Although the prime numbers are rigidly determined, they somehow feel like experimental data.
Timothy GowersA typical mathematician does not actively try to be useful. Individual mathematicians are motivated primarily by a subtle mixture of ambition and intellectual curiosity, and not by a wish to benefit society, nevertheless, mathematics as a whole does benefit society.
Timothy GowersIt is obvious that mathematics needs both sorts of mathematicians, theory-builders and problem-solvers.
Timothy GowersThis attitude [the abstract method in mathematics] can be encapsulated in the following slogan: a mathematical object is what it does.
Timothy Gowers