In January, mathematicians, historians, artists, and educators gathered at the Institut Henri Poincaré for a workshop on mathematical meaning. Their focus was to ask what it means for an illustration to be rigorous. The discussions, occurring six months after the workshop, led to an article accepted in the Notices, written in the context of the Leiden Declaration.
The past months have seen a heartfelt outpouring of viewpoints on what it means to do mathematics as a human being. Mathematical illustration, including computer graphics and other media beyond symbolic communication, is one activity that goes beyond proof-writing. Bryna Kra describes the current problem: theorem production is the most important measure of success, though it has always been a proxy for understanding.
AI has broken the scarcity of deep theorems. Silvia De Toffoli and Eamon Duede reject the idea that mathematics is a game machines can win, viewing it instead as a body of knowledge engaged with by a scholarly community. Matilde Marcolli argues the big theorems were never the point, only a chosen value system.
Grant Sanderson asks how to give real credit to other forms of mathematical understanding. The paper traces how hand-drawing was required at Gaspard Monge's École Polytechnique, where historian Frédéric Brechenmacher noted "Drawing was knowing." The tradition persisted despite being set aside in the twentieth century. The Illustrating Mathematics community, shaped during a 2019 ICERM semester, brings together mathematicians who develop images, models, software, and experiences of mathematics.
Source: Hacker News · Summarized by HeadlinesBriefing