Similar experience, I asked it to prove the square root of 2 is irrational. It seemed to try to pretend to do the standard proof using even numbers, but then randomly made a weird leap and declared victory:

"we get 2k^2 = q^2. Since q^2 is even, this means that q must be even as well. But this contradicts the original assumption that q is not equal to 0, so we must conclude that √2 is irrational"

The language of these fake proofs tends to resemble real math well enough that I hope it doesn't fool people.

In areas other than math I've been very impressed however with it overall. While human experts are obviously still better in terms of depth, accuracy and creativity, it's already pretty good. Whereas in terms of breadth, no human could compare. Given the rate of improvements, these things seem destined to launch a new era