The essence of math lies in the artistic progression from observation to theoretical construction. Aesthetics and beauty are diagnostic tools for evaluating mathematical truth.
Podcast: A 4-hour Interview with Carina Hong: AI for Math, Lean, Proofs from The Book, and Intuition
We oftentimes picture math as right or wrong. But Mathematicians have a third axis: beauty.
Aesthetics play a central role. Even if a proof is logically correct, mathematicians will debate whether it is "beautiful" or "natural."
Beauty often signals that two seemingly distinct fields have found a deep, hidden connection. (like the Modularity Theorem as a famous example of elegance. It links algebraic equations with the geometry of elliptic curves.)
This shared artistic intuition acts as a guiding force. Because mathematicians share similar training, they develop a profound sense of what a "natural" progression should look like.
This pairs with Buckminster Fuller's idea that when a finished solution isn't beautiful, something is still wrong.