A theoretical computer scientist, citing sources, says AI labs have quietly started probing whether their models can break important cryptographic protocols (Scott Aaronson/Shtetl-Optimized)

A theoretical computer scientist has informed the public that artificial intelligence labs have begun investigating whether their models can break crucial cryptographic protocols. This revelation was made by Scott Aaronson, known for his work at Shtetl-Optimized.

The scientist's perspective was shaped by a recent event that stirred the mathematical community. His 9-year-old son taunted his wife, a complexity theorist, by claiming that a robot had solved a math problem she had dedicated her career to working on. This anecdote highlights the significance of recent developments in the field.

Among the 372 groundbreaking results unveiled yesterday by OpenAI, there was a notable proof of Subhash Khot's Unique Games Conjecture (UGC). This conjecture, which Khot has been striving to prove for years, has profound implications for various optimization problems. The proof, if valid, suggests that numerous optimization problems are inherently NP-hard, even when seeking solutions slightly better than those obtained through semidefinite programming relaxation.

However, understanding the proof has proven to be an immense challenge. Many mathematicians and computer scientists are struggling to grasp the intricacies of the proof, which has been described as unclear, convoluted, and hard to follow. Some have even suggested that the paper may have been written with the assistance of an AI, as it lacks a coherent structure and fails to provide clear explanations or justifications for its claims.

The scientist's observations shed light on the broader implications of AI in the mathematical community. While some researchers may feel vindicated by the proof's validity, the process of understanding and validating such complex work is fraught with difficulties. The scientist suggests that the mathematical world could be transformed by integrating AI-generated insights, but the current lack of clarity and understanding poses significant hurdles.

The scientist also touches upon the competition among AI models like OpenAI and Anthropic. OpenAI's model, although powerful, has been criticized for producing complex and incomprehensible proofs. In contrast, Anthropic has taken a different approach by providing researchers with the opportunity to digest and communicate AI-generated insights, ensuring that the knowledge is accessible and comprehensible to the human community.

The scientist concludes by emphasizing the immense scope of the breakthroughs unveiled by AI, ranging from solutions to the 3SUM and All-Pairs Shortest Paths problems to progress on longstanding conjectures in number theory, combinatorics, algebraic geometry, and analysis. However, he also notes that certain grand challenges, such as P vs NP, remain unsolved, underscoring the formidable complexity of the mathematical landscape.