Honestly; I not sure; I a working computer scientist, not a working mathematician, and I use a proof assistant (Coq) all the time to have confidence that the proofs I write are correct (and more and more this is a requirement for publication in CS conferences). I want HoTT to succeed because it would turn some the axioms I must assume in the current Coq proof assistant into theorems, with significant implications for engineering at scale (eg, verifying an OS kernel or compiler or database). When I read the math over flow post my emotional response is gladness that I can accidentally conflate a topological space with an infinity groupoid.
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