Editing Interesting number paradox (section)

==History==
In 1945, [[Edwin F. Beckenbach]] published a short letter in ''[[The American Mathematical Monthly]]'' suggesting that<blockquote>One might conjecture that there is an interesting fact concerning each of the positive integers. Here is a "proof by induction" that such is the case. Certainly, 1, which is a factor of each positive integer, qualifies, as do 2, the smallest prime; 3, the smallest odd prime; 4, Bieberbach's number; ''etc''. Suppose the set ''S'' of positive integers concerning each of which there is no interesting fact is not vacuous, and let ''k'' be the smallest member of ''S''. But this is a most interesting fact concerning ''k''! Hence ''S'' has no smallest member and therefore is vacuous. Is the proof valid?<ref>{{Cite journal |last=Beckenbach |first=Edwin F. |date=April 1945 |title=Interesting integers |journal=[[The American Mathematical Monthly]] |volume=52 |issue=4 |pages=211 |jstor=2305682}}</ref></blockquote>

[[Constance Reid]] included the paradox in the 1955 first edition of her [[popular mathematics]] book ''[[From Zero to Infinity]]'', but removed it from later editions.<ref>{{cite journal
 | last = Hamilton | first = J. M. C.
 | doi = 10.2307/2687853
 | issue = 1
 | journal = [[Mathematics Magazine]]
 | jstor = 2687853?
 | mr = 1571022
 | pages = 43–44
 | title = Review of ''From Zero to Infinity'', 2nd ed.
 | volume = 34
 | year = 1960}}</ref> [[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.<ref name=":0" /> A 1980 letter to ''[[The Mathematics Teacher]]'' mentions a jocular proof that "all natural numbers are interesting" having been discussed three decades earlier.<ref>{{cite journal
 | last = Gould | first = Henry W.
 | date = September 1980
 | issue = 6
 | journal = The Mathematics Teacher
 | jstor = 27962064
 | page = 408
 | title = Which numbers are interesting?
 | volume = 73}}</ref>  In 1977, [[Greg Chaitin]] referred to Gardner's statement of the paradox and pointed out its relation to an earlier paradox of [[Bertrand Russell]] on the existence of a smallest undefinable [[Ordinal number|ordinal]] (despite the fact that all sets of ordinals have a smallest element and that "the smallest undefinable ordinal" would appear to be a definition).<ref name=":1" /><ref>{{cite journal
 | last = Russell | first = Bertrand
 | date = July 1908
 | doi = 10.2307/2369948
 | issue = 3
 | journal = American Journal of Mathematics
 | jstor = 2369948
 | pages = 222–262
 | title = Mathematical logic as based on the theory of types
 | volume = 30}}</ref>

In ''[[The Penguin Dictionary of Curious and Interesting Numbers]]'' (1987), David Wells commented that [[39 (number)|39]] "appears to be the first uninteresting number", a fact that made it "especially interesting", and thus 39 must be simultaneously interesting and dull.<ref>{{cite book|first=David |last=Wells |title=The Penguin Dictionary of Curious and Interesting Numbers |title-link=The Penguin Dictionary of Curious and Interesting Numbers |page=120 |publisher=Penguin Books |year=1987 |oclc=17634415}}</ref>