Mathematical Quotes

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I've played Bach since I was a little girl. I can't let a day go by without playing him. He's so witty and secretive and funny and mathematical and brilliant.

Joanna MacGregor

If we believe that the task of physics is the discovery of a timeless mathematical equation that captures every aspect of the universe, then we believe that the truth about the universe lies outside the universe.

I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would be claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming... and a little mad.

Alfred North Whitehead

In short, I do not write for mathematicians, nor as a mathematician, but as an economist wishing to convince other economists that their science can only be satisfactorily treated on an explicitly mathematical basis.

William Stanley Jevons

But, one will say, if raw experience can not legitimatize reasoning by recurrence, is it so of experiment aided by induction? We see successively that a theorem is true of the number 1, of the number 2, of the number 3 and so on; the law is evident, we say, and it has the same warranty as every physical law based on observations, whose number is very great but limited. But there is an essential difference. Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe, an order outside of us. Mathematical induction, that is, demonstration by recurrence, on the contrary, imposes itself necessarily, because it is only the affirmation of a property of the mind itself.

Henri Poincaré

As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict new facts of the same kind. The catch in this criterion lies in the word "simplest." It is really an aesthetic canon such as we find implicit in our criticisms of poetry or painting. The layman finds such a law as much less simple than "it oozes," of which it is the mathematical statement. The physicist reverses this judgment, and his statement is certainly the more fruitful of the two, so far as prediction is concerned. It is, however, a statement about something very unfamiliar to the plainman, namely, the rate of change of a rate of change.

J. B. S. Haldane

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.

Profound study of nature is the most fertile source of mathematical discoveries.

It is clear that the building of models is not a purely mechanical process but requires skill of a high order – not merely mathematical skill but a sensitivity to the relative importance of different factors and a critical, almost an artistic, faculty in the selection of behaviour equations which are reasonable, tentative hypotheses in explaining the behaviour of actual economies.

Kenneth Boulding

The professional mathematician can scarcely avoid specialization and needs to transcend his private interests and take a wide synoptic view of the whole landscape of contemporary mathematics. His scientific colleagues are continually seeking enlightenment on the relevance of mathematical abstractions. The undergraduate needs a guidebook to the topography of the immense and expanding world of mathematics. There seems to be only one way to satisfy these varied interests... a concise historical account of the main currents... Only by a study of the development of mathematics can its contemporary significance be understood.

George Frederick James Temple

Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect.

The modern scientific worldview with all its hope for clarity and precision, has a "flipside," a complementary set of views which it generates as its train. And this is its misology, sophistry, its abandonment of rationality in the world of human significance. There is thus a quite literal type of schizophrenia in the world bequeathed to us by the Cartesians. It is, on the one hand, hyper-rational; it seeks to extend the purview of mathematical physics throughout the universe. On the other hand, it relegates the world in which the physicist himself dwells, the unique world of humanity and its communities, to the junkpile of the irrational. We who know so much are prohibited from knowing ourselves.

Wisdom is not mathematical, nor astronomical, nor zoological; when it talks too much of any one thing it ceases to be itself. There are wise physicists, but wisdom is not physical; there are wise physicians, but wisdom is not medical.

As mathematical and absolute certainty is seldom to be attained in human affairs, reason and public utility require that judges and all mankind in forming their opinions of the truth of facts should be regulated by the superior number of the probabilities on the one side or the other whether the amount of these probabilities be expressed in words and arguments or by figures and numbers.

William Murray, 1st Earl of Mansfield

If everything, everything were known, statistical estimates would be unnecessary. The science of probability gives mathematical expression to our ignorance, not to our wisdom.

Samuel R. Delany

The mathematical activity of Ancient Greece reached its peak during the glorious era of Euclid, Eratosthenes, Archimedes and Apollonius, a time when Greek letters, art and philosophy were already on the decline.... it was not Greece proper but its outposts in Asia Minor, in Lower Italy, in Africa that had contributed most to the development of mathematics.

We must be exact, mathematical and geometrical, in order to be equal to nature. Number and fantasy, law and abundance are the feverish forces of nature; not sitting down beneath a green tree, but creating crystals and ideas denotes becoming as nature; creating laws and forms; penetrating matter with glowing flashes of divine computation.

We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.

Steven Weinberg

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 is, strictly, no such thing as mathematical proof; that we can::: do nothing but point; that proofs are what Littlewood and I call gas, rhetorical flourishes designed to affect psychology, pictures on the board in the lectures, devices to stimulate the imagination of pupils.

It is from this absolute indifference and tranquillity of the mind, that mathematical speculations derive some of the most considerable advantages; because there is nothing to interest the imagination; because the judgment sits free and unbiased to examine the point. All proportions, every arrangement of quantity, is alike to the understanding, because the same truths result to it from all; from greater from lesser, from equality and inequality.

Astronomers... if they would be more than mere artisans, must be more or less mathematicians, and must separately study the mathematical grounds of their science...

William Rowan Hamilton

Mathematical Knowledge adds a manly Vigour to the Mind, frees it from Prejudice, Credulity, and Superstition.

Mathematics is found to be the special, necessary lens through which nature must be observed since nature is defined as being exactly a structure of mathematical entities and relations.