A Quote by Arthur Cayley

As for everything else, so for a mathematical theory: beauty can be perceived but not explained. — © Arthur Cayley
As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
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.
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.
A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data.
Nothing fortuitous happens in a child's world. There are no accidents. Everything is connected with everything else and everything can be explained by everything else. . . . For a young child everything that happens is a necessity.
What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating.
String theory has had a long and wonderful history. It originated as a technique to try to understand the strong force. It was a calculational mechanism, a way of approaching a mathematical problem that was too difficult, and it was a promising way, but it was only a technique. It was a mathematical technique rather than a theory in itself.
The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should take simplicity into consideration in a subordinate way to beauty ... It often happens that the requirements of simplicity and beauty are the same, but where they clash, the latter must take precedence.
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.
Some people would claim that things like love, joy and beauty belong to a different category from science and can't be described in scientific terms, but I think they can now be explained by the theory of evolution.
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.
The most important single thing about string theory is that it's a highly mathematical theory, and the mathematics holds together in a very tight and consistent way. It contains in its basic structure both quantum mechanics and the theory of gravity. That's big news.
I think it laughable, frankly, that the physics community comes up with a theory for everything. There isn't one theory for everything. There is not one explanation. We may eventually have several theories that can tie things together nicely but there is not a single theory of everything.
What would it mean if there were a theory that explained everything? And just what does "everything" actually mean, anyway? Would this new theory in physics explain, say the meaning of human poetry? Or how economics work? Or the stages of psychosexual development? Can this new physics explain the currents of ecosystems, or the dynamics of history, or why human wars are so terribly common?
Einstein's theory of General Relativity has a mathematical structure very similar to Yang-Mills theory.
If a theory can not be explained to a child, then the theory is probably worthless.
[Referring to Fourier's mathematical theory of the conduction of heat] ... Fourier's great mathematical poem.
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