[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"branding":3,"analytics":7,"article-a-35-year-math-problem-falls-with-an-ais-help":10,"sections":41},{"siteName":4,"siteTagline":5,"publisherName":4,"contactEmail":6},"The Revision","Tech news, decoded.","editor@therevision.news",{"gaMeasurementId":8,"adsenseClientId":9},"G-ZW2MV82GYR","ca-pub-8533917693782264",{"article":11},{"id":12,"slug":13,"title":14,"dek":15,"body_md":16,"tags_json":17,"published_at":18,"created_at":19,"updated_at":20,"status":21,"review_note":22,"review_notes":23,"image_url":22,"persona_id":22,"persona_name":22,"section":30,"tags":31,"sources":36,"feedback":40,"feedback_at":22,"cost_usd":40,"total_tokens":40},3858,"a-35-year-math-problem-falls-with-an-ais-help","A 35-Year Math Problem Falls, With an AI's Help","Researchers used ChatGPT to help crack a stochastic-process uniqueness problem open for more than 35 years, then verified every step themselves.","A math problem open for more than 35 years now has a proof, and a chatbot helped find it.\n\nResearchers posted a preprint resolving what's called the finite-signed uniqueness problem for the basic adjoint relationship (BAR) conjecture. The conjecture asks whether a specific mathematical relationship uniquely pins down the stationary distribution of a reflected diffusion, a model class used in queueing network analysis. The result applies within stable Harrison-Reiman data where the reflection matrix satisfies a nonsingular M-matrix condition, a setting the authors show is structurally necessary. The proof was discovered with ChatGPT's assistance, the paper states, and then independently verified by the authors.\n\nThe result matters because it closes both sides of a question posed by Dai and Dieker: uniqueness holds in the M-matrix class, but not in the broader completely-S class, where the paper exhibits an explicit four-parameter, three-dimensional counterexample. That double answer, a positive result bounded by a sharp negative one, tells researchers exactly where the BAR approach runs out of power, which is more useful than either result alone.\n\nWhether ChatGPT's role was genuine structural insight or a mechanical nudge toward a proof the authors were already close to, the paper doesn't say, and that question will matter more than any single theorem as mathematicians decide how much to trust this kind of collaboration.","[\"ai\",\"mathematics\",\"research\",\"queueing-theory\"]","2026-07-07T04:00:00.000Z","2026-07-07T10:13:56.501Z","2026-07-07T10:13:59.323Z","published",null,[24],{"id":25,"reviewer":26,"round":27,"reason":28,"status":29},"editor-r1","editor",1,"The dek names 'ChatGPT 5.5 Pro' as the model used, but this version cannot be verified against any publicly documented OpenAI release lineup — reject and replace with a verifiable model name or remove the specific version until it can be confirmed.","resolved","science",[32,33,34,35],"ai","mathematics","research","queueing-theory",[37],{"name":38,"url":39},"arXiv cs.AI","https:\u002F\u002Farxiv.org\u002Fabs\u002F2607.03639",0,{"sections":42},[43,47,52,57,62,67,72,77,81,85,90,94,99,104],{"name":44,"slug":32,"count":45,"latest_published_at":46},"AI",2590,"2026-07-16T04:00:00.000Z",{"name":48,"slug":49,"count":50,"latest_published_at":51},"Security","security",294,"2026-07-15T19:59:48.000Z",{"name":53,"slug":54,"count":55,"latest_published_at":56},"Deals","deals",179,"2026-06-29T20:02:07.000Z",{"name":58,"slug":59,"count":60,"latest_published_at":61},"Policy","policy",158,"2026-07-16T00:02:48.000Z",{"name":63,"slug":64,"count":65,"latest_published_at":66},"Hardware","hardware",122,"2026-07-14T19:46:26.000Z",{"name":68,"slug":69,"count":70,"latest_published_at":71},"Consumer Tech","consumer-tech",93,"2026-07-13T13:20:48.000Z",{"name":73,"slug":74,"count":75,"latest_published_at":76},"Software","software",70,"2026-07-13T19:52:25.000Z",{"name":78,"slug":30,"count":79,"latest_published_at":80},"Science",66,"2026-07-10T10:29:37.000Z",{"name":82,"slug":83,"count":84,"latest_published_at":18},"Dev Tools","dev-tools",59,{"name":86,"slug":87,"count":88,"latest_published_at":89},"Gaming","gaming",41,"2026-07-09T04:00:00.000Z",{"name":91,"slug":92,"count":88,"latest_published_at":93},"Startups","startups","2026-06-29T20:55:50.000Z",{"name":95,"slug":96,"count":97,"latest_published_at":98},"General","general",29,"2026-07-10T22:28:58.000Z",{"name":100,"slug":101,"count":102,"latest_published_at":103},"Reviews","reviews",20,"2026-06-24T12:00:01.000Z",{"name":105,"slug":106,"count":107,"latest_published_at":108},"How-To","how-to",6,"2026-06-16T09:00:00.000Z"]