>> In the preface to the first edition of Dedekind's WsuwsdZ, he refers to
>> the Greek phrase (my transliteration) 'aei ho anthropos arithmetidzei'as
>> a well-known (bekannt) saying. I'm a little embarrassed to say, however,
>> that it is not so well-known as to be known by me. Could someone please
>> tell me who authored this 'well-known' phrase ... and tell me what they
>> meant by it. To me it says something like "Man is (or has) always (been)
>> 'arithmetizing' or 'numbering' or 'counting'". But that supposed that
>> arithmetidzo is a verb, and I can't find an entry for it in my lexicon,
>> much less a pointer to the author of the 'well-known' saying.
Avinoam Mann responded:
> To me, it sounds like Dedekind is paraphrasing a "well-known" saying of
> Plato: 'God geometrizes'. So Dedekind is answering by 'Man arithmetizes'.
> Does anybody know if that paraphrase originates with Dedekind, or is it
> earlier? And please remind us of the reference for Plato's saying.
Cf.:
Plato said "a)ei\ o( qeo\s gewmetrei=." Jacobi changed this to
"a)ei\ o( qeo\s a)riqmhti/zei." Then came Kronecker and created the
memorable expression "Die ganzen Zahlen hat Gott gemacht, alles andere ist
Menschenwerk."
- Klein, F., Jahrebericht der Deutschen Mathematiker Vereinigung, Bd. 6,
p. 136.
In: Robert Edouard Moritz, Memorabilia Mathematica.
MAA, c1993 [1st publ. 1914], pp. 269-270, # 1635
Antreas