logic-foundationsAug 19, 2026Significance 14/100Registry: lean verified
Prior state unknown→independent
Independent of ZFC, which is why this entry is the first to carry that result rather than proved or disproved. Both directions are formalized: Hechler's 1972 construction gives a model where the answer is no, and adding $\mathfrak{c}^+$ random reals over a model of CH gives one where it is yes.
The credit is shared and mostly human. Newelski, Pawlikowski and Seredynski settled the problem's second question in 198…
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algebraJul 20, 2026Significance 14/100Registry: lean verified
Prior state unknown→proved
Can a nonabelian group admit a Rota-Baxter operator that is surjective but not injective? A construction shows yes.
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algebraJul 20, 2026Significance 13/100Registry: lean verified
Prior state unknown→disproved
Must the right-relatively convex subgroups of a right-orderable nonabelian group form a sublattice of its subgroup lattice? A construction shows they need not.
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number-theoryJul 20, 2026Significance 13/100Registry: lean verified
Prior state unknown→proved
Proves positive lower density. The Formal Conjectures encoding asks for Set.HasPosDensity, a density that exists and is positive; erdosproblems.com says Erdos most likely meant lower density.
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algebraJul 20, 2026Significance 13/100Registry: lean verified
Prior state unknown→disproved
For an extension $G = A \rtimes B$ of elementary abelian $p$-groups with $a \in A$ satisfying $C_B(a) = 1$, must $H = \langle a, B\rangle$ satisfy $\operatorname{rank}(Z(H) \cap H') \le \operatorname{rank}(B)$? An explicit extension violates the bound.
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number-theoryJul 19, 2026Significance 13/100Registry: lean verified
Prior state unknown→proved
The headline is the constant, and its two halves have different histories. The lower bound, $\liminf (f(n)-2n)/(n/\log n) \ge 4029639598/25970038185$, is not new here: it is Mausberg's thirteen-layer valuation cut, posted to the erdosproblems.com forum in May 2026 and credited as such in the paper. Its author wrote there that it "does not prove an upper bound, nor does it prove that an asymptotic constant exists."…
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combinatoricsJul 23, 2026Significance 13/100Registry: lean verified
Prior state unknown→proved
Which finite triple systems occur in every triple system of uncountable chromatic number? The claimed characterization: exactly those that, after removing isolated vertices, are linear, have every hyperedge-node of their Levi graph meeting a bridge, and have every Berge cycle even.
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algebraJul 20, 2026Significance 13/100Registry: lean verified
Prior state unknown→proved
If the power graph of a finite group contains no induced path on four vertices, must it also contain no induced cycle of length at least four - that is, is every cograph power graph chordal?
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algebraJul 20, 2026Significance 13/100Registry: lean verified
Prior state unknown→proved
If $\operatorname{CT}_{(k)}$ is generated by all horizontal class transpositions with modulus at most $k$, is $\operatorname{CT}_{(k)} \cong S_{\operatorname{lcm}(2,\dots,k)}$ for every $k \ge 4$?
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number-theoryMay 21, 2026Significance 12/100Registry: lean verified
Prior state unknown→proved
parts (i) and (ii) resolved - a near-linear-density construction exists, refuting the N^{1-c} decay; the reciprocal-sum part remains open
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number-theoryApr 23, 2026Significance 12/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #202.” The registry entry and named primary source contain the available statement and scope.
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analysisJun 22, 2026Significance 12/100Registry: lean verified
Prior state unknown→proved
Both parts claimed answered affirmatively, with a Lean formalization; two proof claims are filed on erdosproblems.com but the problem is still listed open
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number-theoryMar 31, 2026Significance 11/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #997.” The registry entry and named primary source contain the available statement and scope.
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number-theoryJul 1, 2026Significance 11/100Registry: lean verified
Prior state unknown→proved
Let $a,b,c>1$ be pairwise coprime integers. Is every large integer a sum of distinct numbers of the form $a^k b^l c^m$ ($k,l,m\ge 0$), none dividing another?
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geometry-topologyJul 29, 2026Significance 11/100Registry: lean verified
Prior state unknown→disproved
If $f(n)$ is the maximum total side length of $n$ interior-disjoint squares packed in the unit square, is $f(k^2 + 1) = k$? An exact rational configuration packs $17$ squares with total side length greater than $4$, refuting the identity at $k = 4$.
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combinatoricsJun 21, 2026Significance 11/100Registry: lean verified
Prior state unknown→proved
a polynomial bound for N(k,2), stronger than the exponential bound asked for; the two-parameter problem remains open
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combinatoricsApr 21, 2026Significance 11/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #610.” The registry entry and named primary source contain the available statement and scope.
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analysisApr 30, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
An elementary solution via a primitive-row decomposition of the Chebyshev-node measures; the main theorem is formalized in Lean, but erdosproblems.com still lists the problem open
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number-theoryJan 17, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #281.” The registry entry and named primary source contain the available statement and scope.
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algebraMay 21, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
For a pure O-sequence $h = (h_0, \dots, h_e)$ of codimension three and type two, is $h_i^2 \ge h_{i-1} h_{i+1}$ for every interior index $i$? The stated monomial case is proved; the broader level-Hilbert-function case remains open.
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combinatoricsApr 23, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #1014.” The registry entry and named primary source contain the available statement and scope.
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number-theoryMay 3, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #351.” The registry entry and named primary source contain the available statement and scope.
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number-theoryJan 5, 2026Significance 10/100Registry: lean verified
Prior state unknown→disproved
VibeMathed records this result as “Erdős Problem #871.” The registry entry and named primary source contain the available statement and scope.
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number-theoryApr 9, 2026Significance 10/100Registry: lean verified
Prior state unknown→disproved
VibeMathed records this result as “Erdős Problem #1141.” The registry entry and named primary source contain the available statement and scope.
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number-theoryJan 10, 2026Significance 10/100Registry: lean verified
Prior state unknown→disproved
VibeMathed records this result as “Erdős Problem #397.” The registry entry and named primary source contain the available statement and scope.
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number-theoryJul 8, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
h₄(n) = 4 for every n ≥ 331,777, with improved global bounds; the broader problem remains open
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quantum-information-computingMay 21, 2026Significance 10/100Registry: lean verified
Prior state unknown→disproved
the N = 4, D ≥ 4 family is fully ruled out; the general two-parameter problem remains open
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geometry-topologyJul 13, 2026Significance 10/100Registry: lean verified
Prior state unknown→disproved
natural readings of the ambiguous historical statement are disproved
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number-theoryJan 10, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #729.” The registry entry and named primary source contain the available statement and scope.
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geometry-topologyJul 13, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
the infinite-chromatic subquestion is proved; the rest of the problem remains open
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number-theoryFeb 4, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #347.” The registry entry and named primary source contain the available statement and scope.
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number-theoryMar 16, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #1148.” The registry entry and named primary source contain the available statement and scope.
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number-theoryJan 11, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #401.” The registry entry and named primary source contain the available statement and scope.
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combinatoricsJun 9, 2026Significance 10/100Registry: lean verified
Prior state unknown→disproved
VibeMathed records this result as “Erdős Problem #619.” The registry entry and named primary source contain the available statement and scope.
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number-theoryApr 14, 2026Significance 10/100Registry: lean verified
Prior state unknown→proved
VibeMathed records this result as “Erdős Problem #258.” The registry entry and named primary source contain the available statement and scope.
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quantum-information-computingMay 21, 2026Significance 10/100Registry: lean verified
Prior state unknown→disproved
the diagonal family is ruled out; the broader two-parameter problem remains open
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