Mathematician Proposes Elevating 'Motivated Explanations' Alongside Proofs in Academia

The Evolving Role of Proofs in Mathematics

The mathematics community widely believes that solving problems and generating proofs serve as proxies for the ultimate goal of furthering human understanding. However, the emergence of AI capable of generating proofs without human understanding challenges the traditional value of proofs as the primary measure of contribution.

Introducing 'Motivated Explanations'

The author proposes that academia should formally define and credit "motivated explanations." These explanations focus on answering "how would you think of that?" rather than merely presenting a solution or proof. This type of work, distinct from popularization, requires deep expertise and aims to clarify the underlying intuition and thought processes behind mathematical concepts.

Elevating Non-Traditional Contributions

The proposal suggests that giving academic credit to motivated explanations would elevate their status, aligning with the significant mindshare mathematicians already dedicate to such work. This shift would also help those outside the field better understand the diverse contributions of mathematicians, countering the misconception that proof-generating machines could render human mathematicians obsolete.