--- title: Erdős Unit Distance Problem: What It Is and What AI Found description: A database consultant explores the Erdős unit distance problem—an 80-year-old conjecture about how many equal-length line segments can connect points in a... canonical: https://daily.dev/posts/erd-s-unit-distance-problem-what-it-is-and-what-ai-found-lkw90rb5n twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: Erdős Unit Distance Problem: What It Is and What AI Found | daily.dev og:description: A database consultant explores the Erdős unit distance problem—an 80-year-old conjecture about how many equal-length line segments can connect points in a... og:url: https://daily.dev/posts/erd-s-unit-distance-problem-what-it-is-and-what-ai-found-lkw90rb5n og:image: https://api.daily.dev/og/posts/LkW90rb5n.png og:image:alt: Erdős Unit Distance Problem: What It Is and What AI Found og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # Erdős Unit Distance Problem: What It Is and What AI Found **[SQL Authority](https://daily.dev/sources/sql-authority)** · 9 min read · 0 upvotes · 0 comments ## Summary A database consultant explores the Erdős unit distance problem—an 80-year-old conjecture about how many equal-length line segments can connect points in a plane—using SQL Server to recreate the classic grid-based construction with T-SQL self-joins and spatial queries (STDistance, geometry points). The post explains Erdős's 1946 conjecture, the 1984 Spencer-Szemerédi-Trotter upper bound, and reports that on May 20, 2026, an OpenAI internal reasoning model produced a 125-page proof disproving the conjecture using algebraic number theory, later verified by nine mathematicians. Includes runnable SQL queries to reproduce the grid trick and visualize it in SSMS's Spatial results tab, plus notes on real-world applications like geofencing and delivery radius queries. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Questions this post answers ### What is the Erdős unit distance problem and was it solved? It is an 80-year-old conjecture posed by Paul Erdős in 1946 asking how fast the number of unit-distance pairs among n points can grow, with his grid construction long believed near-optimal. On May 20, 2026, an OpenAI internal reasoning model produced a 125-page counterexample proving the conjecture wrong, later checked and confirmed by nine mathematicians, with Will Sawin computing a growth rate exceeding n^1.014. _Developers tracking how AI models are reshaping math and problem-solving can follow breakthroughs like this on daily.dev._ ### How can I use SQL Server spatial functions like STDistance to count points at a fixed distance apart in a grid? Build a grid of points as geometry::Point values, then join each pair and filter with ABS(p.pin.STDistance(q.pin) - length) < tolerance, since floating point distances rarely equal exactly. A 40x40 grid checked against √65 found 9,744 pairs in about four seconds by scanning all 1,279,200 point pairs, matching results from an integer squared-distance self-join. _Anyone building geospatial or proximity queries in SQL Server can find practical patterns like this through daily.dev._ ## Similar posts on daily.dev - [Why the Legendary Erdős Problems Are Falling to AI](https://daily.dev/posts/why-the-legendary-erd-s-problems-are-falling-to-ai-wwmtmigyt) · Hacker News · 0 upvotes · 0 comments - [The story of Erdős problem \#1026](https://daily.dev/posts/the-story-of-erd-s-problem-1026-mdgrbdzff) · Hacker News · 1 upvotes · 0 comments --- Tags: [#math](https://daily.dev/tags/math), [#microsoft-sql-server](https://daily.dev/tags/microsoft-sql-server) [View this post on daily.dev](https://daily.dev/posts/erd-s-unit-distance-problem-what-it-is-and-what-ai-found-lkw90rb5n) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"Erdős Unit Distance Problem: What It Is and What AI Found","url":"https://daily.dev/posts/erd-s-unit-distance-problem-what-it-is-and-what-ai-found-lkw90rb5n","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/erd-s-unit-distance-problem-what-it-is-and-what-ai-found-lkw90rb5n"},"datePublished":"2026-09-29T03:45:44.846Z","dateModified":"2026-09-29T03:46:11.486Z","description":"A database consultant explores the Erdős unit distance problem—an 80-year-old conjecture about how many equal-length line segments can connect points in a...","image":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/568e0c5f917755d41b3ae96fa2e26b4c?_a=AQAEuop","thumbnailUrl":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/568e0c5f917755d41b3ae96fa2e26b4c?_a=AQAEuop","isAccessibleForFree":true,"articleSection":"SQL Authority","inLanguage":"en","publisher":{"@type":"Organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180}},"author":{"@type":"Organization","name":"SQL Authority","logo":"https://media.daily.dev/image/upload/s--reCGnvgi--/f_auto,q_auto/v1780213436/logos/sql-authority?_a=BAMAMiWQ0","url":"https://daily.dev/sources/sql-authority"},"commentCount":0,"discussionUrl":"https://daily.dev/posts/erd-s-unit-distance-problem-what-it-is-and-what-ai-found-lkw90rb5n","interactionStatistic":[{"@type":"InteractionCounter","interactionType":{"@type":"LikeAction"},"userInteractionCount":0},{"@type":"InteractionCounter","interactionType":{"@type":"CommentAction"},"userInteractionCount":0}],"keywords":"math,microsoft-sql-server","timeRequired":"PT9M"} {"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://daily.dev"},{"@type":"ListItem","position":2,"name":"SQL Authority","item":"https://daily.dev/sources/sql-authority"},{"@type":"ListItem","position":3,"name":"Erdős Unit Distance Problem: What It Is and What AI Found"}]} {"@context":"https://schema.org","@type":"FAQPage","@id":"https://daily.dev/posts/erd-s-unit-distance-problem-what-it-is-and-what-ai-found-lkw90rb5n#faq","mainEntity":[{"@type":"Question","name":"What is the Erdős unit distance problem and was it solved?","acceptedAnswer":{"@type":"Answer","text":"It is an 80-year-old conjecture posed by Paul Erdős in 1946 asking how fast the number of unit-distance pairs among n points can grow, with his grid construction long believed near-optimal. On May 20, 2026, an OpenAI internal reasoning model produced a 125-page counterexample proving the conjecture wrong, later checked and confirmed by nine mathematicians, with Will Sawin computing a growth rate exceeding n^1.014. Developers tracking how AI models are reshaping math and problem-solving can follow breakthroughs like this on daily.dev."}},{"@type":"Question","name":"How can I use SQL Server spatial functions like STDistance to count points at a fixed distance apart in a grid?","acceptedAnswer":{"@type":"Answer","text":"Build a grid of points as geometry::Point values, then join each pair and filter with ABS(p.pin.STDistance(q.pin) - length) < tolerance, since floating point distances rarely equal exactly. A 40x40 grid checked against √65 found 9,744 pairs in about four seconds by scanning all 1,279,200 point pairs, matching results from an integer squared-distance self-join. Anyone building geospatial or proximity queries in SQL Server can find practical patterns like this through daily.dev."}}]} ```