reading
AI, proof, and how mathematical work is changing
A few reflections to keep around while thinking about AI, proof, and how mathematical work is changing.
Mathematical methods and human thought in the age of AI
Preprint, arXiv:2603.26524
Use AI if it helps; Tao does too (argument from authority, yes). But keep taste and exposition on your side: check the mathematics, and make the idea visible.
“[I]t not just shows that [...] but provides a causal narrative for how that entailment was possible.”
Correctness, Artificial Intelligence, and the Epistemic Value of Mathematical Proof
Forthcoming in the Journal for the Philosophy of Mathematics
Good for separating correctness from what a proof actually teaches us.
“That a mathematical proof be correct is neither sufficient nor necessary for it to have epistemic value.”
Varieties of mathematical understanding
Bulletin of the American Mathematical Society 59(1), 99–117
Avigad is a good reminder that understanding is not a vague bonus after the proof, but part of what a proof is supposed to give.
“It is common to say that the goal of mathematics is to obtain a conceptual understanding of mathematical phenomena, and a deep understanding at that.”
On proof and progress in mathematics
Bulletin of the American Mathematical Society 30(2), 161–177
A very old paper, in the best sense, arguing that mathematics is above all good communication.
“The measure of our success is whether what we do enables people to understand and think more clearly and effectively about mathematics.”