which are mutually dependent.

Econometrics is the name for a field of science in which mathematical-economic and mathematical-statistical research are applied in combination. Econometrics, therefore, forms a borderland between two branches of science, with the advantages and disadvantages thereof; advantages, because new combinations are introduced which often open up new perspectives; disadvantages, because the work in this field requires skill in two domains, which either takes up too much time or leads to insufficient training of its students in one of the two respects.

The illiterate expression 'given data' constantly recurs in Lange. It appears to have an irresistable attraction to mathematical economists because it doubly assures them that they know what they do not know. It seems to bewitch them into making assertions about the real world for which they have no empirical justification whatever.

Friedrich Hayek

Mathematicks may help the naturalist, both to frame hypotheses, and to judge of those that are proposed to them, especially such as relate to mathematical subjects in conjunction with others.

In the absolute universe all events can be regarded as absolutely deterministic, and if we can't perceive the greater structures, it's because our vision is faulty. If we had a real grasp of causality down to the molecular level, we wouldn't need to rely on mathematical approximations, on statistics and probabilities, in making predictions. If our perceptions of cause and effect were only good enough, we'd be able to attain absolute knowledge of what is to come. We would make ourselves all-seeing.

Robert Silverberg

To my view there are two methods of research, the apparatus and the calculation. Whoever prefers the first method is an experimenter; otherwise, he is a mathematical physicist. Both of them set up theories and hypotheses...

Wilhelm Röntgen

There are good reasons to believe in God, including the existence of mathematical principles and order in creation. They are positive reasons, based on knowledge, rather than default assumptions based on a temporary lack of knowledge.

Francis Collins

[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.

The Laws of Nature are merely truths or generalized facts, in regard to matter, derived by induction from experience, observation, arid experiment. The laws of mathematical science are generalized truths derived from the consideration of Number and Space.

Charles Davies (professor)