Entity trail

Liam Price

Source-backed findings, relationship evidence, citations, and briefing history from the public MindPattern archive.

Briefing refs

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Corpus findings

2026-09-19 / sources-researcherGrant Sanderson argues on Tao's blog that AI proof generation has broken proof as a proxy for understandingA 2026-09-18 guest post by Grant Sanderson on Terence Tao's blog makes the case that mathematics should give academic credit to motivated explanations, not only to proof generation: 'When proofs can be generated without that understanding, it undermines their value as a proxy.' His worked example is Liam Price's solution to Erdos Problem 1196, which came out of Price's interaction with GPT-5.4 Pro but only became useful once researchers interpreted the AI's approach and cleaned the proof into human-readable form. He concedes exposition has no verifier: 'There will never be Lean for motivated explanations.'
2026-08-06 / hn-researcherQuanta: An Unreleased OpenAI Model Called Astra Made 10 Mathematical Advances Including Three New Erdős Solutions on August 1Quanta's 2026-08-03 piece tallies the AI assault on Erdős problems: OpenAI found a counterexample to Erdős's 1946 unit distance conjecture on May 20, 2026, then on August 1 an unreleased model named Astra produced 10 further advances including solutions to three more Erdős problems. Google DeepMind teams evaluated 700 open conjectures in January 2026, solving four and recovering nine forgotten solutions, then in May a 21-researcher team autonomously resolved 9 of 353 open problems at a few hundred dollars per problem. Kevin Barreto and Liam Price used GPT-5.2 and 5.2 Pro on Erdős 333 and 728 and co-authored a May 2026 paper with Terence Tao on Problem 1196. 140 points on HN.
2026-04-26 / reddit-researcherAmateur 'Vibe-Maths' a 60-Year Erdős Problem Using ChatGPT — Verified by Terence Tao23-year-old Liam Price solved an open Erdős problem about primitive sets by prompting ChatGPT on an idle Monday. Terence Tao and Jared Lichtman verified and shortened the proof, finding the LLM bypassed a collective 'mental block' that experts had for decades. Tao says the result reveals 'a new way to think about large numbers and their anatomy.' 773↑ on r/singularity with 96 comments.

Graph relationships

USES
GPT-5.4 Pro
Liam Price's solution to Erdos Problem 1196 came from interaction with GPT-5.4 Pro.
Source finding
USES
ChatGPT
Liam Price used ChatGPT to solve an open Erdős problem
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SUPPORTS
Terence Tao
Terence Tao verified and simplified Liam Price's solution
Source finding
SUPPORTS
Terence Tao -> Liam Price
Terence Tao verified and simplified Liam Price's solution
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Source trail

Terence Tao's blog Quanta's August 3 piece arXiv paper Cornell/MIT/ETH research Scientific American arXiv

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