I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways."
Interpretation
The quote highlights the unexpected significance found in seemingly dull or ordinary things.
In this quote, G. H. Hardy shares an encounter with the mathematician Srinivasa Ramanujan, who turned what Hardy considered an uninteresting taxi cab number, 1729, into a fascinating mathematical subject. This demonstrates how perspectives can transform our understanding and appreciation of even the most mundane aspects of life by revealing hidden beauty and complexity.
In practice
In a lecture on the importance of perspective in mathematics.
A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful-"important" if you like, but the word is very ambiguous, and "serious" expresses what I mean much better.
Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon. It is a pity, but in that case he does not matter a great deal anyhow, and it would be silly to bother about him.
Exposition, criticism, appreciation, is work for second-rate minds.
It is hardly possible to maintain seriously that the evil done by science is not altogether outweighed by the good. For example, if ten million lives were lost in every war, the net effect of science would still have been to increase the average length of life.
Real mathematics must be justified as art if it can be justified at all.
If intellectual curiosity, professional pride, and ambition are the dominant incentives to research, then assuredly no one has a fairer chance of gratifying them than a mathematician.
...I leaped headlong into the Sea, and thereby have become more acquainted with the Soundings, the quicksands, and the rocks, than if I had stayed upon the green shore, and piped a silly pipe, and took tea and comfortable advice.
Looking back on things, the view always improves.
What I really hated, of course, was my mind. There must have been an off switch somewhere, but I was damned if I could find it.
Always there should be a little mistake here and there - I am for it. The people who don't do mistakes are cold like ice. It takes risk to make a mistake. If you don't take risk, you are boring.
We must quit bending the Word to suit our situation. It is we who must be bent to that Word, our necks that must bow under the yoke.
The most formidable weapon against errors of every kind is reason.
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