TITLE: Philosophy behind Mochizuki's work on the ABC conjecture
QUESTION [290 upvotes]: Mochizuki has recently announced a proof of the ABC conjecture. It is far too early to judge its correctness, but it builds on many years of work by him. Can someone briefly explain the philosophy behind his work and comment on why it might be expected to shed light on questions like the ABC conjecture?

REPLY [7 votes]: For the sake of completeness, let me add the references of the published version in Publ. RIMS that appeared earlier in March this year (should be rather a comment, but the references are too long for that):
Mochizuki, Shinichi, Inter-universal Teichmüller theory. I: Construction of Hodge theaters, Publ. Res. Inst. Math. Sci. 57, No. 1-2, 3-207 (2021). ZBL1465.14002.
Mochizuki, Shinichi, Inter-universal Teichmüller theory. II: Hodge-Arakelov-theoretic evaluation, Publ. Res. Inst. Math. Sci. 57, No. 1-2, 209-401 (2021). ZBL1465.14003.
Mochizuki, Shinichi, Inter-universal Teichmüller theory. III: Canonical splittings of the log-theta-lattice, Publ. Res. Inst. Math. Sci. 57, No. 1-2, 403-626 (2021). ZBL1465.14004.
Mochizuki, Shinichi, Inter-universal Teichmüller theory. IV: Log-volume computations and set-theoretic foundations, Publ. Res. Inst. Math. Sci. 57, No. 1-2, 627-723 (2021). ZBL1465.14005.
(Peter Scholze indicates in his review that the versions do not differ with respect to the issues Stix and he raised in 2018).