More than two thirds of the zeros of the Riemann zeta function lie on the critical line

This should conclusively resolve "that's a famous conjecture, yes, but nobody was seriously working on it" objection, which I think had some merits for previous cases.

Let me quote Claude:

History of the problem. That ζ(s) has infinitely many zeros on the critical line was shown by Hardy [Har14] in 1914. That a positive proportion of all zeros lie there is due to Selberg [Sel42] in 1942. Selberg's constant was small and not made explicit. Thirty-two years passed before Levinson [Lev74], by an entirely new and strikingly direct method based on mollifying ζ near the line, showed that one may take κ = 1/3. Conrey [Con89] refined the mollifier to reach κ > 2/5; further refinements by Bui, Conrey and Young [BCY11], Feng [Fen12], and Pratt, Robles, Zaharescu and Zeindler [PRZZ20] have brought the record to κ > 5/12, where it has stood since 2020.

For comparison, More than five-twelfths of the zeros of ζ are on the critical line (PRZZ 2020).