The [De Bruijn-Newman constant](https://en.wikipedia.org/wiki/De_Bruijn%E2%80%93Newman_constant) $\Lambda$ was defined and upper bounded by $\Lambda \leq 1/2$ in 1950. After 58 years of work, in 2008 this upper bound was finally improved to ... $\Lambda < 1/2$ (a 0% improvement) in a [26-page paper](http://web.yonsei.ac.kr/haseo/p23-reprint.pdf). The best known upper bound is [currently][1] $\Lambda \leq 0.22$. The Riemann hypothesis is equivalent to $\Lambda = 0$, so if it's true then we've got quite a ways to go.


  [1]: http://michaelnielsen.org/polymath1/index.php?title=De_Bruijn-Newman_constant