A significant breakthrough in AI capabilities has emerged as GPT-5 Pro successfully proved a previously unsolved mathematical theorem entirely from scratch, drawing widespread attention from industry leaders and researchers.

Sebastien Bubeck, an OpenAI research engineer and former Microsoft AI Vice President and Distinguished Scientist, shared that GPT-5 Pro tackled an unresolved mathematical problem without referencing any existing human methods. Remarkably, the AI's solution surpassed the approaches presented in the original research paper.

The mathematical problem centered on a fundamental question in smooth convex optimization: under what conditions does the step size η in gradient descent ensure that the function values corresponding to iteration points form a convex curve? This research addresses when the gradient descent algorithm - analogous to finding the optimal path down a mountain - maintains consistent progress without erratic jumps.

In the original paper's first version, researchers proved that if η is less than 1/L (where L represents smoothness), the desired property holds. They also constructed a counterexample when η exceeds 1.75/L. However, the behavior within the interval [1/L, 1.75/L] remained unsolved.

GPT-5 Pro advanced the known lower bound from 1/L to 1.5/L, providing an elegant proof that impressed the mathematical community. The AI's approach differed significantly from human methods, representing a genuine evolution of the v1 proof rather than simply searching for existing solutions.

While Bubeck initially considered publishing the discovery, the original paper authors quickly released a v2 version that completely resolved the problem up to 1.75/L. Nevertheless, Bubeck found the result highly encouraging, as it demonstrated GPT-5 Pro's independent reasoning capabilities without accessing the updated version.

This achievement differs from previous AI accomplishments in that it utilized the consumer-facing GPT-5 Pro rather than specialized internal reasoning models. Bubeck verified the proof over 25 minutes, confirming its validity as a former Microsoft AI Vice President and Distinguished Scientist.

OpenAI President Greg Brockman characterized this as a potential sign of AI's emerging vitality in mathematics, suggesting that AI could accelerate mathematical research and expand the boundaries of human knowledge.

The development represents a milestone in AI's progression toward doctoral-level capabilities and beyond. While the specific problem was eventually solved by human researchers, GPT-5 Pro's autonomous discovery ability demonstrates significant potential for future mathematical breakthroughs.

Bubeck, who transitioned from a decade at Microsoft Research to OpenAI, brings extensive expertise in convex optimization, online algorithms, and adversarial robustness in machine learning. His current focus involves understanding how intelligence emerges in large language models and leveraging this understanding to advance toward artificial general intelligence through what he terms "AGI physics" - examining how AI systems coordinate across different scales to produce surprising behaviors.

This achievement highlights AI's growing capacity to contribute meaningfully to frontier research problems, potentially revolutionizing how mathematical discoveries are made while challenging researchers to better understand the mechanisms underlying these powerful models.