Jaffe, ArthurLiu, Zhengwei2018-02-262017Jaffe, Arthur M., and Zhengwei Liu. 2017. “Mathematical picture language program.” Proceedings of the National Academy of Sciences of the United States of America 115 (1): 81-86. doi:10.1073/pnas.1710707114. http://dx.doi.org/10.1073/pnas.1710707114.http://nrs.harvard.edu/urn-3:HUL.InstRepos:34869048We 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.en-USMathematicspictorial mathematicspicture languagepicture proofabstraction and simulationreal and virtualJournal Article2018-02-2610.1073/pnas.1710707114