To claim that Chomsky's knowledge is "superficial" and not in line with the hard/quantitative sciences would suggest to me that you are perhaps not well aware of his revolutionary contributions to the field of linguistics, which is effectively a philosophical and mathematical approach to understanding language (and thus the mind's structure) itself.

His academic work is foundational to an entire branch of anthropology, applied computer science and AI and is woven throughout our modern society in very technical ways that many specialized mathematicians or physicists would only dream of.

You may not like his political philosophies, but he's proven to be worth paying attention to just as you might listen to Einstein's opinions about politics.

As others have said, his political influence in American these days is primarily among left-wing academics, socialist/anarchist thinkers.