A team of more than 80 mathematicians from 12 countries has begun charting the terrain of rich, new mathematical worlds, and sharing their discoveries on the Web. The mathematical universe is filled with both familiar and exotic items, many of which are being made available for the first time.
The "L-functions and Modular Forms Database," abbreviated LMFDB, is an intricate catalog of mathematical objects and the connections between them. Making those relationships visible has been made possible largely by the coordinated efforts of a group of researchers developing new algorithms and performing calculations on an extensive network of computers. The project provides a new tool for several branches of mathematics, physics, and computer science.
A "periodic table" of mathematical objects
Project member John Voight, from Dartmouth College, observed that "our project is akin to the first periodic table of the elements. We have found enough of the building blocks that we can see the overall structure and begin to glimpse the underlying relationships." Similar to the elements in the periodic table, the fundamental objects in mathematics fall into categories. Those categories have names like L-function, elliptic curve, and modular form. The L-functions play a special role, acting like 'DNA' which characterizes the other objects. More than 20 million objects have been catalogued, each with its L-function that serves as a link between related items. Just as the value of genome sequencing is greatly increased when many members of a population have been sequenced, the comprehensive material in the LMFDB will be an indispensible tool for new discoveries.
The LMFDB provides a sophisticated web interface that allows both experts and amateurs to easily navigate its contents. Each object has a "home page" and links to related objects, or "friends." Holly Swisher, a project member from Oregon State University, commented that the friends links are one of the most valuable aspects of the project: "The LMFDB is really the only place where these interconnections are given in such clear, explicit, and navigable terms. Before our project it was difficult to find more than a handful of examples, and now we have millions."