MonitoringPrimary outcome · Prospective cohort · 100 problems
Erdős Problems 1–100 prospective resolution cohort
Prospective resolution rate for the fixed cohort of Erdős Problems 1–100.
0 verified resolutions since 19 August 2026
- Cohort
- 100
- At risk
- 54
- Resolved at freeze
- 46
- New resolutions
- 0
- Source changes
- 96
54 problems at risk
Open: 49
Other at risk: 5
Proved: 31
Disproved or solved: 15
Status breakdown
| Status | Problems | Group |
|---|---|---|
| Open | 49 | At risk |
| Falsifiable | 3 | At risk |
| Decidable | 1 | At risk |
| Verifiable | 1 | At risk |
| Proved | 31 | Resolved at freeze |
| Disproved | 12 | Resolved at freeze |
| Solved | 3 | Resolved at freeze |
| Tag | Problems |
|---|---|
| number theory | 53 |
| graph theory | 31 |
| additive combinatorics | 13 |
| additive basis | 12 |
| distances | 12 |
| geometry | 12 |
| ramsey theory | 12 |
| cycles | 10 |
| primes | 9 |
| sidon sets | 7 |
| chromatic number | 6 |
| convex | 5 |
Verified events
0
Verified post-freeze resolutions
All 100 cohort problems
| # | Status | Prize | Formal solution | Statement formalized | Tags | Catalogue update |
|---|---|---|---|---|---|---|
| 1 | Open | $500 | No | Yes | additive combinatorics, number theory | 2025-08-31 |
| 2 | Disproved | $1000 | No | No | covering systems, number theory | 2025-08-31 |
| 3 | Open | $5000 | No | Yes | additive combinatorics, arithmetic progressions, number theory | 2025-08-31 |
| 4 | Proved | $10000 | No | Yes | number theory, primes | 2025-08-31 |
| 5 | Open | no | No | Yes | number theory, primes | 2025-08-31 |
| 6 | Proved | $100 | No | Yes | number theory, primes | 2025-08-31 |
| 7 | Verifiable | no | No | Yes | covering systems, number theory | 2025-08-31 |
| 8 | Disproved | no | No | No | covering systems, number theory | 2025-08-31 |
| 9 | Open | no | No | Yes | additive basis, number theory, primes | 2025-08-31 |
| 10 | Open | no | No | Yes | additive basis, number theory, primes | 2025-08-31 |
| 11 | Open | no | No | Yes | additive basis, number theory | 2026-03-14 |
| 12 | Open | no | No | Yes | number theory | 2025-08-31 |
| 13 | Proved | $100 | No | Yes | number theory | 2025-08-31 |
| 14 | Open | no | No | Yes | additive combinatorics, number theory, sidon sets | 2025-08-31 |
| 15 | Open | no | No | Yes | number theory, primes | 2025-08-31 |
| 16 | Disproved | no | Lean | Yes | additive basis, number theory, primes | 2026-02-24 |
| 17 | Open | no | No | Yes | number theory, primes | 2025-08-31 |
| 18 | Open | no | No | Yes | divisors, factorials, number theory | 2025-08-31 |
| 19 | Decidable | $500 | No | No | chromatic number, graph theory | 2025-08-31 |
| 20 | Open | $1000 | No | Yes | combinatorics | 2025-08-31 |
| 21 | Proved | $500 | No | No | combinatorics, intersecting family | 2025-08-31 |
| 22 | Proved | no | No | Yes | graph theory | 2025-08-31 |
| 23 | Falsifiable | no | No | Yes | graph theory | 2025-08-31 |
| 24 | Proved | no | Lean | Yes | graph theory | 2026-04-23 |
| 25 | Open | no | No | Yes | number theory | 2025-08-31 |
| 26 | Disproved | no | Lean | Yes | divisors, number theory | 2025-12-28 |
| 27 | Disproved | $100 | No | No | covering systems, number theory | 2025-08-31 |
| 28 | Open | $500 | No | Yes | additive basis, number theory | 2025-08-31 |
| 29 | Proved | $100 | No | No | additive basis, number theory | 2025-08-31 |
| 30 | Open | $1000 | No | Yes | additive combinatorics, number theory, sidon sets | 2025-08-31 |
| 31 | Proved | no | Lean | Yes | additive basis, number theory | 2025-11-24 |
| 32 | Open | no | No | Yes | additive basis, number theory | 2025-08-31 |
