Mathematical papers are seldom written fully formally. This is in no small part because the most commonly accepted foundation of mathematics (ZFC atop first-order logic) was only designed to make formalization possible “in principle”. It's precisely because of this that researchers in formal verification are looking for systems that make formalization actually possible in practice, such as various flavors of type theory.
Formal here is not "Mathy and jargony and with a lot of greek symbols" as is understood normally.