Science
Researcher reports lowering upper bound for de Bruijn–Newman constant
A computer-assisted proof reduces the ceiling for the constant linked to the Riemann hypothesis to 0.1787854.
The short version
- Independent researcher Jude Gomila announced a computer-assisted proof lowering the upper bound of the de Bruijn–Newman constant (Λ) from 0.2 to 0.1787854.
- The result relies on exact arithmetic and millions of machine-checked interval certificates, leaving the constant bounded between 0 and 0.1787854.
- Because the Riemann hypothesis holds if and only if Λ ≤ 0, reducing its upper bound narrows the mathematical interval required to prove the hypothesis.
Key facts
- Jude Gomila reported lowering the upper bound of the de Bruijn–Newman constant (Λ) to at most 0.1787854 using a computer-assisted proof.[Hacker News]
- The proof uses exact arithmetic based on over 3.1 million machine-checked interval certificates.[Hacker News]
- The Riemann hypothesis is mathematically equivalent to the statement that the de Bruijn–Newman constant is less than or equal to zero (Λ ≤ 0).[Hacker News]
- Rodgers and Tao established in 2018 that Λ ≥ 0, fixing the lower bound of the constant.[Hacker News]
- The new bound builds on Terence Tao's Polymath 15 barrier method and Platt and Trudgian's 2020 verification height for the Riemann hypothesis.[Hacker News]
What remains uncertain
- The proof relies on open peer and community review of the posted audit repository and GitHub issue tracking to verify all machine-checked steps.[Hacker News]