Theorems’ Almanack

This article is part of a series on The Structure of Theorems. See also:
1. Theorems’ Almanack; 2. The Greatest Theorem; 3. Game of Theorems

Theorems are the hallmark of the mathematical trade. In them reside mathematical rigor, mathematics’ unspoken holy grail. They also possess a kind of mystique. “I’m scared of upper-division math classes,” I once overheard a student say. “It’s all proofs.”

Theorems, independent of their mathematical content, are interesting in their own right, because they delineate the mathematical landscape. Open a textbook of mathematics, and you’ll find the difficult universe of mathematics, once uncharted and unknown, arrayed and packaged before your eyes. “Theorem: ___________. Proof: _____________.

I attempt here to understand mathematical theorems, in a purely logical sense: for what they are, for what they do, and for what role they play. Continue reading