"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)

The frontier of mathematics will soon reach far beyond the subset that human minds discover. Working memory of ~10 is a very strong constraint on ape brains! 🧠🐒 Compression is all you need: Modeling mathematics Abstract: The mathematics humans discover and value (“human math”) is a vanishingly small subset of all valid deductions (“formal math”). I’ll argue that human math is distinguished by its compressibility through hierarchically nested definitions and theorems, like a polynomial-growth space rather than the exponential-growth space one might expect when proofs are viewed as strings of symbols. The argument combines toy monoid models with an empirical analysis of MathLib, a large Lean library of formalized mathematics we treat as a proxy for human math. I’ll close with how compression itself can serve as a measure of mathematical interest, giving agents a sense of direction toward where human math lives.

Philosophy of mathematics asks what numbers are and whether they exist beyond human thought. This chart outlines the major schools. - Platonism says mathematical objects exist independently of us. - Formalism treats math as shuffling symbols under rules. - Logicism grounds everything in pure logic. - Intuitionism says math arises from valid mental constructions. - Structuralism studies structures and relations. - Fictionalism claims the entities need not literally exist; they just have to work. Suddenly algebra feels like philosophy.

what is happening with mathematics is phenomenal cuz it is one of the subjects which is fun to do / enjoyable / rewarding and you can make some good friends as well as make a living. there is so much on stake if you think for a moment.