Artificial intelligence has defeated mathematicians. The USA Is Losing Its Edge

 

“AI developed in Beijing—working without human intervention—solved a mathematical problem that had remained open for a decade in a mere 80 hours. Researchers assert that the technological gap in AI between the USA and China has been closed.

 

A team from Peking University, led by researcher Dong Bin, has achieved a remarkable breakthrough. Their AI system—based on the collaboration of two specialized agents—independently solved and formalized the proof of the so-called Anderson Hypothesis [1]. This problem, deeply rooted in commutative algebra, was formulated in 2014 by the late Prof. Dan Anderson (who passed away a few years ago) and had steadfastly resisted traditional research efforts for years. It took the Chinese machine just over three days to crack it. 

An Era of Algorithmic Breakthroughs?

 

Approximately 80 hours of computational work were sufficient to achieve this scientific success; the key was an innovative inference module called Rethlas, which utilized the powerful mathematical theorem search engine Matlas in real time. These tools enabled the algorithms to transition seamlessly and effectively from natural-language reasoning to flawless, formal verification. However, this victorious clash between algorithms and complex algebra is not an isolated incident. Recently, advanced models—such as OpenAI’s GPT-5.4 and neural networks developed by the specialized startup Axiom—have also successfully tackled tasks previously considered nearly unsolvable.

 

For instance, Google DeepMind’s FunSearch garnered significant attention for aiding in the solution of classic combinatorial problems, including those involving 'cap sets.' The system does not merely guess pre-existing answers; instead, it generates and tests programs within the vast space of possibilities. In the case of the "cap set problem"—a classic challenge in extremal combinatorics—it discovered new constructions of large sets of points where no three points lie on the same straight line, thereby improving upon previously known results. In practical terms, this means that the AI ​​did not so much prove a theorem as facilitate the discovery of superior examples and bounds for a problem that had resisted traditional methods for years.

 

Meanwhile, in the field of physics, significant interest has been sparked by THOR AI—a system that has accelerated the computation of the so-called configuration integral (one of the most computationally vexing problems in materials physics) by a factor of more than 400 compared to previous simulation methods.

 

This demonstrates that AI is no longer merely supporting scientific endeavors; it is beginning to genuinely push the boundaries of what was previously considered unsolvable.

 

**China Catches Up to the USA in AI**

 

The success achieved by researchers at Peking University proves something else as well: AI technology from China no longer lags behind the innovations being developed in Silicon Valley. This fact is corroborated by the recently published *AI Index 2026* report. This document—spanning over 400 pages and compiled by Stanford University—delivers a surprising verdict: the gap between American and Chinese AI models has ceased to exist. As of March, the top-performing model from the USA led the leading system from China by a marginal 2.7 percentage points on the Arena Leaderboard rankings.

 

Experts note, however, that the ecosystems of the two superpowers operate differently. In 2025, the USA released 50 "frontier models" (compared to China’s mere 30) and significantly outpaces its rival in terms of private investment ($285.9 billion versus $12.4 billion). On the other hand, Beijing—having bolstered the market with subsidies totaling $184 billion over the course of decades—clearly leads the world in patents, publications, and the mass deployment of industrial robots.

 

 

In a recent interview with the program *60 Minutes*, Sundar Pichai, CEO of Google, firmly asserted that "America must lead" in the field of artificial intelligence. He called for the responsible, yet "extremely bold, pursuit of innovation."

 

 

As recently as February 2026, Google released its new flagship model, Gemini 3.1 Pro. The leap in performance is impressive: the system achieved a score of 77.1% on the demanding ARC-AGI-2 reasoning test, thereby setting entirely new industry standards. It is also worth noting that Alphabet’s planned capital expenditures for this year amount to as much as $185 billion (nearly double last year’s spending), with the majority of this astronomical sum earmarked specifically for AI infrastructure.”

 

1. Commutative algebra is the branch of abstract algebra studying commutative rings, their ideals, and modules over them. It serves as the mathematical foundation for algebraic geometry and algebraic number theory, focusing on structures like polynomial rings, Dedekind domains, and localization. Key concepts include Noetherian rings, dimension theory, and homological methods.

 

The Anderson Hypothesis (or question) in commutative algebra, often attributed to D. D. Anderson, concerns whether "weak quasi-completeness" implies "quasi-completeness" for Noetherian local rings. This property relates to the structure of ideal filtrations and has recently been tackled using automated theorem provers. The conjecture was formally verified in 2026.