Chaitin is a serious scientist/mathematician who knows what he is talking about, and there is plenty of discussion to other works and references in his own rese

Chaitin is a serious scientist/mathematician who knows what he is talking about, and there is plenty of discussion to other works and references in his own research. And his published work on algorithmic information theory is quite extensive. He is using the notion of randomness as "uncompressibility", which is a very mainstream view (perhaps better known as Kolmogorov complexity, who is much more well known than Chaitin). Just because you are not convinced doesn't mean he's a crank, it just means your background in this area is limited. I would also note that you're reading a popular text, one that is purposefully designed to reach a mass audience, so the lack of formalism is likewise intentional, and not a reflection of crankism. You're welcome to look up his research papers if you'd like to see the difference.