Moreover, if one selects a problem, works on it in isolation for a few years and finally solves it, there is a danger, unless the problem is very famous, that it will no longer be regarded as all that significant.

... the atlas is a manifold. This is a typical mathematician's use of the word "is", and should not be confused with the normal use.

Moreover, if one selects a problem, works on it in isolation for a few years and finally solves it, there is a danger, unless the problem is very famous, that it will no longer be regarded as all that significant.

Although the prime numbers are rigidly determined, they somehow feel like experimental data.

Here is something Category-Theorists like: it is trivial, but not trivially trivial.

It is obvious that mathematics needs both sorts of mathematicians, theory-builders and problem-solvers.

What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.