大模型在解决未解数学问题上具结构优势

LLMs have a structural advantage over humans when it comes to cracking unsolved math problems. They...

LLMs have a structural advantage over humans when it comes to cracking unsolved math problems. They’re not necessarily better at coming up w/ ideas - but they’ll grind on the details and don’t get “polluted” by bad approaches. From @OpenAI ’s @mehtaab_sawhney and @MarkSellke 👇 Your browser does not support the video tag. 🔗 View on Twitter a16z @a16z OpenAI's Mark Sellke and Mehtaab Sawhney with a16z's Lisha Li, on the state of AI and mathematics: Before OpenAI released GPT‑6 Astra last week, the model was already doing original mathematics. Recorded before the launch, this conversation tells the story of how it got there. It began with GPT‑5. Mehtaab Sawhney pasted in an Erdős problem still listed as open. Five minutes later, the model surfaced a paper that had solved it. The exercise eventually uncovered published solutions to 10 more problems thought to be open. Then Astra went further. Told to "go have fun" with a high-dimensional sphere-packing problem, it improved a bound that had stood since the 1970s. Mehtaab had spent six months on the same problem in graduate school and made "absolutely zero progress." Another Astra result established that non-sofic groups exist with a roughly 15-page proof. A related human breakthrough took 250 pages and machinery from quantum complexity theory. OpenAI’s Mark Sellke and Mehtaab Sawhney join a16z’s Lisha Li on why wrong ideas pollute a human’s context window, why polished papers hide how mathematics is actually made, why a breakthrough can stop one prompt early, and what math rewards once proving stops being the bottleneck. 00:00 Intro 02:44 Cracking an Erdős problem in 5 minutes 06:20 Why a human quits and a model doesn't 08:50 Wrong ideas pollute your context window 11:45 Why math papers are bad training data 16:20 Nobody knows how to stack spheres in high dimensions 18:28 The orange-stacking proof 21:04 The 1970s Russian paper nobody could beat 24:14 The function that won a Fields Medal 27:09 How Astra beat the sphere-stacking record 29:20 Why error correction is sphere packing in disguise 35:15 The breakthrough Astra almost didn't bother with 39:22 Solving harder problems means it has better taste 41:00 One model for taste, one for the grind 44:40 Astra found an infinite group no finite one can imitate 52:00 250 pages of quantum complexity, or 15 of group theory 56:18 Only humans write 200-page proofs 1:00:38 What changes when proving stops being the bottleneck 1:02:44 The problems AI may never solve YouTube: youtube.com/watch?v=1JvyLG… @mehtaab_sawhney @MarkSellke @OpenAI @lishali88 Your browser does not support the video tag. 🔗 View on Twitter 🔗 View Quoted Tweet 💬 3 🔄 0 ❤️ 11 👀 1573 📊 3 ⚡