Someone Solved One of Math's Biggest Problems — No One Can Tell If He's Right

🔴 Support the channel and get exclusive content:   / meridianlabs   On the morning of August 30, 2012, a mathematician in Kyoto uploaded four papers to his website, closed his laptop, and told no one. Just over 500 pages, claiming to solve one of the most important unsolved problems in the history of numbers. Almost 14 years later, some of the sharpest minds alive still cannot agree on whether it is a work of genius or the most elaborate mistake in modern mathematics, and there is no procedure left that can settle it. This is the story of the one thing mathematics was never supposed to be able to produce: a proof that may be complete and correct and still cannot be checked. From the abc conjecture and its deceptively simple statement to the alien machinery of inter-universal Teichmüller theory, from the failed workshops in Oxford to the week Peter Scholze and Jakob Stix spent across a table from Mochizuki in Kyoto, from a proof published in the author's own journal to a million-dollar prize nobody has claimed, we follow a single question to its most unsettling conclusion. That the certainty you feel about mathematics, the one kind of truth that was supposed to be beyond argument, was never bedrock at all. It was borrowed trust. And it holds right up until the moment it doesn't. 0:00 Intro 2:18 The Silent Upload 10:40 The Master Key 19:05 One of the Brighter Ones 27:30 A Paper from Outer Space 36:15 The Cloud of Fog 44:50 A Week in Kyoto 56:20 A Theorem in One City 1:06:10 Awarding Themselves the Prize 1:15:00 What a Proof Actually Is 1:26:30 The Machine Locked Out 1:37:20 Borrowed Certainty 1:47:40 Still Waiting Grounded in primary sources, including: Shinichi Mochizuki, "Inter-universal Teichmüller Theory I–IV" (2012; published in Publications of the RIMS, 2021) Peter Scholze and Jakob Stix, "Why abc is Still a Conjecture" (2018) Brian Conrad, notes and report on the Oxford IUT workshop (2015) Joseph Oesterlé and David Masser, the original formulation of the abc conjecture (1985), following Lucien Szpiro Go Yamashita, "A Proof of the abc Conjecture After Mochizuki" (2017) Ivan Fesenko, survey papers and reports on inter-universal Teichmüller theory Jordan Ellenberg, commentary describing the work "as if from the future, or from outer space" Frank Calegari, "The ABC conjecture has (still) not been proved" (2017–2020) Erica Klarreich, "Titans of Mathematics Clash Over Epic Proof of ABC Conjecture," Quanta Magazine (2018) Davide Castelvecchi, Nature reporting on inter-universal Teichmüller theory (2015, 2016, 2021) Andrew Wiles, "Modular Elliptic Curves and Fermat's Last Theorem" (1995) Thomas Hales et al., the Flyspeck project and the formal verification of the Kepler conjecture (2014–2017) Kirti Joshi, preprints on arithmetic Teichmüller theory (2021–2024) Peter Woit, "Not Even Wrong" coverage of the proof and the prizes #abcConjecture #Mochizuki #InterUniversalTeichmullerTheory #IUT #NumberTheory #Mathematics #MathDocumentary #PeterScholze #MathProof #FermatsLastTheorem #PureMathematics #Kyoto #RIMS #UnsolvedProblems #MathHistory #PhilosophyOfMathematics #FoundationsOfMathematics #ScienceDocumentary #Documentary #MathMystery #Grothendieck #AndrewWiles #FieldsMedal #FormalVerification #AnabelianGeometry