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Saturday, August 25, 2018

G. H. Hardy and mathematical reality


Photo source: Wikimedia Commons


G. H. Hardy (1877-1947) was a British mathematician best known for his contributions to number theory and population genetics. Philosopher Brand Blanshard said,


"I do not think that G. H. Hardy was talking nonsense when he insisted that the mathematician was discovering rather than creating, nor was it wholly nonsense for Kepler to exult that he was thinking God's thoughts after him." (The Philosophy of Brand Blanshard, 1980)


Mathematician Bruce Berndt said,


"Paul Erdos has passed on to us Hardy's personal ratings of mathematicians. Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100. Hardy gave himself a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100." (Ramanujan's Notebooks, 1994)


The rest of this post is some quotes from Hardy.


Mathematical discovery


"The function of a mathematician then, is simply to observe the facts about his own intricate system of reality, that astonishingly beautiful complex of logical relations which forms the subject matter of his science, as if he were an explorer looking at a distant range of mountains, and to record the results of his observations in a series of maps..." (The Theory of Numbers, 1922)


"317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is, because mathematical reality is built that way (A Mathematician's Apology, 1941)


"I believe that mathematical reality lies outside us, that our function is yo discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our 'creations', are simply our notes of our observations." (


"We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas." (


"The mathematician's patterns, like the painter's of the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way." (