A Quote by Paul Dirac
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.
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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.
The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena. The verbal interpretation, on the other hand - i.e., the metaphysics of quantum theory - is on far less solid ground. In fact, in more than forty years physicists have not been able to provide a clear metaphysical model.
When I speak of the beauty of a game of chess, then naturally this is subjective. Beauty can be found in a very technical, mathematical game for example. That is the beauty of clarity.
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.
The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena.
As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
Einstein's theory of General Relativity has a mathematical structure very similar to Yang-Mills theory.
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.
As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.
If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.
It is quite clear that beauty does depend on one's culture and upbringing for certain kinds of beauty, pictures, literature, poetry and so on...But mathematical beauty is of a rather different kind. I should say perhaps it is of a completely different kind and transcends these personal factors. It is the same in all countries and at all periods of time.
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.
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.
[Referring to Fourier's mathematical theory of the conduction of heat] ... Fourier's great mathematical poem.
Beauty saves. Beauty heals. Beauty motivates. Beauty unites. Beauty returns us to our origins, and here lies the ultimate act of saving, of healing, of overcoming dualism.
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