There is no such thing as "public reason". Reason is always private. What there is is "public form".

I think that's the misunderstanding that pisses me off reading professors of philosophy. What's fantasized as public reason is no more or less than civility: an element of trust among compatriots, and between collaborators and opponents in a public game.
[Prosecutors and defense attorneys.]

Expertise is not public reason. Mathematics is not public reason.