“It’s a fun thing and it’s certainly a challenge.” Ryan’s theorem has been a challenge for him. He completed a proof last summer, but Mr. Nowosielski discovered errors in it.

Using a recently developed Perron-type integration theory, we prove a new form of Green's theorem in the plane, which holds for any rectifiable, closed, continuous curve under very general assumptions ...

The Enormous Theorem's proof may be beyond the scope of most mathematicians—to say nothing of curious amateurs—but its organizing principle provides a valuable tool for the future.