frontiers / frontier
Erdős problems frontier
- id
- vfr_37aec80d874a0239
- license
- CC-BY-4.0
- findings
- 1,256
- accepted core
- 6
- contested
- 0
- links
- 17
- sources
- 1,234
- evidence
- 1,256
- avg conf
- 0.98
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Brief & export
findings 1256 · accepted 0 · open questions 862 · contested 0
strongest · none formally accepted
bibliography · 1234
- cap_61973ee16b553d57 · vc_0b8d42651478ba5c
- cap_61973ee16b553d57 · vc_10652d5605c710a4
- cap_61973ee16b553d57 · vc_edf93f3feefa98b9
- cap_61973ee16b553d57 · vc_18ab22bfdf5f22c9
- cap_61973ee16b553d57 · vc_89ce0c93438e9d34
- cap_61973ee16b553d57 · vc_601ddd52c88d735e
- cap_61973ee16b553d57 · vc_56dbc792dde278f5
- cap_61973ee16b553d57 · vc_631ecd4b3685c88d
- cap_61973ee16b553d57 · vc_945fc4898649822e
- cap_61973ee16b553d57 · vc_f3c4b7477fe4e685
- cap_61973ee16b553d57 · vc_c6c83b329e3da7d7
- cap_61973ee16b553d57 · vc_7b7f65f955e39db9
- cap_61973ee16b553d57 · vc_13758e63de497e47
- cap_61973ee16b553d57 · vc_beb30fc3032ec0b9
- cap_61973ee16b553d57 · vc_86c0670c151d4d3c
- cap_61973ee16b553d57 · vc_74ebe3e862d5a69e
- cap_61973ee16b553d57 · vc_bbc2adf45fcd362b
- cap_61973ee16b553d57 · vc_26611cd79466920d
- cap_61973ee16b553d57 · vc_5d6a576e27532863
- cap_61973ee16b553d57 · vc_58ded8f552235c54
- cap_61973ee16b553d57 · vc_0b6f6f791a2f7f7a
- Guth, Katz 2015, Annals of Mathematics (2015)
- cap_61973ee16b553d57 · vc_3f409d09aaf42b70
- cap_61973ee16b553d57 · vc_27b5bd200aa50906
- cap_61973ee16b553d57 · vc_363bac7946a3c9f1
- cap_61973ee16b553d57 · vc_590c031fd46bdcf5
- cap_61973ee16b553d57 · vc_216b1ebb9d80271b
- cap_61973ee16b553d57 · vc_5227bc43a197f60a
- cap_61973ee16b553d57 · vc_9f07e8a7cea36c38
- cap_61973ee16b553d57 · vc_64e9e3a505e94b0c
export
# Erdős problems frontier
This frontier holds 1256 findings (0 accepted) over 1234 sources.
## Significance
- Erdős Problem #105 has status 'disproved (lean)'. Topics: geometry. Erdős prize: $50. Not yet formalized in Lean. OEIS: N/A. (ingest)
- Erdős Problem #40 remains OPEN. Statement: For what functions $g(N) → \infty$ is it true that $$\lvert A\cap \{1,\ldots,N\}\rvert \gg \frac{N^{1/2}}{g(N)}$$ implies $\limsup 1_A\ast 1_A(n)=\infty$? Topics: number theory, additive basis. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. (ingest)
- Erdős Problem #461 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. (ingest)
- Erdős Problem #861 is SOLVED. Topics: number theory, sidon sets. Erdős prize: no. Not yet formalized in Lean. OEIS: A143824, A227590, A003022, A143823. (ingest)
- Erdős Problem #71 has been PROVED (Erdős's conjecture holds). Topics: graph theory, cycles. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. (ingest)
- Erdős Problem #641 has been DISPROVED (a counterexample is known). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. (ingest)
- Erdős Problem #343 has been PROVED (Erdős's conjecture holds). Topics: number theory, complete sequences. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. (ingest)
- Erdős Problem #903 has been PROVED (Erdős's conjecture holds). Topics: combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. (ingest)
- Erdős Problem #610 has been PROVED (Erdős's conjecture holds). Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: possible. (ingest)
- Erdős Problem #749 remains OPEN. Statement: Let $\epsilon>0$. Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1-\epsilon$ and yet $1_A\ast 1_A(n) \ll_\epsilon 1$ for all $n$? Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A. (ingest)
- Erdős Problem #802 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A. (ingest)
- Erdős Problem #186 is SOLVED. Topics: additive combinatorics. Erdős prize: no. Not yet formalized in Lean. OEIS: A389784. (ingest)
## Open questions
- Erdős Problem #105 has status 'disproved (lean)'. Topics: geometry. Erdős prize: $50. Not yet formalized in Lean. OEIS: N/A.
- Erdős Problem #40 remains OPEN. Statement: For what functions $g(N) → \infty$ is it true that $$\lvert A\cap \{1,\ldots,N\}\rvert \gg \frac{N^{1/2}}{g(N)}$$ implies $\limsup 1_A\ast 1_A(n)=\infty$? Topics: number theory, additive basis. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
- Erdős Problem #461 remains OPEN. Topics: number theory, primes. Erdős prize: no. Not yet formalized in Lean. OEIS: possible.
- Erdős Problem #749 remains OPEN. Statement: Let $\epsilon>0$. Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1-\epsilon$ and yet $1_A\ast 1_A(n) \ll_\epsilon 1$ for all $n$? Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
- Erdős Problem #802 remains OPEN. Topics: graph theory. Erdős prize: no. Not yet formalized in Lean. OEIS: N/A.
- Erdős Problem #719 remains OPEN. Topics: graph theory, hypergraphs. Erdős prize: no. Not yet formalized in Lean. OEIS: possible.
- Erdős Problem #14 remains OPEN. Topics: number theory, sidon sets, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A143824, possible.
- Erdős Problem #1002 remains OPEN. Statement: For any $0<\alpha<1$, let $f(\alpha,n)=\frac{1}{\log n}\sum_{1\leq k\leq n}(\tfrac{1}{2}- \{ \alpha k\})$. Does $f(\alpha,n)$ have an asymptotic distribution function? In other words, is there a non-decreasing function $g$ such that $g(-\infty)=0$, $g(\infty)=1$, and $\lim_{n\to \infty}\lvert \{ \alpha\in (0,1): f(\alpha,n)\leq c\}\rvert=g(c)$? Topics: analysis, diophantine approximation. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.