When a scientist doesn't know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty darn sure of what the result is going to be, he is still in some doubt. We have found it of paramount importance that in order to progress we must recognize our ignorance and leave room for doubt. Scientific knowledge is a body of statements of varying degrees of certainty - some most unsure, some nearly sure, but none absolutely certain.

Philosophers say a great deal about what is absolutely necessary for science, and it is always, so far as one can see, rather naive, and probably wrong.

So, ultimately, in order to understand nature it may be necessary to have a deeper understanding of mathematical relationships. But the real reason is that the subject is enjoyable, and although we humans cut nature up in different ways, and we have different courses in different departments, such compartmentaliz ation is really artificial, and we should take our intellectual pleasures where we find them.

The same equations have the same solutions

I'm smart enough to know that I'm dumb.

I don't think that the laws can be considered to be like God because they have been figured out.

Some things that satisfy the rules of algebra can be interesting to mathematicians even though they don't always represent a real situation.