My argument is about the rigor of theorems. ZFC may be incomplete, but every existing theorem that builds up the entirety of modern mathematics is (in theory, a

My argument is about the rigor of theorems. ZFC may be incomplete, but every existing theorem that builds up the entirety of modern mathematics is (in theory, admittedly) built upon a rigorous chain of truth, traced back to those axioms and definitions. Most mathematicians who don't study metamathematics or philosophy of math have no reason to ever think about formalism or computability. An aside for people who think Godel's incompleteness theorem somehow invalidates math: don't forget about the much lesser known Godel's completeness theorem, which states that if something is true in every model