AI Challenges the Mathematical Conjecture 'ETH'? Researchers Explain

OpenAI and Google's DeepMind have announced that their respective AI models produced results that contradict the Exponential Time Hypothesis (ETH), a major unsolved conjecture in computer science. ETH refers to the idea that certain types of computational problems inherently require enormous amounts of time to solve, or in other words, that "it is impossible to solve them efficiently." This announcement has sent ripples not only through the AI industry but also through the field of theoretical computer science.

ETH is a mathematical and computer science conjecture proposed from the 1990s through the early 2000s, serving as the foundation for the belief that no efficient algorithms exist for solving specific problem classes (such as the "satisfiability problem"). If this conjecture were proven false, it could potentially impact the very foundations of modern computer science, including cryptographic theory and algorithm design. It is natural that such an announcement, claiming that AI has shaken this fundamental question, would require careful verification from experts.

In response to this matter, TechCrunch sought comment from a computer scientist at MIT. The researcher explained both the significance and limitations of the claim that AI models have shown "counterarguments" to mathematical proofs. They noted that careful consideration is needed to determine whether the results derived by AI models carry the same weight as rigorous mathematical proofs, and that at present, the situation remains at the stage where "AI has presented specific counterexamples." It was emphasized that AI's computational outputs cannot constitute mathematical counterarguments to theorems without verification by human researchers.

The fact that both OpenAI and GoogleDeepMind have made such announcements in succession demonstrates that the application scope of AI technology is expanding into pure mathematics and theoretical computer science. While AI has previously achieved success in fields such as natural language processing and image recognition, its application to mathematical proposition exploration and proof assistance represents a relatively new trend. There is an increasingly common pattern of frontier AI, large-scale models, tackling problems that have remained unsolved by experts for years, and some observers suggest that the direction of AI research is shifting.

However, the phrase "AI has disproven ETH" warrants caution. Counterargument in mathematics means demonstrating the falsity of a hypothesis through rigorous logical procedure. Results such as counterexamples found by AI during computation do not automatically constitute mathematical proof. As MIT researchers point out, verification and organization by human experts based on AI's output is essential, and only through the cooperation of both does the work acquire scientific value. AI research and mathematics and computer science operate at an intersection where human expertise remains indispensable in validating discoveries.

This episode raises the question of how society should evaluate AI "discoveries." AI's ability to explore vast computational spaces and identify patterns and counterexamples that humans might overlook has significant potential to play an important role in future scientific research. At the same time, it has reaffirmed the principle that accepting results as "proofs" or "discoveries" requires a verification process by humans that cannot be omitted. The intersection of AI research and mathematics and computer science is likely to continue drawing attention.