http://en.wikipedia.org/wiki/Paul_Dirac
Dr. Yoichiro Nambu says in his lecture, “The Legacies of Yukawa and Tomonaga”, 2006, that there are three distinct types of theoretical physicists, each type being represented by Heisenberg, Einstein, and Dirac, respectively. He says that: Heisenberg’s is heuristic, bottom-up, and inductive. Einstein’s is axiomatic, top-down, and deductive. Dirac’s is abstract, revolutionary, and esthetic.
Here are some of the famous remarks by Dirac.
“The Relation between Mathematics and Physics”, 1939.
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 theory of relativity introduced mathematical beauty to an unprecedented extent into the description of Nature.
We now see that we have to change the principle of simplicity into a principle of mathematical beauty. The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should still take simplicity into consideration in a subordinate way to beauty. (For example Einstein, in choosing a law of gravitation, took the simplest one compatible with his space-time continuum, and was successful.). It often happens that the requirements of simplicity and of beauty are the same, but where they clash the latter must take precedence.
“The Evolution of the Physicist’s Picture of Nature”, 1963.
One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.
It is always a great wonder to me that the nature is something not only comprehensible but describable in terms of mathematics.