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The Open Problems Project

• Domain: mathematics
• Role: prestige ledger
• Metric: dated resolutions per year across 78 scored rows
• Coverage: list begun 2001; dated resolutions 2000–2024; statuses read 2026-08-14
• Data: topp-problems.csv
• Upstream: https://topp.openproblem.net/, with the rows transcribed from the project's GitHub sources
• Verdict: no acceleration — 0 resolutions in 2026 and 0 since 2024; 17 dated resolutions over 2000–2024

Per-problem resolution timeline

Open problems sit on the right edge. Hover a point for resolver and notes.

Definition

The Open Problems Project is a maintained list of computational-geometry problems begun in 2001 by Erik Demaine, Joseph Mitchell and Joseph O'Rourke [@demaine2001topp]. Each entry carries a statement, a bibliography, and a Status/Conjectures line the maintainers update when something happens.

A "discovery" in this series is an entry whose status line states solved, settled or closed, dated by the year that line gives; where the maintainers give a month, only the year is scored. The wording is the maintainers' own rather than an independent consensus review, and it is qualified in places: entry 12 is counted on the "Solved (in a certain sense)" quoted in its register entry. One entry, 27 (hexahedral meshing), is scored partial on its "Partially closed" status line and contributes no event.

Facts

• rows: 78 scored; 17 resolved with a dated year; 60 open; 1 partial
• span: dated resolutions 2000–2024
• by-year: 2000: 1 · 2002: 1 · 2003: 1 · 2004: 3 · 2006: 1 · 2007: 1 · 2008: 1 · 2009: 3 · 2010: 1 · 2015: 1 · 2019: 1 · 2023: 1 · 2024: 1
• ai-attributed: 0 of 17 dated resolutions
• earliest event: 2000 (entry 18), predating the project's 2001 start

The collection-wide cumulative index redraws the ledger as rows remaining:

1 — Minimum Weight Triangulation

• status: resolved
• resolved: 2006
• resolver:

"Just solved by Wolfgang Mulzer and Günter Rote, January 2006!" — topp.openproblem.net, problem 1, read 2026-08-14 [@demaine2001topp]

2 — Voronoi Diagram of Moving Points

• status: resolved
• resolved: 2015
• resolver:

"Long conjectured to be nearly quadratic. Solved now: [Rub15]." — topp.openproblem.net, problem 2, read 2026-08-14 [@demaine2001topp]

12 — Dynamic Planar Convex Hull

• status: resolved
• resolved: 2002
• resolver:

"Solved (in a certain sense) by Gerth Brodal and Riko Jacob in a FOCS 2002 paper [BJ02]." — topp.openproblem.net, problem 12, read 2026-08-14 [@demaine2001topp]

14 — Binary Space Partition Size

• status: resolved
• resolved: 2009
• resolver: Csaba Tóth

"Solved by Csaba Tóth [Tót09], [Tót11]." — topp.openproblem.net, problem 14, read 2026-08-14 [@demaine2001topp]

18 — Pushing Disks Together

• status: resolved
• resolved: 2000
• resolver:

"Solved by K. Bezdek and R. Connelly. … (Update as of 3 Aug. 2000.)" — topp.openproblem.net, problem 18, read 2026-08-14 [@demaine2001topp]

20 — Minimum Stabbing Spanning Tree

• status: resolved
• resolved: 2003
• resolver:

"Solved, October 2003: the problem is NP-complete." — topp.openproblem.net, problem 20, read 2026-08-14 [@demaine2001topp]

21 — Shortest Paths among Obstacles in 2D

• status: resolved
• resolved: 2023
• resolver:

"Solved by Haitao Wang [Wan23] …" — topp.openproblem.net, problem 21, read 2026-08-14 [@demaine2001topp]

27 — Hexahedral Meshing

• status: partial
• resolved:
• resolver:
• notes: partial results; Partially closed, Fall 2006.

"Partially closed, Fall 2006." — topp.openproblem.net, problem 27, read 2026-08-14 [@demaine2001topp]

32 — Bar-Magnet Polyhedra

• status: resolved
• resolved: 2004
• resolver: Bojan Mohar

"Settled by Bojan Mohar, Apr. 2004." — topp.openproblem.net, problem 32, read 2026-08-14 [@demaine2001topp]

36 — Inplace Convex Hull of a Simple Polygonal Chain

• status: resolved
• resolved: 2004
• resolver:

"Solved [BC04]." — topp.openproblem.net, problem 36, read 2026-08-14 [@demaine2001topp]

47 — Hinged Dissections

• status: resolved
• resolved: 2008
• resolver: Abbott et al.

