The interesting number paradox is a humorous paradox which arises from the attempt to classify every natural number as either "interesting" or "uninteresting". The paradox states that every natural number is interesting.[1] The "proof" is by contradiction: if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number, thus producing a contradiction.
"Interestingness" concerning numbers is not a formal concept in normal terms, but an innate notion of "interestingness" seems to run among some number theorists. Famously, in a discussion between the mathematicians G. H. Hardy and Srinivasa Ramanujan about interesting and uninteresting numbers, Hardy remarked that the number 1729 of the taxicab he had ridden seemed "rather a dull one", and Ramanujan immediately answered that it is interesting, being the smallest number that is the sum of two cubes in two different ways.[2][3]
^Gardner, Martin (January 1958). "A collection of tantalizing fallacies of mathematics". Mathematical games. Scientific American. 198 (1): 92–97. doi:10.1038/scientificamerican0158-92. JSTOR 24942039.
^Singh, Simon (15 October 2013). "Why is the number 1,729 hidden in Futurama episodes?". BBC News Online. Retrieved 15 October 2013.
^Baez, John C. (2022-02-28). "Hardy, Ramanujan and Taxi No. 1729". The n-Category Café. Retrieved 2022-10-14.
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