OpenAI announced a major breakthrough in advanced mathematics, stating that a fleet of its artificial intelligence systems cracked a portion of a famous fluid dynamics problem in under four days. The company revealed that it deployed roughly 10,000 autonomous AI agents to tackle aspects of the Navier-Stokes equations, completing the task in 88 hours.

The Navier-Stokes equations describe the movement of liquids and gases, serving as a foundational concept in physics and engineering. For nine decades, key components of these equations have remained unproven, leaving scientists without a complete mathematical understanding of fluid turbulence. The specific challenge addressed by OpenAI involves the existence and smoothness problem, which centers on whether smooth, physically reasonable solutions always exist for these equations.

According to the artificial intelligence firm, the breakthrough was achieved through a newly developed internal model that demonstrated exceptional mathematical aptitude during late August training sessions. Recognizing the model's high capability, researchers directed the network of bots toward high-profile mathematical challenges. The computational effort was massive, with the autonomous agents exchanging nearly three million messages and consuming 130 billion output tokens during the brief operational window.

OpenAI estimated that running a computational workload of this scale using current public pricing models would cost approximately ten million dollars. Despite accomplishing a feat that resolves two of the four required statements for a prestigious one-million-dollar Millennium Prize, the organization stated it has no intention of claiming the award. Instead, the company framed the accomplishment as a demonstration of rapid advancements in machine intelligence capabilities.

The announcement quickly generated skepticism and controversy within the global academic community. New York University mathematics professor Tristan Buckmaster publicly raised questions regarding the timeline and methods behind OpenAI's achievement. Buckmaster stated that he and a researcher from rival company Anthropic had been actively pursuing a solution while utilizing OpenAI's coding assistant tool.

The mathematics professor reported discovering that details concerning his own research progress had reached OpenAI shortly before the company launched its automated assault on the equations. Buckmaster published excerpts from email correspondence to highlight concerns about the sequence of events, explaining that he felt obligated to speak out to prevent a false public narrative regarding the discovery's origins. Independent mathematicians have not yet verified the validity of OpenAI's proof, and the work has not been formally evaluated by the Clay Mathematics Institute.

Reporting based on coverage first published by BBC News. Read the original report at BBC News.