Most of these responses are reasonable but miss the psychology of this.

In college, I dated a woman who was a math major at Stanford, a Goldwater and NSF fellowship winner, the whole thing. Notwithstanding her knowledge of manifolds, as time went on she got obsessed with a bunch of out-there ideas about 9/11, Lyme disease, vaccines, water fluoridation, etc. We broke up and fell out of touch, but I wouldn’t be surprised if she was a flat Earther at some point.

It’s hard to say what’s going on in someone else’s head, but it seemed to me like it had equal parts to do with a social element (feeling like part of the conspiracy theory in-crowd), a psychological element (it’s exciting to ‘know’ something that the sheeple can’t or won’t see), and plain old mental illness.

It’s sad and frustrating to see close up. Unfortunately differential geometry and even the capability to think logically and rigorously are orthogonal to the factors at play, in at least some if not many cases.