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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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"Mathematics doesn't care about those beyond the numbers."
""Obvious" is the most dangerous word in mathematics."
"Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions."
"The definition of a good mathematical problem is the mathematics it generates rather than the problem itself."
"He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixteens. The numbers formed up and marched past his brain in terrified obedience. Division and multiplication were discovered. Algebra was invented and provided an interesting diversion for a minute or two. And then he felt the fog of numbers drift away, and looked up and saw the sparkling, distant mountains of calculus."
"I have in later years taken to Euclid, Whitehead, Bertrand Russell, in an elemental way."
"Mathematics allows for no hypocrisy and no vagueness."
"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."
"We are servants rather than masters in mathematics."
Explore more quotes by G. H. Hardy
"Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not."
"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."
"It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that."
"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."
"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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