ABC Conjecture Proof Formalization Stuck on 'The Wall'
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- LANA project at Japan's ZEN Mathematics Center published an interim report saying members have 'yet to land on a conclusive decision' on whether Inter-universal Teichmüller theory holds up, and were 'unable to reach complete consensus on this point.'
- Shinichi Mochizuki at Kyoto University published his 500-page ABC conjecture proof in 2012 using an entirely new field called Inter-universal Teichmüller (IUT) theory that few mathematicians have been able to verify.
- Peter Scholze at the University of Bonn and Jakob Stix at Goethe University Frankfurt identified a flaw in IUT theory in 2018, which the LANA report calls 'the wall' and says has rendered IUT 'impervious to formalisation' so far.
- Abhishek Saha at Queen Mary University of London says the LANA report is 'fully consistent' with the majority view that 'there is a serious gap' in IUT theory, and that failure to formalize it 'is what we would expect if this big theory had some serious gaps.'
- Chris Bowman-Scargill at the University of York warns that 'a large amount of maths has already been built on top of IUT theory, which would be in jeopardy if it is proved incorrect' — a view most mathematicians hold.
- Ivan Fesenko at Westlake University in China defends the theory, saying 'people followed [Scholze's] opinion, accepting that it should be the utmost truth' but '[his] take on IUT is totally wrong.'
Why it matters: If IUT theory is ultimately rejected, the body of mathematics built atop it collapses — a concrete second-order consequence noted by Bowman-Scargill. The 13-year stalemate over Mochizuki's proof, now stuck on the Scholze-Stix 'wall,' means the ABC conjecture remains unresolved despite two separate formalization projects running in parallel.
