Pictures appear throughout mathematical history. The goal of the Mathematical Picture Language Project at Harvard is to reevaluate ways that one can use pictures, not only to gain mathematical insights, but also to prove mathematical theorems.

Arthur Jaffe and Zhengwei Liu began their collaboration by studying some problems in subfactor theory and quantum information. This led them to the discovery of the quon language, after which they realized that the quon language also sheds light on several other areas of mathematics. Here you can find links to this research or to articles about our project.

These events motivated the current project to use virtual and real mathematical concepts, simulated by pictures, as a tool to find new understanding ranging across operator algebras, subfactor theory, harmonic analysis, topology, representation theory, statistical physics, topological field theory, quantum field theory, and possibly other fields.

The Picture Language Project at Harvard was originally made possible by a generous grant from the Templeton Religion Trust, in a program under the auspices of W. Christopher Stewart. This project has support starting May 2019 under a grant from ARO. Starting June 2020 this project is also part of a Multi-University Research Project (MURI) under ARO.