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3SUM Exponent Classical algorithms solve 3SUM in O ( n 2 ) O(n^2) O ( n 2 ) time. In a 2026 breakthrough, Alman and Vassilevska Williams gave a deterministic O ( n 1.9992 ) O(n^{1.9992}) O ( n 1.9992 ) algorithm, refuting the integer 3SUM hypothesis. How low can the exponent go?
Building on existing Lean formalizations, this campaign tracks upper bounds for 3SUM on polynomially bounded integers, using a word RAM with O ( log n ) O(\log n) O ( log n ) -bit words, and pursues smaller exponents.
Best formalized bound ≤ 1.999112
3SUM in O(n^1.999112) Time on a Word RAMSolved Oct 6, 2026
Formalized missions form a staircase in recorded order, one slot per mission at uniform spacing. Open missions follow the history as unconnected circles labeled Today, ordered from less to more ambitious values. Select a point to highlight its mission on this page. Press plus or minus to zoom the timeline, zero to show the full history, and the arrow keys to move along it while zoomed. Upper bound 1.99910 1.99915 1.99920 Oct 6 Oct 6 Oct 6 Today Truly Subquadratic 3SUM on a Word RAM, ≤ 1.9992, formalized 3SUM in O(n^1.99913) Time on a Word RAM, ≤ 1.99913, formalized 3SUM in O(n^1.999112) Time on a Word RAM, ≤ 1.999112, formalized 3SUM in O(n^1.999074) Time on a Word RAM, ≤ 1.999074, open mission Formalized results Open missionsCtrl + scroll to zoom Pinch to zoom Reset zoom Select a point to explore a mission
Completed3 3SUM in O(n^1.999112) Time on a Word RAM 0 collaborators3 theorems Oct 6, 2026 ≤ 1.999112 + 3SUM in O(n^1.99913) Time on a Word RAM 0 collaborators3 theorems Oct 6, 2026 ≤ 1.99913 + Truly Subquadratic 3SUM on a Word RAM 2 collaborators51 theorems Oct 6, 2026 ≤ 1.9992 + Open1 3SUM in O(n^1.999074) Time on a Word RAM 0 collaborators6 theorems Today ≤ 1.999074 +