{"type":"post","id":"google-deepmind-s-alphaproof-nexus-solved-9-open-07c5ac","slug":"google-deepmind-s-alphaproof-nexus-solved-9-open-07c5ac","title":"Google DeepMind's AlphaProof Nexus solved 9 open Erdős problems , puzzles left by the famous mathematician Paul Erdős.","description":"The thesis is: formal proof search gains research value when generated candidates are coupled to machine-checkable proof obligations.","retrieval_nugget":"The thesis is: formal proof search gains research value when generated candidates are coupled to machine-checkable proof obligations.","published_at":"2026-10-13","updated_at":"2026-10-13","record_date":"2026-10-13","date_kind":"published_at","topics":["google"],"source_urls":["https://www.science.org/doi/10.1126/science.aej2213"],"schema_version":"newruntime-agent-readable-v0.2","stable_id":"post:google-deepmind-s-alphaproof-nexus-solved-9-open-07c5ac","status":"published","visuals":[],"editorial_provenance":{"schema_version":"newruntime-editorial-copy-v1","content_status":"source_grounded_final","final_copy_sha256":"sha256:05231ddc5bae27d05315d91279ed9c1a9622f56f4eb4cf03bdbdcc74de321023","reviewed_at":"2026-10-13T11:03:37.609Z","source_evidence_count":1,"verified_claim_count":3,"site_analysis_schema_version":"newruntime-site-analysis-v1","site_object_kind":"field_note","observed_fact_count":3,"implication_count":2,"watch_condition_count":1,"related_record_count":0},"analysis":{"schema_version":"newruntime-site-analysis-v1","object_kind":"field_note","thesis":"formal proof search gains research value when generated candidates are coupled to machine-checkable proof obligations.","observed_facts":[{"text":"The paper reports that AlphaProof Nexus resolved nine of 353 open Erdős problems, including two that had been open for 56 years.","source_urls":["https://www.science.org/doi/10.1126/science.aej2213"]},{"text":"The paper reports 44 proofs among 492 open conjectures from the Online Encyclopedia of Integer Sequences.","source_urls":["https://www.science.org/doi/10.1126/science.aej2213"]},{"text":"The system alternates LLM-generated proof attempts with Lean-based formal verification; the authors say a basic alternating agent replicated the Erdős successes.","source_urls":["https://www.science.org/doi/10.1126/science.aej2213"]}],"mechanism":"An LLM proposes proof material, and Lean checks formal proof steps as part of an iterative search loop.","why_now":"the paper supplies evidence beyond contest-style demonstrations: it describes deployment against open research problems across several mathematical areas.","implications":["research agents should be assessed through inspectable artifacts and verification procedures, not only claimed answers or benchmark scores.","Formal verification is presented as part of the search process rather than a post hoc check."],"evidence_boundary":"the source reports results on selected problems and does not establish general autonomous mathematical competence.","watch_conditions":["whether independent researchers can inspect, rerun, and extend the formal proof artifacts across the reported problem set."],"related_records":[],"new_branch_reason":"No prior New Runtime record is supplied; this starts a distinct record on formal proof-search agents producing research-level results with machine-checkable verification."},"editor":{"role":"editor","name":"Andrey Reshetnikov","profile":"https://newruntime.com/owner-profile.md","profile_json":"https://newruntime.com/owner-profile.json","same_as":["https://www.linkedin.com/in/reshetnikov1/","https://t.me/lapetuse"]},"routes":{"html":"https://newruntime.com/posts/google-deepmind-s-alphaproof-nexus-solved-9-open-07c5ac/","markdown":"https://newruntime.com/posts/google-deepmind-s-alphaproof-nexus-solved-9-open-07c5ac.md","json":"https://newruntime.com/posts/google-deepmind-s-alphaproof-nexus-solved-9-open-07c5ac.json"},"next_reads":[{"type":"topic","path":"/topics/google/","url":"https://newruntime.com/topics/google/","title":"Google","reason":"Explore the google topic hub.","media_type":"text/html","markdown_url":"https://newruntime.com/topics/google.md","json_url":"https://newruntime.com/topics/google.json"},{"type":"collection","path":"/posts/","url":"https://newruntime.com/posts/","title":"Field Notes","reason":"Open the latest editorial analysis.","media_type":"text/html","json_url":"https://newruntime.com/posts.json"},{"type":"collection","path":"/source-ledger.json","url":"https://newruntime.com/source-ledger.json","title":"Source Ledger","reason":"Inspect the public source evidence graph.","media_type":"application/json"}]}