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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.
Prime entries are random variables. -/ measurable_of_prime p : p.Prime → Measurable (f p) /-- Prime entries are independent. -/ iIndepFun_primes : iIndepFun (fun p : Primes ↦ f p) ℙ /-- Primes entries are uniformly distributed on {-1, 1}.…
Let \((\epsilon_k)_{k\geq 0}\) be independently uniformly chosen at random from \(\{-1,1\}\). If \(R_n\) counts the number of real roots of \(f_n(z)=\sum_{0\leq k\leq n}\epsilon_k z^k\) then is it true that, almost surely, \[\lim_{n\to…
OPEN LEANSKIPPEDanalysis · polynomials · probability
Let \(f(z)=\sum_{0\leq k\leq n} \epsilon_k z^k\) be a random polynomial, where \(\epsilon_k\in \{-1,1\}\) independently uniformly at random for \(0\leq k\leq n\). Is it true that, if \(R_n\) is the number of roots of \(f(z)\) in…
Is it true that all except at most \(o(2^n)\) many degree \(n\) polynomials with \(\pm 1\)-valued coefficients \(f(z)\) have \(\lvert f(z)\rvert <1\) for some \(\lvert z\rvert=1\)? The answer is yes: Littlewood [Li66] conjectured the…
Let \(0<\epsilon<1\) and let \(g_\epsilon(N)\) be the minimal \(k\) such that if \(G\) is an abelian group of size \(N\) and \(A\subseteq G\) is a uniformly random subset of size \(k\), and \[F_A(g) = \#\left\{ S\subseteq A : g =…
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.