[FOM] foundational exposition

[Harvey Friedman]

This is a copy of a letter to Pen Maddy in another forum, and it concerns
foundational exposition. Do not necessarily expect a response here from Pen.

Harvey Friedman

Dear Pen,

I am certainly interested to see the papers coming out of this workshop
https://www.youtube.com/playlist?list=PLQw7KTnzkpXfGo93vo3kQk7_jA_HgwbnC.
Of course you are looking for something going well beyond ordinary
observations, and perhaps you are not there yet.

As I discussed before, my main excitement in and around this topic (depth)
is what I call foundational exposition. What I have in mind is powerful
organizational principles that guide the presentation of mathematical
developments. This would definitely generate new research programs of
general interest, and also provide new modes of evaluation of mathematical
developments - putting them into context according to the powerful
organizational principles.

According to this way of thinking, the total emphasis is on intellectual
content of general intellectual interest. Proofs are viewed as a tool for
establishing correctness. Of course, a really "good" (deep is a little
different, with overlap) proof will help with finding new content.

I am not accepting mathematics as it is presented and published. Rather as
something that has a great deal of actual and potential intellectual
content, but where that content needs to be reorganized and reworked
according to powerful organizational principles. With such an ongoing
reorganization, the subject would be a lot more accessible and usable by
outsiders than it is now - and even by mathematicians from different areas.

Of course, I have done almost nothing about this despite babbling on about
it for almost 50 years. I do use some organizational principles at an
informal level to guide my choice of research in f.o.m. and some other
areas. Even more recently in analysis with some joint work. But this is
quite far from really doing anything about it in any generality.
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