Here is something Category-Theorists like: it is trivial, but not trivially trivial.
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
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
... 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.
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
What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the pr…
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
A typical mathematician does not actively try to be useful. Individual mathematicians are motivated primarily by a subtle mixture of ambition and int…
Although the prime numbers are rigidly determined, they somehow feel like experimental data. - Timothy Gowers
Although the prime numbers are rigidly determined, they somehow feel like experimental data.
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
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…
It is obvious that mathematics needs both sorts of mathematicians, theory-builders and problem-solvers. - Timothy Gowers
It is obvious that mathematics needs both sorts of mathematicians, theory-builders and problem-solvers.
This attitude [the abstract method in mathematics] can be encapsulated in the following slogan: a mathematical object is what it does. - Timothy Gowers
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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