As time goes on, it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen.

It 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.

Hopes are always accompanied by fears, and, in scientific research, the fears are liable to become dominant.

When [Erwin Schrödinger] went to the Solvay conferences in Brussels, he would walk from the station to the hotel where the delegates stayed, carrying all his luggage in a rucksack and looking so like a tramp that it needed a great deal of argument at the reception desk before he could claim a room.

A termination of one's life is necessary in the scheme of things to provide a logical reason for unselfishness. . . . The fact that there is an end to one's life compels one to take an interest in things that will continue to live after one is dead.

I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it.

Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.