Time Quote by 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 u(t) “evolves” over time. The Cauchy problem for an evolution equation is the problem of determining this evolution from knowledge of its initial value u(0).””

Timothy Gowers

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More by Timothy Gowers

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

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

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

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

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“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,…

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

Timothy Gowers

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

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

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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

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... 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.

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

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“Can we have genuine knowledge of space without ever leaving our armchairs?”

Timothy Gowers

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Explore all 17 Timothy Gowers quotes

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