Mathematical Quotes

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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.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

In a mathematical sense, space is manifoldness, or combination of numbers. Physical space is known as the 3-dimension system. There is the 4-dimension system, there is the 10-dimension system.

Charles Proteus Steinmetz

Sceptics often make much of the alleged mysteriousness of values—by which, however, they mean little more than that they are claimed to be essentially different from all classes of physical objects and properties, mental states and properties, historical facts, mathematical theorems, scientific concepts, or whatever. In other words, their objection is simply that values are claimed to be of their nature different everything which is not of its nature a value.

R. W. K. Paterson

Men cannot be treated as units in operations of political arithmetic because they behave like the symbols for zero and the infinite, which dislocate all mathematical operations.

Arthur Koestler

We do not discover mathematical truths; we remember them from our passages through this world outside our own.

It is not easy to devise a cure for such a state of things (the declining taste for science). The most obvious remedy is to provide the educated classes with a series of works on popular and practical science, freed from mathematical symbols and technical terms, written in simple and perspicuous language, and illustrated by facts and experiments which are level to the capacity of ordinary minds.

There is no need in these mathematical days to defend the use of symbolism. It is regarded by many schools of modern thought as the only safe form of language. Wittgenstein treats symbols as something more than conventional signs, and regards them as corresponding in some way to the reality to which they refer. He would probably accept Gurdjieff's dictum that:

Symbols not only transmit knowledge but show the way to it.

Even though other thinkers deny any objective reference to symbols, no one questions that symbolism has a power beyond that of ordinary language. It is different with the language of myth. This is despised by superficial thinkers, but the greatest philosophers have known its value.

John G. Bennett

Wenzel and Richter, the latter... of most pronounced mathematical temperament, laid the foundations of stoichiometry, or "the art of measuring the chemical elements".

J. R. Partington

The immediacy of mystic experience simply means that we know God just as we know other objects. God is not a mathematical entity or a system of concepts mutually related to one another and having no reference to experience.

Charles Francis Adams's memory was hardly above the average; his mind was not bold like his grandfather's or restless like his father's, or imaginative or oratorical — still less mathematical; but it worked with singular perfection, admirable self-restraint, and instinctive mastery of form. Within its range it was a model.

We want the mathematical genius - there is work for him. We want the literary genius - there is work for him, especially in my office. We want the scientific brain - there is more than enough work for him. We want the man of brains and we want the man of common sense and little brain. We want the man of initiative and the man of action, the methodical man and even the crank. We open our ranks widely to all.

Hugh Trenchard, 1st Viscount Trenchard

The pragmatist regards any theory as a mere mathematical machine for generating numbers which he then compares with experiment. A pragmatist is concerned with results, not reality. The pragmatist refuses on principle to speculate about deep reality, such a concept being meaningless from his point of view. Pragmatism is an intelectually safe but ultimately sterile philosophy.

When a mathematician engaged in investigating physical actions and results has arrived at his own conclusions, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formulae? If so, would it not be a great boon to such as well to express them so — translating them out of their hieroglyphics that we might also work upon them by experiment?

Michael Faraday

For reasons mathematical, psychological, and sociological, it is a good idea to use a money management system that is relatively forgiving of estimation errors.

William Poundstone

In the social equation, the value of a single life is nil; in the cosmic equation, it is infinite... Not only communism, but any political movement which implicitly relies on purely utilitarian ethics, must become a victim to the same fatal error. It is a fallacy as naïve as a mathematical teaser, and yet its consequences lead straight to Goya's Disasters, to the reign of the guillotine, the torture chambers of the Inquisition, or the cellars of the Lubianka.

Arthur Koestler

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

(Game theory is) essentially a structural theory. It uncovers the logical structure of a great variety of conflict situations and describes this structure in mathematical terms. Sometimes the logical structure of a conflict situation admits rational decisions; sometimes it does not.

Anatol Rapoport

"Yes," I continued, "I discovered this model recently and her style never fails to be mathematically perfect. She seems to come by it naturally. As if she were born resonant. I notice Japanese models tend to do this. Like I said, they seem to have resonance somewhere deep in their culture. But Yuri Nakagawa, she's the best I've ever seen. The best model, with the most powerful resonance. I need her to probe deeper into this profound mathematical instinct, which I call resonance."

Alexei Maxim Russell

The 'physical' does not mean any particular kind of reality, but a particular kind of denoting reality, namely a system of concepts in the natural sciences which is necessary for the cognition of reality. 'The physical' should not be interpreted wrongly as an attribute of one part of reality, but not of the other ; it is rather a word denoting a kind of conceptual construction, as, e.g., the markers 'geographical' or 'mathematical', which denote not any distinct properties of real things, but always merely a manner of presenting them by means of ideas..

So, ultimately, in order to understand nature it may be necessary to have a deeper understanding of mathematical relationships. But the real reason is that the subject is enjoyable, and although we humans cut nature up in different ways, and we have different courses in different departments, such compartmentalization is really artificial, and we should take our intellectual pleasures where we find them.

Richard Feynman

It is to be feared that few who are not experts in the history of mathematics have any acquaintance with the details of the original discoveries in mathematics of the greatest mathematician of antiquity, perhaps the greatest mathematical genius that the world has ever seen.

Thomas Little Heath

Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.

A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

All science as it grows toward perfection becomes mathematical in its ideas.

Alfred North Whitehead