Editing Interesting number paradox (section)

{{Short description|On the smallest non-interesting number}}
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.<ref name=":0">{{cite journal
 | last = Gardner | first = Martin
 | date = January 1958
 | department = Mathematical games
 | issue = 1
 | journal = Scientific American
 | jstor = 24942039
 | pages = 92–97
 | title = A collection of tantalizing fallacies of mathematics
 | volume = 198| doi = 10.1038/scientificamerican0158-92
 }}</ref> The "[[mathematical proof|proof]]" is [[proof by contradiction|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 theory|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 (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 [[taxicab number|sum of two cubes in two different ways]].<ref>{{cite news|url=https://www.bbc.co.uk/news/magazine-24459279|title=Why is the number 1,729 hidden in Futurama episodes?|work=BBC News Online|first=Simon|last=Singh|author-link=Simon Singh|date=15 October 2013|access-date=15 October 2013}}</ref><ref>{{Cite web |last=Baez |first=John C. |author-link=John C. Baez |date=2022-02-28 |title=Hardy, Ramanujan and Taxi No. 1729 |url=https://golem.ph.utexas.edu/category/2022/02/hardy_ramanujan_and_taxicab_no.html |access-date=2022-10-14 |website=The n-Category Café |language=en}}</ref>