"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)

"Mathematics is a continuing creative endeavor with aesthetic values similar to those found in art and music. In particular, mathematics is a living subject, not one that has long since been embalmed in textbooks." - From 1955 College Board Mathematics Commission's report.

What makes mathematics so powerful? Every law in nature seems to be mathematically consistent which makes it the primary language of physics. Why does it work? Perhaps nobody knows. But without its backing your theory is just a simple imagination.

From the Contemporary Mathematics series: Symmetries and Integrability of Difference Equations, this volume contains a collection of six lecture notes from the Abecedarian School of SIDE15 (ASIDE15-Milano-Italy), held before the 15th International Conference on Symmetries and Integrability of Difference Equations. This book introduces contemporary research topics in discrete integrable systems, including applications of classical algebraic geometry, classical and modified Yang-Baxter equations, r-matrices, Fermi-Pasta-Ulam-Tsingou-type models, Hamiltonian approaches to differential-difference equations, and orthogonal polynomials with connections to discrete Painlevé equations. Access via your institution: Buy the volume: Don’t have access? Ask your library to contact cust-serv@ams.org to subscribe!