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.

I do not see how a man can work on the frontiers of physics and write poetry at the same time. They are in opposition.

The methods of theoretical physics should be applicable to all those branches of thought in which the essential features are expressible with numbers.

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

I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics.

The physicist, in his study of natural phenomena, has two methods of making progress: (1) the method of experiment and observation, and (2) the method of mathematical reasoning. The former is just the collection of selected data; the latter enables one to infer results about experiments that have not been performed. There is no logical reason why the second method should be possible at all, but one has found in practice that it does work and meets with reasonable success.