A Quote by G. H. Hardy
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.
Related Quotes
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.
It was as though applied mathematics was my spouse, and pure mathematics was my secret lover.
Love was even more mathematical than poetry. It was the pure mathematics of the spirit.
I didn't feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.
In the field of Egyptian mathematics Professor Karpinski of the University of Michigan has long insisted that surviving mathematical papyri clearly demonstrate the Egyptians' scientific interest in pure mathematics for its own sake. I have now no doubt that Professor Karpinski is right, for the evidence of interest in pure science, as such, is perfectly conclusive in the Edwin Smith Surgical Papyrus.
The notion that "applied" knowledge is somehow less worthy than "pure" knowledge, was natural to a society in which all useful work was performed by slaves and serfs, and in which industry was controlled by the models set by custom rather than by intelligence. Science, or the highest knowing, was then identified with pure theorizing, apart from all application in the uses of life; and knowledge relating to useful arts suffered the stigma attaching to the classes who engaged in them.
By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful.
Mathematics my foot! Algorithms are mathematics too, and often more interesting and definitely more useful.
I don't want to convince you that mathematics is useful. It is, but utility is not the only criterion for value to humanity. Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that - by some mysterious agency - capture patterns of the universe around us? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature.
String theory has had a long and wonderful history. It originated as a technique to try to understand the strong force. It was a calculational mechanism, a way of approaching a mathematical problem that was too difficult, and it was a promising way, but it was only a technique. It was a mathematical technique rather than a theory in itself.
The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.
In mathematics I can report no deficiency, except it be that men do not sufficiently understand the excellent use of Pure Mathematics.
Applied mathematics will always need pure mathematics just as anteaters will always need ants.
Theology, Mr. Fortune found, is a more accommodating subject than mathematics; its technique of exposition allows greater latitude. For instance when you are gravelled for matter there is always the moral to fall back upon. Comparisons too may be drawn, leading cases cited, types and antetypes analysed and anecdotes introduced. Except for Archimedes mathematics is singularly naked of anecdotes.
My technique is laughable at times. I have developed a style of my own, I suppose, which creeps around. I don't have to have too much technique for it. I've developed the parts of my technique that are useful to me. I'll never be a very fast guitar player. I don't really know what to say about my style. There's always a melodic intent in there.
Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.
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