If math is more than proof, we need to better celebrate the rest of it
Points and comments are a snapshot, not live.
Grant Sanderson argues mathematics should better celebrate motivated explanations, not just proofs.
Sanderson proposes that mathematical work be valued not solely by proofs but by 'motivated explanations' that address how one would discover an idea. He defines these as explanations where definitions sit in the middle, not at the start, and where flawed initial attempts are allowed. He cites exemplars: the Princeton Companion to Mathematics, Bill Thurston's essay, Timothy Chow's beginner's guide to forcing, and a 2026 paper clarifying an AI-generated proof of Erdős problem #1196. Practical suggestions include treating small problems as talk defenses, establishing journals focused on exposition, and adjusting hiring to value textbooks. The broader goal is to reassure young mathematicians that the field's purpose-advancing human understanding-remains valuable despite AI.
The author acknowledges a personal bias as a math video creator and notes that motivated explanations are inherently more subjective than proofs, but argues that checking motivation is nearly as verifiable as checking logical steps.
What commenters are saying
Top commenters support the direction but raise concerns. The highest-ranked comment invokes Goodhart's Law: when proofs become targets they lose meaning, and difficulty was a signal of understanding now made hollow by AI. Another comment warns the proposal sounds like retreating into 'medieval science' of intuition when machines can already prove. A third thread debates whether AI will ever match human explanation, given explanation requires empathy and shared experience. Two camps emerge: those welcoming a shift toward understanding as the true goal, and those fearing it abandons the objective rigor that attracted many to math. A specific correction notes that Grant Sanderson, not Terence Tao, authored the post.