Timothy Gowers Inspirational Quotes (3)

This attitude [the abstract method in mathematics] can be encapsulated in the following slogan: a mathematical object is what it does.

... 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.