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"Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics."
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"The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes."
"The infinite in mathematics is alway unruly unless it is properly treated."
"It is hard to know what you are talking about in mathematics, yet no one questions the validity of what you say. There is no other realm of discourse half so queer."
"You can not apply mathematics as long as words still becloud reality."
"I went to Princeton from Amherst, where I split my interests between mathematics and philosophy."
"The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing."
"I was so pleased to be at university to do physics and mathematics."
"We are servants rather than masters in mathematics."
"To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be."
"I finally reached the conclusion that mathematics was the study I was best fitted to follow, though I did not clearly see in what way I should turn the subject to account."
Explore more quotes by G. H. Hardy
"There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds."
"A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas."
"Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not."
"It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that."
"Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics."
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