Mathematics Quotes by Timothy Gowers

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

— Timothy Gowers

“if, for each t, we write u(t) for the function from to that takes x to u(x, t), then it describes how the function…

— 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…

— Timothy Gowers

“ut = -uux - uxxx. Why is it that this equation gives rise to the remarkable stability of the solutions that was observed experimentally…

— Timothy Gowers

“It is a remarkable phenomenon that children can learn to speak without ever being consciously aware of the sophisticated grammar they are using.”

— Timothy Gowers

“The function ei(kx-ωt) represents a wave that travels at a speed of ω/k, which we have just shown to be equal to -k2. Therefore,…

— Timothy Gowers

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

— Timothy Gowers

“differential equations that can be solved in “closed form,” that is, by means of a formula for the unknown function f, are the exception…

— 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

At the other end of the spectrum is, for example, graph theory, where the basic object, a graph, can be immediately comprehended. One will…

— 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

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

— Timothy Gowers