Tilting at Mathematical Windmills?
Estimated Reading Time: 5 minutes
TL;DR
We discuss continued developments in the long-running controversy surrounding Mochizuki’s claimed proof of the ABC conjecture and also cover some interesting papers from around the web.
Joshi’s Quest Continued
The controversy around Shinichi Mochizuki’s claimed proof of the ABC conjecture, initially released in 2012, has been continuing for over a decade. Mochizuki’s original claimed proof used non-standard mathematical language, making it difficult for other mathematicians to understand or even critique the work. Following a paper released in 2018 by the mathematicians Scholze and Stix which highlighted a potentially serious issue in Mochizuki’s work, most of the mathematical community has concluded that Mochizuki’s original proof is flawed.
However, a small community of mathematicians persists in believing in Mochizuki’s work. The most interesting of this group is Kirti Joshi who has been working through a multi-year journey to translate Mochizuki’s insights into standard mathematical language and fix holes in the original claimed proof. Joshi has now completed a revision of a series of papers that claim to address the issues in Mochizuki’s original proof and to disprove Scholze’s and Stix’s critique. Joshi’s account of the saga can be found at https://math.arizona.edu/~kirti/Final-Mochizuki-Scholze-Stix-Controversy.pdf and his claimed proof of the ABC conjecture can be found at https://arxiv.org/pdf/2403.10430.
I’ve read through several of the papers involved, but I am not an expert at the relevant mathematics so it isn’t possible for me to judge the arguments on their technical merits. Joshi says he is working on a detailed worked example of his theory on a simple system which may help clarify the situation for other mathematicians. An interesting project may be to attempt converting Joshi’s claimed proof into a proof engine like Lean4 to see if it is possible to independently verify, but such a project would likely be a mammoth undertaking in its own right.
Interesting Links from Around the Web
https://www.nature.com/articles/s41587-025-02645-5: A very nice brief spotlight article about cancer immunotherapies.
https://www.nature.com/articles/s41587-024-02446-2: CAR-T therapies are expanding to solid tumors through the use of bispecific CAR-Ts and other strategies.
https://www.nature.com/articles/d41586-025-01269-8: Researchers have pinpointed the genetic architecture that underlies four genes originally characterized by Mendel.
https://physics.aps.org/articles/v18/s55: Interesting theoretical modeling of self-knotting polymers.
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.161901: Progress in QCD calculations.
https://www.nature.com/articles/s41563-025-02212-y: Very interesting work using biopolymer scaffolds for stem cells to enhance muscle regeneration. Currently only tested in mice, but could one day be very interesting for human patients.
https://www.nature.com/articles/s42256-025-01019-5: A transformer-based approach to peptide sequencing through mass-spec.
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Credits
Author: Bharath Ramsundar, Ph.D.
Editor: Sandya Subramanian, Ph.D.