Interesting number paradox
logical contradiction in which every possible solution to the problem is exempt: if there were some uninteresting natural numbers, there would be a smallest uninteresting number, which would be therefore interesting
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. 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.
Paradoxical nature
Attempting to classify all numbers this way leads to a paradox or an antinomy of definition. Any hypothetical partition of natural numbers into interesting and uninteresting sets seems to fail. Since the definition of interesting is usually a subjective, intuitive notion, it should be understood as a semi-humorous application of self-reference in order to obtain a paradox.
The paradox is alleviated if "interesting" is instead defined objectively: for example, as of 2023, the smallest natural number that does not appear in an entry of the On-Line Encyclopedia of Integer Sequences (OEIS) was 20,067. This definition of uninteresting is possible only because the OEIS lists only a finite number of terms for each entry.
The public source identifies “Interesting number paradox” as logical contradiction in which every possible solution to the problem is exempt: if there were some uninteresting natural numbers, there would be a smallest uninteresting number, which would be therefore interesting. This brief keeps that definition visible, then builds a research path around Interesting, number and paradox.
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Vocabulary and entity names are the principal evidence signals here, because they determine the precision of every later search. The source revision retrieved here is dated Jun 17, 2026. The linked authority identifier is Q1665996. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1729 and 2023.
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This entry incorporates text from “Interesting number paradox” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.