In the preface to the first edition of Essays on the Theory of Numbers, Dedekind writes:
"In this sense which I wish to express by the word formed after a well-known saying ἀεί ὁ ἄνθρωπος ἀριθμητίζει, I hope that the following pages, as an attempt to establish the science of numbers upon a uniform foundation will find a generous welcome..."
Source: Hawking, God Created the Integers, reprinted courtesy of Dover Publications
I'm taking the Greek to mean something like "Man always mathematizes", which in the context Dedekind is using it, relates to his idea that: "Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things."
The phrase is quite similar to ἀεὶ ὁ θεὸς γεωμετρεῖ, attributed to Plato, translated as "God always geometrizes."
Three related questions, answers to any of which are welcome:
Is my translation accurate?
What's going on with ἀριθμητίζει? I can't find that specific form, although the root and meaning seem clear.
Is there a source for this phrase? Does it come from the Classical period, or is it a later play on Plato's phrase?