--- title: Mathematical Experiments Are Becoming Abundant Through... description: An author spent a weekend running parallel AI agents, exact-arithmetic checkers and the Lean proof assistant against two open math problems: constructing a... canonical: https://daily.dev/posts/mathematical-experiments-are-becoming-abundant-through-human-machine-teaming-at6d9wesn twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: Mathematical Experiments Are Becoming Abundant Through Human-Machine Teaming | daily.dev og:description: An author spent a weekend running parallel AI agents, exact-arithmetic checkers and the Lean proof assistant against two open math problems: constructing a... og:url: https://daily.dev/posts/mathematical-experiments-are-becoming-abundant-through-human-machine-teaming-at6d9wesn og:image: https://api.daily.dev/og/posts/At6D9WESn.png og:image:alt: Mathematical Experiments Are Becoming Abundant Through Human-Machine Teaming 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. # Mathematical Experiments Are Becoming Abundant Through Human-Machine Teaming **[Towards Data Science](https://daily.dev/sources/tds)** · 26 min read · 1 upvotes · 0 comments ## Summary An author spent a weekend running parallel AI agents, exact-arithmetic checkers and the Lean proof assistant against two open math problems: constructing a Hadamard matrix of order 668, and a candidate proof bounding equilibria in Maxwell's electrostatics problem. The Hadamard search closed 44 regions of the search space and audited five nonexistence-proof routes without finding a solution or disproof. The Maxwell effort produced a full proof candidate with a machine-checked algebraic core in Lean, but the geometric bridges remain unformalized and unreviewed by specialists. The piece argues AI is making mathematical experimentation dramatically cheaper (echoing Jeff Dean's propose-implement-evaluate research loop), while proof validation, novelty-checking, and understanding remain expensive human bottlenecks. It surveys related developments (AlphaEvolve, OpenAI's Erdős unit-distance counterexample, Zahavy's induction/deduction/abduction framing) and closes on institutional concerns around attribution, credit, and the need for a searchable registry of claims and failed attempts as AI-generated math proliferates. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Questions this post answers ### Has anyone found a Hadamard matrix of order 668 or proven it doesn't exist? No, order 668 remains the smallest order for which existence is unknown. A weekend project using parallel AI agents, exact-arithmetic search, and constraint solvers closed 44 precisely defined regions of the search space and audited five standard nonexistence-proof routes (including Bruck-Ryser-Chowla and Hasse-Minkowski), but none supplied the missing obstruction and no matrix was found. _Developers tracking open problems in computational math can follow these searches unfold on daily.dev._ ### Has Maxwell's conjecture about equilibrium points of point charges been disproven? Yes, a July 2026 paper by Arathoon, Ball, and Kvalheim constructed five point charges with at least 24 nondegenerate equilibria, disproving Maxwell's proposed formula of (k-1)squared for k charges. A separate July 2026 paper by Gabrielov, Novikov, Novikov, and Shapiro sharpened the bound for three positive charges from twelve to six nondegenerate equilibria for every positive Riesz exponent. _daily.dev helps engineers and researchers keep up with fast-moving math and AI research like this._ ### Can Lean fully verify an AI-generated mathematical proof candidate? Not necessarily the whole argument. In one case, a partial Lean formalization completed successfully with 33 named theorems covering the central moment inequality and endpoint-gap algebra, but it did not formalize the barycentric correspondence, differential identities, global index, or compactness arguments, so Lean checked only the algebraic core rather than the complete theorem. _Anyone evaluating AI-assisted proofs can track how far tools like Lean actually verify versus assume on daily.dev._ ## Similar posts on daily.dev - [Human mathematicians are being outcounterexampled](https://daily.dev/posts/human-mathematicians-are-being-outcounterexampled-ocacgpf22) · Hacker News · 3 upvotes · 0 comments - [AI control is losing the proof race\!](https://daily.dev/posts/ai-control-is-losing-the-proof-race--wkn43rye0) · Medium · 0 upvotes · 0 comments - [DeepMind’s latest: An AI for handling mathematical proofs](https://daily.dev/posts/deepmind-s-latest-an-ai-for-handling-mathematical-proofs-p88dclgu1) · Ars Technica · 3 upvotes · 0 comments --- Tags: [#llm](https://daily.dev/tags/llm), [#ai-agents](https://daily.dev/tags/ai-agents), [#math](https://daily.dev/tags/math) [View this post on daily.dev](https://daily.dev/posts/mathematical-experiments-are-becoming-abundant-through-human-machine-teaming-at6d9wesn) ```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":"Mathematical Experiments Are Becoming Abundant Through Human-Machine Teaming","url":"https://daily.dev/posts/mathematical-experiments-are-becoming-abundant-through-human-machine-teaming-at6d9wesn","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/mathematical-experiments-are-becoming-abundant-through-human-machine-teaming-at6d9wesn"},"datePublished":"2026-08-15T15:48:51.482Z","dateModified":"2026-09-14T07:54:40.899Z","description":"An author spent a weekend running parallel AI agents, exact-arithmetic checkers and the Lean proof assistant against two open math problems: constructing a...","image":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/77c7d7c360d4d821eeff2ffe984a1206?_a=AQAEuop","thumbnailUrl":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/77c7d7c360d4d821eeff2ffe984a1206?_a=AQAEuop","isAccessibleForFree":true,"articleSection":"Towards Data Science","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":"Towards Data Science","logo":"https://media.daily.dev/image/upload/t_logo,f_auto/v1/logos/tds","url":"https://daily.dev/sources/tds"},"commentCount":0,"discussionUrl":"https://daily.dev/posts/mathematical-experiments-are-becoming-abundant-through-human-machine-teaming-at6d9wesn","interactionStatistic":[{"@type":"InteractionCounter","interactionType":{"@type":"LikeAction"},"userInteractionCount":1},{"@type":"InteractionCounter","interactionType":{"@type":"CommentAction"},"userInteractionCount":0}],"keywords":"llm,ai-agents,math","timeRequired":"PT26M"} {"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://daily.dev"},{"@type":"ListItem","position":2,"name":"Towards Data Science","item":"https://daily.dev/sources/tds"},{"@type":"ListItem","position":3,"name":"Mathematical Experiments Are Becoming Abundant Through Human-Machine Teaming"}]} {"@context":"https://schema.org","@type":"FAQPage","@id":"https://daily.dev/posts/mathematical-experiments-are-becoming-abundant-through-human-machine-teaming-at6d9wesn#faq","mainEntity":[{"@type":"Question","name":"Has anyone found a Hadamard matrix of order 668 or proven it doesn't exist?","acceptedAnswer":{"@type":"Answer","text":"No, order 668 remains the smallest order for which existence is unknown. A weekend project using parallel AI agents, exact-arithmetic search, and constraint solvers closed 44 precisely defined regions of the search space and audited five standard nonexistence-proof routes (including Bruck-Ryser-Chowla and Hasse-Minkowski), but none supplied the missing obstruction and no matrix was found. Developers tracking open problems in computational math can follow these searches unfold on daily.dev."}},{"@type":"Question","name":"Has Maxwell's conjecture about equilibrium points of point charges been disproven?","acceptedAnswer":{"@type":"Answer","text":"Yes, a July 2026 paper by Arathoon, Ball, and Kvalheim constructed five point charges with at least 24 nondegenerate equilibria, disproving Maxwell's proposed formula of (k-1)squared for k charges. A separate July 2026 paper by Gabrielov, Novikov, Novikov, and Shapiro sharpened the bound for three positive charges from twelve to six nondegenerate equilibria for every positive Riesz exponent. daily.dev helps engineers and researchers keep up with fast-moving math and AI research like this."}},{"@type":"Question","name":"Can Lean fully verify an AI-generated mathematical proof candidate?","acceptedAnswer":{"@type":"Answer","text":"Not necessarily the whole argument. In one case, a partial Lean formalization completed successfully with 33 named theorems covering the central moment inequality and endpoint-gap algebra, but it did not formalize the barycentric correspondence, differential identities, global index, or compactness arguments, so Lean checked only the algebraic core rather than the complete theorem. Anyone evaluating AI-assisted proofs can track how far tools like Lean actually verify versus assume on daily.dev."}}]} ```