A picture is worth 1,000 words, the saying goes, but a group of Harvard-based scientists is hoping that it may also be worth the same number of equations.
Pictorial laws appear to unify ideas from disparate, interdisciplinary fields of knowledge, linking them beautifully like elements of a da Vinci painting. The group is working to expand the pictorial mathematical language first outlined last year by Arthur Jaffe, the Landon T. Clay Professor of Mathematics and Theoretical Science, and postdoctoral fellow Zhengwei Liu.
“There is one word you can take away from this: excitement,” Jaffe said. “And that’s because we’re not trying just to solve a problem here or there, but we are trying to develop a new way to think about mathematics, through developing and using different mathematical languages based on pictures in two, three, and more dimensions.”
Last year they created a 3-D language called quon, which they used to understand concepts related to quantum information theory. Now, new research has offered tantalizing hints that quon could offer insights into a host of other areas in mathematics, from algebra to Fourier analysis, as well as in theoretical physics, from statistical physics to string theory. The researchers describe their vision of the project in a paper that appeared Jan. 2 in the journal Proceedings of the National Academy of Sciences.
“There has been a great deal of evolution in this work over the past year, and we think this is the tip of the iceberg,” Jaffe said. “We’ve discovered that the ideas we used for quantum information are relevant to a much broader spectrum of subjects. We are very grateful to have received a grant from the Templeton Religion Trust that enabled us to assemble a team of researchers last summer to pursue this project further, including undergraduates, graduate students, and postdocs, as well as senior collaborators at other institutions.”
The core team involves distinguished mathematicians such as Adrian Ocneanu, a visiting professor this year at Harvard, Vaughan Jones, and Alina Vdovina. As important are rising stars who have come to Harvard from around the world, including Jinsong Wu from the Harbin Institute of Technology and William Norledge, a recent graduate from the University of Newcastle. Also involved are students such as Alex Wozniakowski, one of the original members of the project and now a student at Nanyang Technological University in Singapore, visiting graduate students Kaifeng Bu from Zhejiang University in Hangzhou, China, Weichen Gu and Boqing Xue from the Chinese Academy of Sciences in Beijing, Harvard graduate student Sruthi Narayanan, and Chase Bendarz, an undergraduate at Northwestern University and Harvard.