Regenerated from the community database (Apache-2.0), dated, and linked back to it
from every problem. erdosproblems.com no longer shows statuses (Bloom's reasons); this is the database's record, not our verdict.
908 of 1221 statements are formalized in Lean (Formal Conjectures) · 107 carry an Erdős prize · 3 are independent of ZFC and 9 more can't be proved, or can't be disproved, from ZFC alone · “open” counts the computable and Lean-checked ones too.
**The Erdős discrepancy problem** If \(f\colon \mathbb N \rightarrow \{-1, +1\}\) then is it true that for every \(C>0\) there exist \(d, m \ge 1\) such that \[\left\lvert \sum_{1\leq k\leq m}f(kd)\right\rvert > C?\] This is true, and was…
OPENPRIZE $500PARTIALcombinatorics · ramsey theory · discrepancy · hypergraphs
Let \(\alpha\in[0,1/2)\) and \(n,t\geq 1\). Let \(F^{(t)}(n,\alpha)\) be the smallest \(m\) such that we can \(2\)-colour the edges of the complete \(t\)-uniform hypergraph on \(n\) vertices such that if \(X\subseteq [n]\) with…
OPENFOUNDcombinatorics · ramsey theory · discrepancy
Let \(\alpha > 0\) and \(n \geq 1\). Let \(F(n,\alpha)\) be the largest \(k\) such that there exists some 2-colouring of the edges of \(K_n\) in which any induced subgraph \(H\) on at least \(k\) vertices contains more than…
Let \(A_1,A_2,\ldots\) be an infinite collection of infinite sets of integers, say \(A_i=\{a_{i1}<a_{i2}<\cdots\}\). Does there exist some \(f:\mathbb{N}\to\{-1,1\}\) such that \[\max_{m, 1\leq i\leq d} \left\lvert \sum_{1\leq j\leq m}…
Question 1: Is it true that \(\limsup_{k \to \infty} A_k = \infty\)? Erdős [Er64b] remarks it is "easy to see" that \(\limsup_k \sup_n |\sum_{j \le n} e(k x_j)| = \infty\). Erdős [Er65b] later found a "very easy" proof that…
Let \(E\subseteq (0,1)\) be a meaurable subset with Lebesgue measure \(\lambda(E)\). Is it true that, for almost all \(\alpha\), \[\lim_{n\to \infty}\frac{1}{n}\sum_{1\leq k\leq n}1_{\{k\alpha \}\in E}=\lambda(E)\] for all \(E\)? This is a…
Erdős Problem 995: For every lacunary sequence \((n_k)\) of integers and every \(f \in L^2([0,1])\) with \(\int_0^1 f = 0\), is it true that for almost all \(\alpha\), \[\sum_{k < N} f(\{\alpha n_k\}) = o\!\left(N \sqrt{\log\log…
Is it true that, for every \(\alpha\), the sequence \(\{ \alpha p_n\}\) is not well-distributed, if \(p_n\) is the sequence of primes? The answer is yes, by [APSSV26, Section 4]; a Lean formalisation is available in [Mo26].
Source: teorth/erdosproblems (its own interactive table), Apache-2.0, pulled 2026-10-21. A status here is what that database records, not an independent verification by us, except where a problem page says so.