| 33 | Open | no | No | Yes | additive basis, number theory | 2025-08-31 |
| 34 | Disproved | no | Lean | Yes | number theory | 2026-02-05 |
| 35 | Proved | no | No | No | additive basis, number theory | 2025-08-31 |
| 36 | Open | no | No | Yes | additive combinatorics, number theory | 2025-08-31 |
| 37 | Disproved | no | No | No | additive combinatorics, number theory | 2025-08-31 |
| 38 | Proved | no | Lean | Yes | number theory | 2026-05-01 |
| 39 | Open | $500 | No | Yes | additive combinatorics, number theory, sidon sets | 2025-08-31 |
| 40 | Open | $500 | No | Yes | additive basis, number theory | 2025-08-31 |
| 41 | Open | $500 | No | Yes | additive combinatorics, number theory, sidon sets | 2025-08-31 |
| 42 | Solved | no | Lean | Yes | additive combinatorics, number theory, sidon sets | 2026-05-10 |
| 43 | Disproved | $100 | No | Yes | additive combinatorics, number theory, sidon sets | 2025-08-31 |
| 44 | Open | no | No | Yes | additive combinatorics, number theory, sidon sets | 2025-08-31 |
| 45 | Proved | no | Lean | Yes | number theory, ramsey theory, unit fractions | 2026-05-06 |
| 46 | Proved | no | Lean | Yes | number theory, ramsey theory, unit fractions | 2025-12-29 |
| 47 | Proved | $100 | Lean | Yes | number theory, unit fractions | 2025-11-28 |
| 48 | Proved | no | No | Yes | number theory | 2025-08-31 |
| 49 | Proved | no | No | No | number theory, primes | 2025-08-31 |
| 50 | Open | $250 | No | Yes | number theory | 2025-08-31 |
| 51 | Open | no | No | Yes | number theory | 2025-08-31 |
| 52 | Open | $250 | No | Yes | additive combinatorics, number theory | 2026-05-28 |
| 53 | Proved | no | No | No | additive combinatorics, number theory | 2025-08-31 |
| 54 | Solved | $100 | No | No | number theory, ramsey theory | 2025-08-31 |
| 55 | Solved | $250 | No | No | number theory, ramsey theory | 2025-08-31 |
| 56 | Disproved | $10 | Lean | Yes | intersecting family, number theory | 2025-11-26 |
| 57 | Proved | no | No | No | chromatic number, cycles, graph theory | 2025-08-31 |
| 58 | Proved | no | No | No | chromatic number, cycles, graph theory | 2025-08-31 |
| 59 | Disproved | no | No | No | graph theory, turan number | 2025-08-31 |
| 60 | Open | no | No | Yes | cycles, graph theory | 2025-08-31 |
| 61 | Open | no | No | Yes | graph theory | 2025-08-31 |
| 62 | Open | no | No | No | graph theory | 2025-08-31 |
| 63 | Proved | no | No | No | chromatic number, cycles, graph theory | 2025-08-31 |
| 64 | Falsifiable | $1000 | No | Yes | cycles, graph theory | 2025-08-31 |
| 65 | Open | no | No | No | cycles, graph theory | 2025-08-31 |
| 66 | Open | $500 | No | Yes | additive basis, number theory | 2025-08-31 |
| 67 | Proved | $500 | No | Yes | discrepancy | 2025-08-31 |
| 68 | Open | no | No | Yes | irrationality, number theory | 2025-08-31 |
| 69 | Proved | no | No | Yes | irrationality, number theory | 2025-12-02 |
| 70 | Open | no | No | Yes | graph theory, ramsey theory, set theory | 2025-08-31 |
| 71 | Proved | no | Lean | Yes | cycles, graph theory | 2026-06-07 |
| 72 | Proved | $100 | No | No | cycles, graph theory | 2025-08-31 |
| 73 | Proved | no | No | No | graph theory | 2025-08-31 |
| 74 | Open | $500 | No | Yes | chromatic number, cycles, graph theory | 2025-08-31 |
| 75 | Open | no | No | Yes | chromatic number, graph theory | 2025-08-31 |
| 76 | Proved | no | No | No | graph theory, ramsey theory | 2025-08-31 |
| 77 | Open | $250 | No | No | graph theory, ramsey theory | 2025-08-31 |
| 78 | Open | $100 | No | No | graph theory, ramsey theory | 2025-08-31 |
