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AI 'Proves' Aaronson-Ambainis Conjecture in 3 Days—Experts Push Back

PSI claimed its research system proved the 18-year-old Aaronson-Ambainis conjecture in about three days, drawing wide attention. Experts soon pushed back, saying the claim involves misreadings, leaving the result unverified.

2026-11-06 ~ 2026-11-08 · 2 episodes · 16 posts

Episode 1 · PSI's AI System Proves 18-Year-Open Aaronson-Ambainis Conjecture in Three Days (2026-11-06, 14 posts)

Physical Superintelligence (PSI) announced that its in-house research system produced a complete proof of the Aaronson-Ambainis conjecture—open since 2008—in a single run, verified step by step with the Lean proof assistant. According to multiple secondhand accounts, the system runs on an unreleased Anthropic model, and the entire proof took only 3 days. This marks a core advance in quantum computing and complexity theory, and a landmark case of AI-assisted research.

Confirmed

  • PSI (Physical Superintelligence PBC) officially announced that its system proved the Aaronson-Ambainis conjecture, one of the most central open problems in quantum complexity theory, with major implications for quantum speedups
  • The proof was verified step by step with the Lean proof assistant
  • @Hesamation relayed David Turturean's account that the system is a research system he built for Paul Christiano's team (psipbc)

Consistent across sources but secondhand

  • The underlying model is an unreleased Anthropic model; @1411337, @Pyros-SD-Models, @Hesamation, and @rickasaurus all relayed this, while PSI's official announcement (m1) did not directly mention the model's origin
  • The proof took 3 days, per multiple secondhand accounts

Why it matters

  • Open since 2008, the Aaronson-Ambainis conjecture bears on when quantum computers can achieve speedups over classical ones, and is a structural question in quantum complexity theory
  • If the Lean verification holds, this is a rare instance of an AI system independently completing a top-tier mathematical proof, demonstrating frontier models' capability on long-horizon research tasks
  • @rickasaurus used this to argue that such models should be made available to researchers beyond Anthropic, sparking debate over access to frontier models

Not yet confirmed

  • The specific identity and version of the Anthropic model used remain undisclosed
  • Full proof details and verification materials await broader independent review

Episode 2 · Aaronson-Ambainis Conjecture Reportedly Proved Amid Misreading Backlash (2026-11-07, 2 posts)

The Aaronson-Ambainis conjecture, linking polynomial quantum speedups to a conjecture about polynomials, has reportedly been proved. Researchers are pushing back against widespread misreadings, clarifying that it does not rule out super-polynomial speedups like Shor's algorithm.