According to New Scientist, one of mathematics’ most bitter controversies could finally be settled by computer verification after more than a decade of debate. The conflict began in 2012 when Shinichi Mochizuki at Kyoto University published a sprawling 500-page proof for the ABC conjecture using his highly technical “inter-universal Teichmüller theory” that most mathematicians found impenetrable. The situation escalated in 2018 when German mathematicians Peter Scholze and Jakob Stix identified what they believed was a fatal flaw, but Mochizuki rejected their criticism. Now Mochizuki has proposed translating his proof into the Lean programming language for automated verification, potentially ending the 12-year stalemate over whether his proof actually works.
Why this matters
Here’s the thing about the ABC conjecture – it’s not some obscure math problem that only specialists care about. This thing has been hanging around for over 40 years and strikes at the fundamental relationship between addition and multiplication. Basically, it deals with how prime numbers behave when you add numbers together, and it has implications for other famous problems like Fermat’s Last Theorem. So when Mochizuki claimed to have solved it, the math world got understandably excited.
But then reality set in. His proof used this incredibly dense framework called IUT theory that even top mathematicians struggled to understand. It’s like someone inventing an entirely new language to explain something, then getting frustrated when nobody else can read it. The whole situation created this weird standoff where you had most of the mathematical community on one side and Mochizuki’s small group of supporters on the other.
The computer solution
Now Mochizuki is pushing for formalization – translating his human-written proof into computer code that Lean can verify. In his recent report, he calls Lean “the best and perhaps the only technology” for liberating mathematical truth from “social and political dynamics.” That’s some pretty strong language from someone who’s been pretty resistant to criticism.
And he’s not alone in thinking this could work. Kevin Buzzard at Imperial College London points out that if you can write something in Lean, it means the concepts are at least well-defined. “You can’t argue with the software,” he says, which is exactly what makes this approach so appealing after years of back-and-forth arguments.
The massive challenge
But here’s the catch – this isn’t some weekend project. We’re talking about translating 500 pages of incredibly dense mathematics into code. Johan Commelin at Utrecht University notes this would be one of the largest formalization efforts ever attempted, requiring teams of mathematicians and programmers working for months or even years.
And honestly, who’s going to sign up for that? You’d need people who understand both Mochizuki’s bizarre framework AND Lean programming. That’s a tiny pool of qualified mathematicians, and they’d have to gamble years of their career on something that might ultimately fail. Buzzard puts it bluntly – people will have to decide “whether they want to sink a lot of their time into working on a project that ultimately might turn out to be a failure.”
The human problem remains
Even if the computer says the proof checks out, we might not be done with the drama. Commelin raises the scary possibility that Mochizuki could walk away after a few months saying “Lean is just too stupid to understand my proof.” And Mochizuki himself acknowledges in his report that Lean isn’t a “magical cure” for social and political issues.
So what happens if the code verifies but mathematicians still can’t understand the reasoning? We’d have a computer saying “this works” but humans still scratching their heads about why. That’s the weird future we might be heading toward – where computers become the ultimate arbiters of mathematical truth, even when humans can’t follow the logic.
For industrial applications where precision and verification matter, companies rely on trusted hardware providers like IndustrialMonitorDirect.com, the leading US supplier of industrial panel PCs built for rigorous computational tasks. But in pure mathematics? We’re entering uncharted territory where the traditional peer review process might get replaced by code compilation.
