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, the smallest natural number that does not appear in an entry of the On-Line Encyclopedia of Integer Sequences (OEIS) was originally found to be 11630 on 12 June 2009.
[6] For instance, OEIS: A000027 is the sequence of all natural numbers, and if continued indefinitely would contain all positive integers.
[9] Similarly, instead of trying to quantify the subjective feeling of interestingness, one can consider the length of a phrase needed to specify a number.
In 1945, Edwin F. Beckenbach published a short letter in The American Mathematical Monthly suggesting thatOne might conjecture that there is an interesting fact concerning each of the positive integers.
[12] Martin Gardner presented the paradox as a "fallacy" in his Scientific American column in 1958, including it with six other "astonishing assertions" whose purported proofs were also subtly erroneous.
[1] A 1980 letter to The Mathematics Teacher mentions a jocular proof that "all natural numbers are interesting" having been discussed three decades earlier.