%0 Journal Article
%A Jaffe, Arthur M.
%A Liu, Zhengwei
%T Mathematical picture language program
%D 2018
%R 10.1073/pnas.1710707114
%J Proceedings of the National Academy of Sciences
%P 81-86
%V 115
%N 1
%X We reevaluate ways that one can use pictures, not only to gain mathematical insights, but also to prove mathematical theorems. As an example, we describe ways that the quon language, invented to study quantum information, sheds light on several other areas of mathematics. It results in proofs and algebraic identities of interest in several fields. Motivated by this success, we outline a picture-language program for further research.We give an overview of our philosophy of pictures in mathematics. We emphasize a bidirectional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different subjects, using virtual and real mathematical concepts simulated by pictures.
%U http://www.pnas.org/content/pnas/115/1/81.full.pdf