Really? This seems like the exact sort of thing GPT-3 would be very bad at. The statements aren't the product of an internally consistent logical model, they are statistically plausible word sequences learned in a really clever way from a huge corpus of text.

That said, before dismissing it sight unseen there are effective and quick ways to test its powers with mathematics. You could prime an instance with the axioms defining a group, or a topology, and ask it to produce proofs of varying difficulty from intro abstract algebra or topology textbooks. Whatever the answer it would make an interesting blog post. What happens when you ask it to generate repeated outputs for the same prompt? What happens if you ask it to prove an untrue proposition?