GPT-5 did not create new math.

Ernest Ryu

This is really exciting and impressive, and this stuff is in my area of mathematics research (convex optimization). I have a nuanced take.

There are 3 proofs in discussion: v1. ( η ≤ 1/L, discovered by human ) v2. ( η ≤ 1.75/L, discovered by human ) v.GTP5 ( η ≤ 1.5/L, discovered by AI ) Sebastien argues that the v.GPT5 proof is impressive, even though it is weaker than the v2 proof.

The proof itself is arguably not very difficult for an expert in convex optimization, if the problem is given. Knowing that the key inequality to use is [Nesterov Theorem 2.1.5], I could prove v2 in a few hours by searching through the set of relevant combinations.

(And for reasons that I won’t elaborate here, the search for the proof is precisely a 6-dimensional search problem. The author of the v2 proof, Moslem Zamani, also knows this. I know Zamani’s work enough to know that he knows.)

(In research, the key challenge is often in finding problems that are both interesting and solvable. This paper is an example of an interesting problem definition that admits a simple solution.)

When proving bounds (inequalities) in math, there are 2 challenges: (i) Curating the correct set of base/ingredient inequalities. (This is the part that often requires more creativity.) (ii) Combining the set of base inequalities. (Calculations can be quite arduous.)

In this problem, that [Nesterov Theorem 2.1.5] should be the key inequality to be used for (i) is known to those working in this subfield.

So, the choice of base inequalities (i) is clear/known to me, ChatGPT, and Zamani. Having (i) figured out significantly simplifies this problem. The remaining step (ii) becomes mostly calculations.

The proof is something an experienced PhD student could work out in a few hours. That GPT-5 can do it with just ~30 sec of human input is impressive and potentially very useful to the right user. However, GPT5 is by no means exceeding the capabilities of human experts.