There is no way to guarantee in advance what pure mathematics will lat — Mathematics

"As soon as a thought or word becomes a tool, one can dispense with actually ‘thinking’ it, that is, with going through the logical acts involved in verbal formulation of it. As has been pointed out, often and correctly, the advantage of mathematics—the model of all neo-positivistic thinking—lies in just this ‘intellectual economy.’ Complicated logical operations are carried out without actual performance of the intellectual acts upon which the mathematical and logical symbols are based. … Reason … becomes a fetish, a magic entity that is accepted rather than intellectually experienced."

"Mathematics may be compared to a mill of exquisite workmanship, which grinds your stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat flour from peascods, so pages of formulæ will not get a definite result out of loose data."

"In doing mathematics, I express something personal. It is a source of joy to know that, despite this personal aspect, the fruit of my work can be of interest to other mathematicians."

"If a religion is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one."

"It might have been beans, successful hunts, or victories in battle, but, for millennia, people were using maths to describe things - counting them, measuring them, dividing them up."

"“There’s more to life than mathematics,” Joan said. “But not much more.”"