It used to be thought that studying certain subjects ( like Latin) made you better at learning others, or smarter generally – “They supple the mind, sir; they render it pliant and receptive.” This doesn’t appear to be the case, certainly not for Latin – although it seems to me that math can help you understand other subjects?
A different question: to what extent does being (some flavor of) crazy, or crazy about one subject, or being really painfully wrong about some subject, predict how likely you are to be wrong on other things? We know that someone can be strange, downright crazy, or utterly unsound on some topic and still do good mathematics… but that is not the same as saying that there is no statistical tendency for people on crazy-train A to be more likely to be wrong about subject B. What do the data suggest?
I’m mostly talking about cases where A and B have no obvious relationship – we know that a dedicated Marxist is more likely to have wrong notions about genetics, since heritability offends him ( probably gravity and levity do as well). Probably also worth considering whether the individual in question achieved craziness on his own or was immersed in it from birth.
Lastly, sometimes that correlation must be negative: certain flavors of crazy likely make you less likely to be wrong about certain other things.