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GPT-6 Astra improved a decades-old sphere-packing bound, a16z says

a16z contrasts Astra’s claimed original math results with an earlier GPT-5 exercise that uncovered published solutions to problems still thought to be open.

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1 Source, 23d ago, first seen 23d ago

TLDR

a16z says GPT-6 Astra improved a bound on packing spheres in high-dimensional spaces that had stood since the 1970s. According to a16z, OpenAI’s Mehtaab Sawhney had spent six months on the same problem in graduate school with “absolutely zero progress.”

The account distinguishes that claimed advance from finding existing answers. a16z says Sawhney gave GPT-5 an Erdős problem still listed as open; five minutes later, it surfaced a paper that had solved it. That exercise eventually uncovered published solutions to 10 more problems thought to be open.

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1 Source, first seen 23d ago

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Combined views

94.4K

1 Source, first seen 23d ago

122 likes15 comments72 saves17 reposts

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@a16zOpenAI'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: https://www.youtube.com/watch?v=1JvyLGd2Sfs @mehtaab_sawhney @MarkSellke @OpenAI @lishali8823d
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    1 Source

    @a16zOpenAI'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: https://www.youtube.com/watch?v=1JvyLGd2Sfs @mehtaab_sawhney @MarkSellke @OpenAI @lishali8823d
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