A guest post by Grant Sanderson argues that solving problems and generating proofs have long served as proxies for the true goal of mathematicians: furthering human understanding. When proofs can be generated without that understanding, it undermines their value as a proxy. Sanderson proposes that the mathematics community more firmly define a notion of a “motivated explanation” and give such work academic credit similar to what generating new proofs of open problems has had historically.

He believes elevating motivated explanations is an important step to help those outside of math better understand what mathematicians contribute. If outsiders believe that proof-generating machines render mathematicians obsolete, while insiders see that as a misconception, it’s incumbent on this community to better project its true values through the kind of work that it rewards. Outsiders can be forgiven for this misunderstanding if the work most celebrated skews heavily toward generating proofs, while clarification and exposition are treated as second-class.

Sanderson acknowledges an obvious personal bias, noting his non-traditional career in math focused on producing videos. He clarifies that elevating motivated explanations doesn’t mean popularization, but any work primarily aiming to answer the question “how would you think of that?”, even if the subject matter requires deep expertise to appreciate. He defines a motivated explanation as work where definitions sit in the middle, new constructions enter only if the problem has been clearly established, and it’s okay to start with an idea that’s not quite right but relatable.