theory

One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.

I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: "The author discusses valueless measures in pointless spaces."

I think that there is a moral to this story, namely that it is more important to have beauty in one's equations that to have them fit experiments. If Schroedinger had been more confident of his work, he could have published it some months earlier, and he could have published a more accurate equation. 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 development of the theory.

[Scientific enterprise] is usually conceived as being made up of four main kinds of interrelated activities: gathering data, finding parsimonious descriptions of the data, formulating explanatory theories, and testing the theories. Sometimes the second category (description) and third (explanation) are merged. (note that they do not consider new data measuring devices among other things)

The modern physicist is a quantum theorist on Monday, Wednesday, and Friday and a student of gravitational relativity theory on Tuesday, Thursday, and Saturday. On Sunday he is neither, but is praying to his God that someone, preferably himself, will find the reconciliation between the two views.

The ultimate, most holy form of theory is action.

We all agree that your theory is crazy. The question which divides us is whether it is crazy enough.

We all agree that your theory is crazy, but is it crazy enough?

If facts do not conform to theory, they must be disposed of.

Statistics: the mathematical theory of ignorance.