Socialising proof

The following presentation will explore the social mechanisms involved in validating proofs within pure mathematics. I will use the high profile example of Mochizuki’s Proof of the ABC conjecture to demonstrate the challenges involved in validating proofs. The acceptance of proofs depends upon their conformity to certain standards, on possessing relationships to existing bodies of knowledge, as well as being certified by reputable members of the community of practice. Proofs thus need to be socialised before they can be fully accepted. I shall demonstrate the socialisation processes Mochizuki’s proof underwent, and explore the continuing challenges the proof encounters in its bid to gain legitimacy within the mathematical community.