A Proof Is More Than a Correct Answer
A result can be correct without making its reason clear. On proof, explanation, and the kind of mathematical understanding I want AI to help us pursue.
MATHEMATICS / 6 ESSAYS
Proof, with feeling.
A correct answer can close a problem without ending its questions. These essays follow the space between proof and understanding, including what AI can contribute and what we still need to ask.
AI Can Find the Lemma. I Still Want to Know Why.
AI proof systems can help discover a path through a mathematical problem. I care just as much about whether the path teaches us where we are.
The Seduction of a Beautiful Counterexample
One counterexample can undo a confident claim. I love that power, and I think enjoying it too much can make a mathematician worse at listening.
Probability Is a Lesson in Humility
A probability is a commitment to uncertainty, not an escape from it. On base rates, surprising evidence, and the danger of a confident number.
There Is More to Mathematics Than Being Fast
Fast answers are useful. I think treating speed as the main signal of mathematical ability teaches people to hide the work that produces understanding.
The Comfort of an Unfinished Proof
On wanting an answer more than wanting to understand.