Renormalization is just a stop-gap procedure. There must be some fundamental change in our ideas, probably a change just as fundamental as the passage from Bohr's orbit theory to quantum mechanics. When you get a number turning out to be infinite which ought to be finite, you should admit that there is something wrong with your equations, and not hope that you can get a good theory just by doctoring up that number.

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.

It is more important to have beauty in one's equations than to have them fit experiment... It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.

A great deal of my work is just playing with equations and seeing what they give.

Well, in the first place, it leads to great anxiety as to whether it's going to be correct or not ... I expect that's the dominating feeling. It gets to be rather a fever... At age 60, when asked about his feelings on discovering the Dirac equation.

A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data.

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.