| 79 | Proved | no | No | No | graph theory, ramsey theory | 2025-08-31 |
| 80 | Open | no | No | Yes | graph theory, ramsey theory | 2025-08-31 |
| 81 | Open | no | No | No | graph theory | 2025-08-31 |
| 82 | Open | no | No | Yes | graph theory | 2025-08-31 |
| 83 | Proved | $500 | No | No | combinatorics | 2025-08-31 |
| 84 | Open | no | No | No | cycles, graph theory | 2025-08-31 |
| 85 | Open | no | No | Yes | graph theory | 2026-03-14 |
| 86 | Open | $100 | No | No | graph theory | 2025-08-31 |
| 87 | Open | no | No | No | graph theory, ramsey theory | 2025-08-31 |
| 88 | Proved | $100 | No | No | graph theory, ramsey theory | 2025-08-31 |
| 89 | Open | $500 | No | Yes | distances, geometry | 2025-08-31 |
| 90 | Disproved | $500 | Lean | Yes | distances, geometry | 2026-06-07 |
| 91 | Open | no | No | Yes | distances, geometry | 2025-08-31 |
| 92 | Disproved | $500 | No | Yes | distances, geometry | 2026-05-21 |
| 93 | Proved | no | Lean | Yes | convex, distances, geometry | 2025-02-17 |
| 94 | Proved | £25 | Lean | Yes | convex, distances, geometry | 2026-01-15 |
| 95 | Proved | $500 | No | No | convex, distances, geometry | 2025-08-31 |
| 96 | Open | no | No | Yes | convex, distances, geometry | 2025-08-31 |
| 97 | Falsifiable | $100 | No | Yes | convex, distances, geometry | 2025-08-31 |
| 98 | Open | no | No | Yes | distances, geometry | 2025-08-31 |
| 99 | Open | $100 | No | Yes | distances, geometry | 2025-08-31 |
| 100 | Open | no | No | Yes | distances, geometry | 2025-08-31 |
Event and date rules
- Membership
- All and only integer-numbered Erdős Problems 1 through 100 at the frozen source commit.
- Event
- After the freeze, count a resolution only after a named primary or verification source establishes the resolution date and the required checking level.
- Date
- informal_status.last_update is catalogue metadata and is not a solution or verification date.
- At-risk states
- decidable, falsifiable, open, verifiable
- Formalization
- Formal-solution and statement-formalization fields are quality dimensions and do not silently replace the human-reviewed informal status.
- AI exposure
- None at baseline
Analysis and limits
Analysis
Report exact event counts and problem-time exposure. Once enough events exist, estimate an incidence rate with a risk-set offset and exact or Poisson uncertainty; do not annualize a zero-event partial period into an acceleration verdict.
- Show results under narrower and broader unresolved-state definitions
- Separate prize and non-prize problems
- Separate statement formalization from verified mathematical resolution
- Vary the required verification threshold only through a versioned prospective specification
- Report narrow, medium, and broad AI-attribution bands separately if AI-assisted events occur
Limits
- The first 100 Erdős problem numbers are a fixed and interpretable cohort, not a representative random sample of mathematics.
- Baseline resolved statuses are not reconstructed as historical events because catalogue update dates are not solution dates.
- A status transition can lag the mathematical result while expert checking and catalogue maintenance occur.
- Problem difficulty and importance vary sharply; raw resolution counts must be shown alongside prize, formalization, and problem-tag strata.
- The prospective series begins with zero post-freeze events and cannot estimate a rate change until follow-up accumulates.
Data and sources
Source commit 881735e82124ab8ad7adea9b7d0aeb3c026dcb95
SHA-256: 69719796f01fbe3a33913d14d1307502fa4361a307fa8e4674d20163a745eb0c