[{"data":1,"prerenderedAt":30},["ShallowReactive",2],{"nr-en-anthropic-claude-elliptic-curve-rank-31":3},{"slug":4,"title":5,"dek":6,"date":7,"time":8,"publishedAt":9,"updated":10,"updatedAt":10,"dateFmt":11,"updatedFmt":10,"kind":12,"tier":13,"author":14,"authorName":15,"topics":16,"tracker":22,"trackerLabel":23,"headlineStat":24,"image":25,"ogImage":26,"imageAlt":5,"csv":10,"minutes":27,"words":28,"html":29},"anthropic-claude-elliptic-curve-rank-31","Anthropic's Claude Breaks Mathematical Record – Discovers Most Complex Elliptic Curve","Claude discovered elliptic curves with ranks 30 and 31 in days—a feat that took mathematicians decades. A breakthrough showing how AI tackles classical math problems differently.","2026-09-17","10:12","2026-09-17T10:12:00+02:00","","September 17, 2026","news","standard","ideal-syka","Ideal Syka",[17,18,19,20,21],"AI Research","Mathematics","Anthropic","Claude","Breakthrough","\u002Fstand-der-ki","AI Progress","Elliptic curve with rank 31 discovered in days instead of decades","\u002Fnewsroom\u002Fimg\u002Fanthropic-claude-elliptic-curve-rank-31.webp","\u002Fog-nr\u002Fanthropic-claude-elliptic-curve-rank-31.en.png",2,468,"\u003Cp>Anthropic has achieved a mathematical milestone that's turning heads in the research community: the company presented two elliptic curves with ranks of at least 30 and 31—discovered within days. What sounds like a technical footnote is actually a breakthrough mathematicians have pursued unsuccessfully for decades.\u003C\u002Fp>\n\u003Ch2>Key Facts\u003C\u002Fh2>\n\u003Cul>\n\u003Cli>\u003Cstrong>Levent Alp­öge\u003C\u002Fstrong> (Anthropic) and cryptographer \u003Cstrong>Ava Howell\u003C\u002Fstrong> used Claude to find elliptic curves with ranks of at least \u003Cstrong>30 and 31\u003C\u002Fstrong>\u003C\u002Fli>\n\u003Cli>The previous record was rank \u003Cstrong>29\u003C\u002Fstrong>, achieved in August 2024 after \u003Cstrong>18 years\u003C\u002Fstrong> of research\u003C\u002Fli>\n\u003Cli>Claude found both curves in just \u003Cstrong>days\u003C\u002Fstrong>\u003C\u002Fli>\n\u003Cli>Elliptic curves measure complexity through their "rank"—higher ranks mean more independent patterns\u003C\u002Fli>\n\u003C\u002Ful>\n\u003Ch2>What Are Elliptic Curves and Why Are They So Hard?\u003C\u002Fh2>\n\u003Cp>Elliptic curves look deceptively simple: they follow the formula \u003Cstrong>y² = x³ + Ax + B\u003C\u002Fstrong>. Yet their mathematical structure is treacherous. Mathematicians focus on so-called \u003Cstrong>rational points\u003C\u002Fstrong>—coordinates expressible as fractions that satisfy the equation.\u003C\u002Fp>\n\u003Cp>A curve's rank describes how many independent "families" of such points exist. A rank-1 curve has infinitely many rational points, but they can all be constructed from a single starting point. Rank 2 requires two independent points to generate all others. The higher the rank, the more complex the internal structure.\u003C\u002Fp>\n\u003Ch2>Decades of Stagnation, Then AI in Days\u003C\u002Fh2>\n\u003Cp>Progress has been painfully slow. The jump from rank 28 to rank 29 took \u003Cstrong>over 18 years\u003C\u002Fstrong>. In August 2024, a rank-29 curve was discovered using an elaborate method: analyzing cross-sections through higher-dimensional objects.\u003C\u002Fp>\n\u003Cp>Then Claude arrived. Alp­öge and Howell deployed the language model to systematically search for higher-rank curves—and found not just rank 30, but rank 31 within days.\u003C\u002Fp>\n\u003Cdiv class=\"tbl-scroll\">\u003Ctable>\n\u003Cthead>\n\u003Ctr>\n\u003Cth>Milestone\u003C\u002Fth>\n\u003Cth>Year\u003C\u002Fth>\n\u003Cth>Time Required\u003C\u002Fth>\n\u003C\u002Ftr>\n\u003C\u002Fthead>\n\u003Ctbody>\u003Ctr>\n\u003Ctd>Rank 28 → 29\u003C\u002Ftd>\n\u003Ctd>2024\u003C\u002Ftd>\n\u003Ctd>18+ years\u003C\u002Ftd>\n\u003C\u002Ftr>\n\u003Ctr>\n\u003Ctd>Rank 29 → 30 & 31\u003C\u002Ftd>\n\u003Ctd>2026\u003C\u002Ftd>\n\u003Ctd>days (Claude)\u003C\u002Ftd>\n\u003C\u002Ftr>\n\u003C\u002Ftbody>\u003C\u002Ftable>\u003C\u002Fdiv>\n\u003Ch2>Open Questions Remain\u003C\u002Fh2>\n\u003Cp>The discovery reopens a central question in number theory: \u003Cstrong>Can elliptic curves have infinitely high ranks, or is there an upper limit?\u003C\u002Fstrong> Until now, it was unclear whether previous records were simply extremely hard to find or whether fundamental limits exist.\u003C\u002Fp>\n\u003Cp>Claude could help answer this question faster—not through mathematical intuition, but through systematic exploration of vast solution spaces inaccessible to humans.\u003C\u002Fp>\n\u003Ch2>What This Means\u003C\u002Fh2>\n\u003Cp>For German research institutions and companies, this is a signal: AI systems like Claude aren't just text and code generators. They can serve as \u003Cstrong>tools for mathematical exploration\u003C\u002Fstrong>, especially for problems requiring massive computational search spaces. This could accelerate applications in cryptography, optimization, and theoretical computer science—areas where Germany has traditional strength. At the same time, it's clear: whoever has access to advanced AI models gains an edge on classical research questions.\u003C\u002Fp>\n\u003Ch2>Sources\u003C\u002Fh2>\n\u003Cul>\n\u003Cli>\u003Ca href=\"https:\u002F\u002Fwww.scientificamerican.com\u002Farticle\u002Fanthropics-ai-steals-mathematicians-record-for-most-complicated-curve\u002F\">Scientific American\u003C\u002Fa>\u003C\u002Fli>\n\u003C\u002Ful>\n\u003Cp>\u003Cem>Editorially owned by \u003Ca href=\"\u002Fen\u002Fautor\u002Fideal-syka\">Ideal Syka\u003C\u002Fa>. Sources and method: \u003Ca href=\"\u002Fen\u002Fredaktion\">Newsroom & method\u003C\u002Fa>. Tips and corrections: \u003Ca href=\"mailto:ai@i6eal.de\">ai@i6eal.de\u003C\u002Fa>.\u003C\u002Fem>\u003C\u002Fp>\n",1789638862389]