The philosophy of mathematics[1] is a deep and interesting subject, with a long history of important contributions by people like Hilbert, Brouwer, Russel, Wittgenstein, Turing, Quine and Putnam among others. It's very hard to tell from this short piece whether the author simply subscribes to one of the famous old positions or makes any new claims, and if so, where those claims are positioned relative to all the old ones.

EDIT: A quick read of the relevant Wikipedia entry shows that Tegmark's view is basically good-old mathematical Platonism, with a radical, monistic twist.

EDIT2: A question I would pose to a mathematical Platonist monist like Tegmark would then be, what is the cardinality of the collection of universes? Brouwer could reject large infinities only because he insisted that mathematics is limited by the physical, but if the physical and the mathematical are the same, I can see no justification for rejecting a large set of universes.

[1]: https://plato.stanford.edu/entries/philosophy-mathematics/

[2]: https://en.wikipedia.org/wiki/Mathematical_universe_hypothes...