R Hansen says: >It is the process that takes place after the rules have been set. The rules of chess are quite finite and simple but figuring out and organizing the resultant complexity is abstraction.
Perhaps reading the dictionary definition or even the Wikipedia article of abstract and abstraction would help clue you in on how the rest of the English speaking public uses the term.
R Hansen asks: >I am not sure what you mean by "gold standard" with regard to proofs.
I simply meant that logic based "proof" has become the sine qua non of "real math" over the last 150 years or so. I believe (probably with Kirby, perhaps) that that may change over the next 150 years to where exploratory, computation based math becomes just as important, or more so.
The point of that paragraph (which I wrote in a hurry) was that from a certain view, or sense of the term, Hilbert's program was a call to make math *less* abstract, by grounding in something (in a sense) more concrete.