"Now settled: Hinged dissections exist [AAC+08]." — topp.openproblem.net, problem 47, read 2026-08-14 [@demaine2001topp]

48 — Bounded-Degree Minimum Euclidean Spanning Tree

• status: resolved
• resolved: 2009
• resolver:

"Solved: Proved NP-hard in [FH09]." — topp.openproblem.net, problem 48, read 2026-08-14 [@demaine2001topp]

50 — Pointed Spanning Trees in Triangulations

• status: resolved
• resolved: 2004
• resolver: Aichholzer et al.

"Settled negatively, January 2004." — topp.openproblem.net, problem 50, read 2026-08-14 [@demaine2001topp]

53 — Minimum-Turn Cycle Cover in Planar Grid Graphs

• status: resolved
• resolved: 2019
• resolver:

"Solved: proved NP-hard by Fekete and Krupke [FK19]" — topp.openproblem.net, problem 53, read 2026-08-14 [@demaine2001topp]

56 — Packing Unit Squares in a Simple Polygon

• status: resolved
• resolved: 2024
• resolver:

"Solved: proved NP-hard by Abrahamsen and Stade [AS24]." — topp.openproblem.net, problem 56, read 2026-08-14 [@demaine2001topp]

65 — Magic Configurations

• status: resolved
• resolved: 2007
• resolver: Abrego et al.

"Settled positively, 2007: [ABK+08]" — topp.openproblem.net, problem 65, read 2026-08-14 [@demaine2001topp]

69 — Isoceles Planar Graph Drawing

• status: resolved
• resolved: 2010
• resolver: Frati

"Settled negatively in 2010: [Fra10]." — topp.openproblem.net, problem 69, read 2026-08-14 [@demaine2001topp]

71 — Stretch-Factor for Points in Convex Position

• status: resolved
• resolved: 2009
• resolver:
• notes: Now closed: false; counterexample appeared in the 2009 CCCG proceedings.

"Now closed: false. [This entry awaiting updating.]" — topp.openproblem.net, problem 71, read 2026-08-14 [@demaine2001topp]

Method

The 78 rows were transcribed by hand from the project's GitHub problem directory (edemaine/topp), and the notes column keeps the maintainers' own status wording; the site publishes no machine-readable index, so there is no fetch.py. All 78 status lines were re-read at topp.openproblem.net on 2026-08-14 and match the ledger's statuses. One wording has moved since transcription: entry 71's status line now reads the shorter form quoted in its register entry, while the notes column keeps the transcribed CCCG-counterexample wording; the status and year are unchanged.

figure.py calls the shared problem_list_chart() in ../../lib/families.py, which keeps the rows whose status is resolved with a non-empty resolved_year and draws annual event bars from the earliest dated event to the present; the corner note states how many of the 78 rows have dated resolutions. No ai_problem argument is passed, because no entry credits an AI system. The cumulative view is the shared ledger_remaining_chart(). check.py recomputes the fact lines and the register entries from the CSV.

Limitations

• no entry-addition dates. The 78 entries accumulated after 2001 and the ledger does not record when each was added, so this is a dated-resolution ledger and not a fixed-cohort solve rate.
• one row predates the list. Entry 18's 2000 resolution sits a year before the project's 2001 start, so the event timeline begins before the list itself.
• maintainer language. Statuses are the maintainers' own wording, not independent review, and some are qualified — entry 12 is counted on "Solved (in a certain sense)".
• unmaintained entries look open. An entry whose status line was never updated is indistinguishable here from an unsolved problem, so the 60-row open count is an upper bound on the genuinely open entries.
• empty resolver fields. Many status lines name a citation rather than a person, so several resolver fields are empty and the series cannot be split by finder.
• effort. Resolution landmarks are not effort-adjusted discovery rates; nothing records how much search each fall took.

AI attribution

No status line among the 78 entries names an AI system or agent, as of the 2026-08-14 read of topp.openproblem.net, and no resolver or notes field in topp-problems.csv carries an AI credit. The two most recent dated resolutions are human papers: Wang (2023, entry 21) and Abrahamsen–Stade (2024, entry 56).

Sources

• [@demaine2001topp] — the project itself: entries, bibliographies and status lines; the register quotes its status wording as read 2026-08-14.
• [@deepmind2026nexus] — formal proof search over open problems, reporting 9 of 353 open Erdős problems resolved.
• [@arxiv2026horizonmath] — a 2026 benchmark of over 100 predominantly unsolved problems chosen so that "verification is computationally efficient and simple"; frontier models score near 0% on it.
• [@sherry2021fast] — measured improvement rates across algorithm families, including multi-decade stationary stretches, with no AI involved.
• Sibling ledgers of the same instrument type: Hilbert, Landau, Thurston, Smale and Millennium.
• Erdős — a catalogue ledger over a different corpus, counting a different unit (catalogue problems with imputed solution years).