Reuse in Mathematical Practice: Stanford 2018

What does a mathematician want when she reads a proof written by one of her colleagues? While she may want to be convinced of the truth of the theorem, she often hopes to achieve something else: to be able to reuse the proof components to solve problems of her own. This desire to “reuse” mathematics is reflected in the comments of a variety of research mathematicians, and thus seems to be a goal of the mathematical community. After presenting some simple examples of proofs that help mathematicians achieve this goal, I will consider (i) their value; (ii) how to write them; and (iii) their relationship to proofs that have other virtues, such as being explanatory.