A Mathematical Picture Language Program
Arthur Jaffe, Zhengwei Liu
TL;DR
This paper discusses a philosophy of using picture language in mathematics, emphasizing a bidirectional relationship between visual representations and mathematical concepts to facilitate understanding and exploration.
Contribution
It proposes a program to understand various mathematical subjects through virtual and real concepts simulated by pictures, highlighting the interplay between visualization and abstraction.
Findings
Introduces a philosophy of picture language in mathematics.
Proposes a bidirectional process of abstraction and simulation.
Suggests a framework for understanding mathematical concepts via pictures.
Abstract
We give an overview of our philosophy of pictures in mathematics. We emphasize a bi-directional 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.
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