If math is more than proof, we need to better celebrate the rest of it

Grant Sanderson argues that mathematics should reward “motivated explanations”—work that clarifies why a theorem is relevant and how it fits into broader context—rather than focusing solely on proofs. He defines motivated explanations as narratives that begin with a relatable, sometimes incorrect idea, then refine it to reveal deeper insights. Elevating this genre would better reflect mathematicians’ contribution to human understanding and counter the misconception that proof-generating machines render researchers obsolete.