There is the science of pure geometry, in which there are many geometries, , , non-Euclidean geometry... [etc.]. Each... is a , a pattern of ideas...… - G.H. Hardy
" "There is the science of pure geometry, in which there are many geometries, , , non-Euclidean geometry... [etc.]. Each... is a , a pattern of ideas... judged by the interest and beauty of... pattern. It is a map or picture, the... product of many hands, a partial and imperfect copy (yet exact so far as it extends) of a section of mathematical reality. But... there is one thing... of which pure geometries are not pictures, and that is the spatio-temporal reality of the physical world. ...[T]hey cannot be, since earthquakes and eclipses are not mathematical concepts.
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About G.H. Hardy
Godfrey Harold Hardy FRS (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of population genetics. Hardy is usually known by those outside the field of mathematics for his 1940 essay A Mathematician's Apology, often considered one of the best insights into the mind of a working mathematician written for the layperson. He had a long collaboration with John Edensor Littlewood, and he discovered and supported the work of Srinivasa Ramanujan.
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Godfrey Harold Hardy
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G. H. Hardy
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Godfrey·Harold·Hardy
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Godfrey Harold
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Additional quotes by G.H. Hardy
A painter makes patterns with shapes and colours, a poet with words. A painting may embody an ‘idea’, but the idea is usually commonplace and unimportant. In poetry, ideas count for a good deal more; but, [...] the importance of ideas in poetry is habitually exaggerated: '... Poetry is not the thing said but a way of saying it.' [In poetry,] the poverty of the ideas seems hardly to affect the beauty of the verbal pattern.
The play is independent of the pages on which it is printed, and 'pure geometries' are independent of lecture rooms, [rough blackboard drawings] or of any other detail of the physical world.
This is the point of view of a pure mathematician. Applied mathematicians, mathematical physicists... take a different view... preoccupied with the physical world itself, which also has its structure or pattern. ...We may be able to trace a ...resemblance between the two sets of relations, and then the pure geometry will become interesting to physicists; it will give us ...a map which 'fits the facts' ...The geometer offers ...a whole set of maps from which to choose.
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