Every problem here was open when it entered the pool.
Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
Number theory
Riemann Hypothesis
The **Riemann Hypothesis**: all non-trivial zeros of the Riemann zeta function have real
part 21. That is, if ζ(s)=0, s=1
, and
s
is not a trivial zero
−2(n+1)
for some
n∈N
, then
Re(s)=21
.
This is the official Millennium Prize Problem as posed by the
[Clay Mathematics Institute](https://www.claymath.org/wp-content/uploads/2022/05/riemann.pdf).
This uses the
RiemannHypothesis
type from Mathlib, which is defined as
∀ (s : ℂ), riemannZeta s = 0 → (¬∃ n : ℕ, s = -2 * (n + 1)) → s ≠ 1 → s.re = 1 / 2
.
$2,662 bounty·nobody has started
week of 29 Sept 2025 · nothing publishedweek of 6 Oct 2025 · nothing publishedweek of 13 Oct 2025 · nothing publishedweek of 20 Oct 2025 · nothing publishedweek of 27 Oct 2025 · nothing publishedweek of 3 Nov 2025 · nothing published
Solve it
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
J. Neukirch, Algebraic Number Theory, Springer (Grundlehren 322), 1999, Chapter VII, §5.
D. A. Marcus, Number Fields, Springer (GTM 81), 1977, Chapter VII.
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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