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<!doctype html><html lang="en"><head><meta charset="utf-8"><script>(function(){try{if(/^https?:$/.test(location.protocol)&&/\/index\.html$/.test(location.pathname))history.replaceState(null,"",location.pathname.slice(0,-10)+location.search+location.hash);var r=document.documentElement;if(sessionStorage.getItem("mais-seen"))r.classList.add("returning");sessionStorage.setItem("mais-seen","1");}catch(e){}})()</script><meta name="color-scheme" content="light"><meta name="viewport" content="width=device-width,initial-scale=1"><title>Fields · MAIS</title><meta name="description" content="Open problems by field of mathematics."><link rel="icon" href="favicon.svg" type="image/svg+xml"><link rel="icon" href="favicon-32.png" sizes="32x32" type="image/png"><link rel="apple-touch-icon" href="apple-touch-icon.png"><meta property="og:type" content="website"><meta property="og:site_name" content="Math for AI Safety"><meta property="og:title" content="Fields · MAIS"><meta property="og:description" content="Open problems by field of mathematics."><meta property="og:url" content="https://invi-bhagyesh.github.io/MAIS-site/fields.html"><meta property="og:image" content="https://invi-bhagyesh.github.io/MAIS-site/assets/og.png"><meta property="og:image:width" content="1200"><meta property="og:image:height" content="630"><meta property="og:image:alt" content="Math for AI Safety, a research organization: open problems stated precisely and checked in public. An engraved pentagon of weight vectors on grid paper."><meta name="twitter:card" content="summary_large_image"><meta name="twitter:title" content="Fields · MAIS"><meta name="twitter:description" content="Open problems by field of mathematics."><meta name="twitter:image" content="https://invi-bhagyesh.github.io/MAIS-site/assets/og.png"><link rel="preconnect" href="https://fonts.googleapis.com"><link rel="preconnect" href="https://fonts.gstatic.com" crossorigin><link href="https://fonts.googleapis.com/css2?family=Geist:wght@300;400;500;600&family=JetBrains+Mono:wght@300;400;500&family=Newsreader:ital,opsz,wght@0,6..72,200..600;1,6..72,200..600&display=swap" rel="stylesheet"><link rel="stylesheet" href="assets/site.css"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.9/katex.min.css"><script defer src="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.9/katex.min.js"></script><script defer src="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.9/contrib/auto-render.min.js" onload="renderMath()"></script></head><body class="pg-fields"><a class="skip" href="#main">Skip to content</a><header class="top"><a class="brand" href="./" aria-label="Math for AI Safety, home"><svg viewBox="0 0 40 40" fill="none" stroke="currentColor" stroke-linecap="round" aria-hidden="true"><path class="lg-a" d="M5 32Q20 4 35 32" stroke-width="1.6"/><path class="lg-p lg-p1" d="M13 32V21.2" stroke-width="1.1"/><path class="lg-p lg-p2" d="M20 32V18.2" stroke-width="1.1"/><path class="lg-p lg-p3" d="M27 32V21.2" stroke-width="1.1"/><path class="lg-b" d="M2 32H38" stroke-width="1.1"/></svg><span>Math for<br>AI Safety</span></a><a class="repo" href="https://github.com/Math-for-AI-Safety/MAIS">Repository ↗</a></header><nav class="notch" aria-label="Main"><a href="./">Home</a><a href="problems.html">Problems</a><a href="agendas.html">Agendas</a><a href="fields.html" aria-current="page">Fields</a><a href="about.html">About</a><a class="wiki-link" href="wiki/">Wiki</a><button class="menu" aria-expanded="false">Menu</button></nav><div class="reg" aria-hidden="true"><i></i><i></i><i></i><i></i><b></b><b></b><b></b></div><main id="main"><div class="wrap two" style="padding-top:84px"><div class="lead"><h1 id="hh">Fields</h1><p>The problems use many parts of mathematics. Open a field to see its problems.