The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.
Paul DiracOne 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.
Paul DiracIt was not until some weeks later that I realized there is no need to restrict oneself to 2 by 2 matrices. One could go on to 4 by 4 matrices, and the problem is then easily soluable. In retrospect, it seems strange that one can be so much held up over such an elementary point. The resulting wave equation for the electron turned out to be very successful. It led to correct values for the spin and the magnetic moment. This was quite unexpected. The work all followed from a study of pretty mathematics, without any thought being given to these physical properties of the electron.
Paul DiracA good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78.
Paul DiracWhat 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.
Paul Dirac