New Bounds for the Grothendieck Constant Pin Down Its Tenths Digit
New Lower and Upper Bounds for the Grothendieck Constant
Researchers have established new lower and upper bounds for the Grothendieck constant, a fundamental quantity in computer science and mathematics. Their work determines the previously unknown tenths digit of the constant to be 7. The lower bound is achieved by a novel approach that limits the performance of asymptotically optimal Krivine schemes, while the upper bound comes from the first asymptotic construction of rounding schemes. These results were discovered through a long-running collaboration between humans and an AI research system.
The bounds were discovered by a long-running collaborative effort of humans and a long-horizon AI research system that we engineered.
- lukeplato
related paper on the long-horizon AI research system used: https://arxiv.org/pdf/2608.11195
- throwaway81523
Interesting. I wonder if there has also been any recent progress on the Legendre constant. Kidding.