A Quote by James Clerk Maxwell

The mathematical difficulties of the theory of rotation arise chiefly from the want of geometrical illustrations and sensible images, by which we might fix the results of analysis in our minds.

James Clerk Maxwell

Quote Topics

Analysis Arise Chiefly Difficulties Fix Illustrations Images Mathematical Might Minds Our Results Rotation Sensible Theory Want Which

Quote Author

James Clerk Maxwell
Scottish - Physicist
June 13, 1831 - November 5, 1879

We shall see that the mathematical treatment of the subject [of electricity] has been greatly developed by writers who express themselves in terms of the 'Two Fluids' theory. Their results, however, have been deduced entirely from data which can be proved by experiment, and which must therefore be true, whether we adopt the theory of two fluids or not. The experimental verification of the mathematical results therefore is no evidence for or against the peculiar doctrines of this theory.

James Clerk Maxwell

A geometrical theory in physical interpretation can never be validated with mathematical certainty ... ; like any other theory of empirical science, it can acquire only a more or less high degree of confirmation.

Carl Gustav Hempel

One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?

Stephen Hawking

Residues arise... naturally in several branches of analysis... Their consideration provides simple and easy-to-use methods, which are applicable to a large number of diverse questions, and some new results...

Augustin-Louis Cauchy

Were I to deduce any system from my feelings on leaving Eton, it might be called The Theory of Permanent Adolescence. It is the theory that the experiences undergone by boys at the great public schools, their glories and disappointments, are so intense as to dominate their lives and to arrest their development. From these it results that the greater part of the ruling class remains adolescent, school-minded, self-conscious, cowardly, sentimental, and in the last analysis homosexual.

Cyril Connolly

The difficulties in the study of the infinite arise because we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this... is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.

Galileo Galilei

The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our age has to boast.

Bertrand Russell

In less than eight years "The Origin of Species" has produced conviction in the minds of a majority of the most eminent living men of science. New facts, new problems, new difficulties as they arise are accepted, solved, or removed by this theory; and its principles are illustrated by the progress and conclusions of every well established branch of human knowledge.

Alfred Russel Wallace

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.

Ada Lovelace

...learning chiefly in mathematical sciences can so swallow up and fix one's thought, as to possess it entirely for some time; but when that amusement is over, nature will return, and be where it was, being rather diverted than overcome by such speculations.

Gilbert Burnet

Well, gauge theory is very fundamental to our understanding of physical forces these days. But they are also dependent on a mathematical idea, which has been around for longer than gauge theory has.

Roger Penrose

An old French mathematician said: "A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street." This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.

David Hilbert

I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.

Isaac Newton

In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.

Ada Lovelace

The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics.