On key difference here is that those mathematician then go through the process of actually proving the theorem. Just having “an intuitive understanding” is never enough, no matter how many times you have been right before.

The author here does not go through that process at all. It just feels like saying: I watch people a lot so I feel like I know what I am talking about, I feel entitled to write a piece about it. Math people have those pieces peer reviewed and experimented upon before they are actually published.