"Mathematics in the Age of AI" In an age of abundant AI-generated proofs, human understanding may become more valuable than proof generation itself. This new paper from Terence Tao argues that AI could make solving hard math problems much cheaper and faster, but at the same time, creates a new problem. If AI can generate thousands of correct proofs, mathematicians can’t possibly read, understand, verify, and teach all of them. So the scarce resource in mathematics shifts from finding proofs to making sense of them. The important work becomes deciding which results matter, explaining the key ideas, connecting them to existing theory, and turning them into knowledge other mathematicians can actually use.

Mathematics is the canary in the coal mine of any education system: It's a delicate pyramid that crumbles if the base is not strong. Using IMO results, here are the countries that improved most from 2006 to 2026 and those that declined the most. Using rank percentile within each year’s field: Most improved 🇸🇦 Saudi Arabia: 2.2% → 69.8% (+67.6pp) 🇲🇾 Malaysia: 22.5% → 83.6% (+61.1pp) 🇰🇬 Kyrgyzstan: 14.6% → 70.7% (+56.1pp) 🇧🇩 Bangladesh: 11.2% → 67.2% (+56.0pp) 🇮🇳 India: 61.8% → 94.8% (+33.0pp) Biggest declines 🇲🇩 Moldova: 91.0% → 55.2% (−35.8pp) 🇮🇹 Italy: 87.6% → 68.1% (−19.5pp) 🇫🇮 Finland: 57.3% → 39.7% (−17.6pp) 🇩🇪 Germany: 96.6% → 83.6% (−13.0pp) 🇹🇼 Taiwan: 89.9% → 80.2% (−9.7pp)

Part of the Contemporary Mathematics series, Lectures on Tight Closure and Its Applications, this volume consists of edited lecture notes from the online International Graduate course on Tight Closure and Its Applications from the ICTP and School on Commutative Algebra and Algebraic Geometry in Prime Characteristics. The lecture notes also come with exercises and solutions. Access via your institution: Buy the volume: Don’t have access? Ask your library to contact cust-serv@ams.org to subscribe!