Thread by Terence Tao (@tao), October 6, 2026 (edited October 6, 2026).
(1/4) In traditional mathematics (“Math 1.0”), a breakthrough proof of a long-standing open conjecture generates a large amount of subsequent activity and excitement in the field. The authors of the proof are invited to give many talks, and meet with other experts in the area. Workshops are set up to discuss the proof, as well as other recent developments. As a result, new connections and collaborations are formed, followup problems are shared, and other mathematicians (both junior and senior) are attracted to the field (including in some cases the authors themselves, if they initially came from a different subject). As a result of all this activity, the proofs naturally become digested, streamlined, placed in context with other results in the field, and ultimately become part of the textbooks and lecture notes for the next generation of mathematicians in the field.
(2/4) Use of AI tools, when done responsibly, can support not just the initial generation of a solution, but all of the valuable followup activities that traditionally flow out of that solution. But at the current time, the opposite is often occurring: problems are being solved autonomously by AI prompters who have no interest in the broader field itself once their initial target is “solved”, and do not understand the AI output well enough to answer questions on the result, give talks, or otherwise interact with the rest of the field. Many fewer seminars, workshops, collaborations, or other activities are being generated from these results compared to traditional breakthroughs; few people are joining the community around the field as a consequence; and promising open directions are now being withheld from the public in fear that this will cause their own research to be “scooped”.
(3/4) This process cannot be easily reversed: a problem that has been “solved” cannot be somehow reverted to become “unsolved”, and even the mere knowledge that a solution exists “contaminates” efforts by both humans and AI to find alternate routes to the problem that reveal additional insights. And so solutions to open problems are now being harvested at large scale in an unsustainable fashion, leaving entire fields of mathematics much less fertile than when such problems were solved in the traditional “Math 1.0” fashion.
(4/4) “Math 1.0” placed a premium on being the first to solve an open problem, even if the solution was not initially well understood. Now that this goal has been optimized to the point of unsustainability, “Math 2.0” will need to decenter the role of raw problem solving and value mathematical progress more holistically—for instance by elevating the role of exposition, but also that of community building and opening up new directions of study. I believe that AI can contribute positively in all of these directions as well; but it will require more imagination and ambition than the “Math 1.0” mindset of simply pointing one’s favorite AI agent at some set of open problems and asking for a solution. And our community will need to explicitly re-evaluate its criteria for education, publication, and career advancement, to reflect the “Math 2.0” era.