> AI will soon be better than almost all human mathematicians at math problem solving.

You misunderstand what mathematicians do. My favorite example is this: Birds can fly, but can they use their intuition to create a theory of flight, and then use that to build a plane ? This book by Bessis paints this really well [1].

[1] https://www.amazon.com/Mathematica-Secret-World-Intuition-Cu...

Bessis [1] argues that formalism - or loosely math writing - is foundational to clarifying intuition/meaning in a way that natural language cannot. Imagine it as a scalpel carving out precise shapes from the blur of images we carry thereby allowing us to "see" things we otherwise cannot.

I am curious to try out lean to understand how definitions in lean are able to operationally capture meaning in an unambiguous manner.

[1] https://www.amazon.com/Mathematica-Secret-World-Intuition-Cu...

Thanks for the mention. I loved the book [1], and it started me off on a journey to spark intuition, and sensory (visual) connection.

On another note, I was shocked to find that some members of my family have aphantasia which is a complete inability to visually imagine geometric figures or pictures, and yet, they were good at math. So, there are faculties beyond visual imagination which are invoked, and even within visual imagination, there is a spectrum among people as to its strength, and quality.

[1] https://www.amazon.com/Mathematica-Secret-World-Intuition-Cu...

With llms and theorem provers doing the formalism, what is left is intuition - love the intuitionist focus in this book, also tying into what Bessis said in [1] I intend to read this book in depth.

Author: please fix the html rendering.

[1] https://www.amazon.com/Mathematica-Secret-World-Intuition-Cu...

Mathematician David Bessis describes similar exercises in his book [ref] - wherein he explores a room blindfolded to awaken other senses, or visualize the places he has been to.

[ref] https://www.amazon.com/Mathematica-Secret-World-Intuition-Cu...