A Modern Reorganization of Mathematics

[Everyone is doing guest posts these days, so here’s one about the Weil conjectures from (in alphabetical order) Bin Dong, Nailin Guan, Jiedong Jiang, Ruochuan Liu, Christian Merten, Xiangyu Pan, Tingxiao Shi, Bin Wu, Edison Xie and Wei Yang] We mathematicians need to put far greater effort into communicating mathematical ideas. To accomplish this, we need to pay much more attention to communicating not just our definitions, theorems, and proofs, but also our ways of thinking. William P. Thurston, On Proof and Progress in Mathematics (1994) Since the beginning of mathematical study, people have been trying to present mathematics and to communicate mathematical ideas. Mathematicians carefully choose names and symbols that match their intuitions in order to improve understanding. For most of this history, the medium for writing down a piece of mathematics has been linear text: a paper consisting of definitions, theorems, and proofs. In modern mathematics, however, the size and…

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