L-Functions and Modular Forms Database

The LMFDB is an extensive database of mathematical objects arising in Number Theory.

The "L-functions and Modular Forms Database," or LMFDB, is a detailed atlas of mathematical objects that maps out the connections between them. The LMFDB exposes deep relationships and provides a guide to previously uncharted territory that underlies current research in several branches of physics, computer science, and mathematics. This coordinated effort is part of a massive collaboration of researchers around the globe.

The scale the computational effort that went into creating the LMFDB is staggering: Multiple teams of researchers spent a total of nearly 1,000 years of computer time on calculations. One recent computation by Principal Research Scientist Andrew Sutherland at MIT used more than 72,000 cores of Google's Compute Engine to complete in one weekend a tabulation that would have taken more than a century on a single computer. As noted by Sutherland, "Computations in number theory are often amenable to massive parallelization, and this allows us to scale them to the cloud." Some of these calculations are so intricate that only a handful of experts know how to do them, and some are so big that it makes sense to run them only once, and then share the verified results.