mathematical-reasoning

[Top, cut off]: "@AnthropicAI please sponsor this man." 💬76 🔁64 ❤️1.1K 📊259K views [bookmark] [share] Nabeel S. Qureshi ✓ @nabeelqu · Jan 18 He put an Erdos Problem into GPT 5.2Pro, no special prompting, and it *thought continuously for 41 minutes and spat out a correct proof*. It's over everyone, we had a good run. [Embedded screenshot of a GPT reasoning session]: "Let $n_1<n_2<\cdots$ be an infinite sequence such that, for any choice of congruence classes $a_i \pmod{n_i}$, the set of integers not satisfying any of the congruences $a_i \pmod{n_i}$ has density $0$. Is it true that for every $\epsilon>0$ there exists some $k$ such that, for every choice of congruence classes $a_i$, the density of integers not satisfying any of the congruences $a_i \pmod{n_i}$ for $1\leq i\leq k$ is less than $\epsilon$?" ↳ Reasoned for 41m 54s "I'm parsing the problem carefully. We have an infinite sequence of moduli and residue classes, and the integers not satisfying any congruence are of density 0. This suggests that a union of these arithmetic progressions should cover almost all integers. But does it imply that a finite subcollection might already cover most of the integers for all residue choices? I need to explore if this resembles compactness or something like Borel-Cantelli. I'm considering the infinite property of moduli and how they form a "covering system," meaning they cover almost all integers no matter the residues chosen. The complement of covered integers, U(a), has zero density. Is this uniform across all sets of residues? I'm thinking this might relate to Dini's theorem, but could the uncovered density decrease slowly..." 281 Anonymous · Jan 16, 2026 [Open in browser] Neel Somani ✓ @neelsomani · Jan 10 [Embedded image: math proof example with equations, "Example (a=2). Here c=49, and the identity becomes..."] Weekend win: The proof I submitted for Erdos Problem #397 was accepted by Terence Tao. The proof was generated by GPT 5.... 💬47 🔁103 ❤️1.4K 📊215K Techartist ✓ @techartist_ · 23h Interactive quantum neural network built with Three.js and GLSL shaders, wrapped in a glassmorphic UI. Click or drag sends pulses while f[orm, colors, and density update in real time through...] [cut off]