At the other end of the spectrum is, for example, graph theory, where the basic object, a graph, can be immediately comprehended. One will not get an…

- Timothy Gowers

... 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.

- Timothy Gowers

What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the pr…

- Timothy Gowers

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

- Timothy Gowers

A typical mathematician does not actively try to be useful. Individual mathematicians are motivated primarily by a subtle mixture of ambition and int…

- Timothy Gowers

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

- Timothy Gowers

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 fam…

- Timothy Gowers

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

- Timothy Gowers

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

- Timothy Gowers