Irrationality among classical odd Riemann zeta values

Is at least one of ζ(7),ζ(9),…,ζ(21) irrational, where ζ is the classical Riemann zeta function? This finite-window target does not identify one particular irrational value.

Why it matters and what counts as progress

Why it matters: It narrows the interval of odd zeta values guaranteed to contain an irrational number, without identifying a particular value.

What counts as progress: Prove that a shorter set of odd zeta values contains an irrational number, or establish irrationality of one specified value.

How the problem developed

2001 · Partial result [1]
Wadim Zudilin Proved that at least one of ζ(5), ζ(7), ζ(9), and ζ(11) is irrational.
30 Sept 2026 · Formal result [2]
Gaurav Devi and Claude agents Reported a Lean-checked alternative: at least one of ζ(7), ζ(9), ζ(11), ζ(13), ζ(15), ζ(17), ζ(19), and ζ(21) is irrational.