</p></div><ul class="flist" id="fl"></ul></div></main><footer class="site-foot"><div class="wrap"><div class="f-mark"><svg viewBox="0 0 40 40" fill="none" stroke="currentColor" stroke-linecap="round" aria-hidden="true"><path d="M5 32Q20 4 35 32" stroke-width="1.6"/><path class="lg-p lg-p1" d="M13 32V21.2" stroke-width="1.1"/><path class="lg-p lg-p2" d="M20 32V18.2" stroke-width="1.1"/><path class="lg-p lg-p3" d="M27 32V21.2" stroke-width="1.1"/><path d="M2 32H38" stroke-width="1.1"/></svg></div><h2 class="f-h">Find a problem worth your time.</h2><div class="f-cols"><a class="f-col" href="problems.html"><b>Explore the problems</b><span>Open problems across eight agendas, each with a precise statement.</span><i>Open ↗</i></a><a class="f-col" href="agendas.html"><b>Read the agendas</b><span>How the problems group into research directions.</span><i>Open ↗</i></a><a class="f-col" href="fields.html"><b>Browse by field</b><span>Pick problems by the mathematics you already know.</span><i>Open ↗</i></a><a class="f-col" href="https://github.com/Math-for-AI-Safety/MAIS"><b>Contribute</b><span>Open an issue, post a partial result, or propose a problem.</span><i>Open ↗</i></a></div><div class="fbase"><small>© 2026 Math for AI Safety</small><div class="r"><a href="https://github.com/Math-for-AI-Safety/MAIS/issues/new/choose">Open an issue</a><a class="sq" href="https://github.com/Math-for-AI-Safety/MAIS" aria-label="GitHub"><svg viewBox="0 0 16 16" aria-hidden="true"><path d="M8 0C3.58 0 0 3.58 0 8c0 3.54 2.29 6.53 5.47 7.59.4.07.55-.17.55-.38 0-.19-.01-.82-.01-1.49-2.01.37-2.53-.49-2.69-.94-.09-.23-.48-.94-.82-1.13-.28-.15-.68-.52-.01-.53.63-.01 1.08.58 1.23.82.72 1.21 1.87.87 2.33.66.07-.52.28-.87.51-1.07-1.78-.2-3.64-.89-3.64-3.95 0-.87.31-1.59.82-2.15-.08-.2-.36-1.02.08-2.12 0 0 .67-.21 2.2.82.64-.18 1.32-.27 2-.27.68 0 1.36.09 2 .27 1.53-1.04 2.2-.82 2.2-.82.44 1.1.16 1.92.08 2.12.51.56.82 1.27.82 2.15 0 3.07-1.87 3.75-3.65 3.95.29.25.54.73.54 1.48 0 1.07-.01 1.93-.01 2.2 0 .21.15.46.55.38A8.013 8.013 0 0016 8c0-4.42-3.58-8-8-8z"/></svg></a><a class="sq" href="https://github.com/Math-for-AI-Safety/MAIS/commits/main.atom" aria-label="Feed of changes"><svg viewBox="0 0 16 16" aria-hidden="true"><circle cx="3" cy="13" r="1.8"/><path d="M1.2 6.2v2.4A6.2 6.2 0 0 1 7.4 14.8h2.4A8.6 8.6 0 0 0 1.2 6.2zM1.2 1.4v2.4A11 11 0 0 1 12.2 14.8h2.4A13.4 13.4 0 0 0 1.2 1.4z"/></svg></a></div></div></div></footer><script type="text/plain" data-page>
scramble(document.getElementById('hh'),250);const P=MAIS.problems;
const F=[['Mathematical logic','logic','O16'],['Probability and statistics',['probability','statistics'],'O35'],['Optimization and convex geometry',['optimization','convex geometry'],'O41'],['Harmonic analysis and representation theory',['harmonic analysis','representation theory'],'O59'],['Algebraic geometry','algebraic geometry','O6'],['Dynamical systems and stochastic processes',['dynamical systems'],'O75'],['Complexity theory','complexity theory','O12'],['Combinatorics','combinatorics','O30']];
const has=(p,k)=>[].concat(k).some(x=>p.math.includes(x));
fl.innerHTML=F.map(([n,k,o])=>{const ps=P.filter(p=>has(p,k)),t=P.find(p=>p.id==='MAIS-'+o);
return `<li><details><summary><span class="bul" aria-hidden="true"></span><h3>${n}</h3><span class="mono">${ps.length} problems, begin with ${t.id}</span></summary><ul>${ps.map(p=>`<li><a href="problems.html#O${p.n}"><span>O${p.n}</span>${esc(p.title)}</a></li>`).join('')}</ul></details></li>`}).join('');</script><script src="assets/data.js"></script><script src="assets/art.js"></script><script src="assets/engrave.js"></script><script src="assets/site.js"></script></body></html>