OpenAI and Anthropic have separately announced that their AI systems generated mathematical results they say challenge a longstanding assumption in theoretical computer science, according to The Daily Star.

The target is the Exponential Time Hypothesis (ETH), a conjecture developed in the late 1990s that has shaped complexity research for over two decades.

ETH holds that solving certain computational problems — particularly Boolean satisfiability, where a computer must decide whether a set of logical conditions can be satisfied simultaneously — inevitably requires computational effort that grows exponentially with problem size.

OpenAI said its internal AI system produced a purported refutation on October 16, which was then formalised in Lean, a proof-verification system.

Anthropic published an AI-generated paper describing a subexponential-time algorithm for a related satisfiability problem, with formal verification materials attached.

The surprise is not just that AI produced new mathematics, but that the claimed result strikes at one of the foundational assumptions of modern complexity theory.

Researchers have relied on ETH for more than twenty years as a working benchmark for what is efficiently computable, and it underpins the way the field classifies hard problems involving logical satisfiability.

If the AI-generated arguments hold up, The Daily Star reports that researchers could be forced to reconsider hundreds of theoretical results that depend on ETH — a sweeping reassessment few in the field would have anticipated.

It is also notable that two rival labs reached claim-worthy results in the same week, suggesting AI-assisted mathematics is advancing faster than the peer-review machinery built to evaluate it.

The claimed findings come with unusual safeguards for results of this magnitude.

Anthropic's contribution takes a different but parallel form: The Daily Star reports the company published an AI-generated research paper presenting a subexponential-time algorithm for a related satisfiability problem, accompanied by its own formal verification materials.

If validated, the results would mark one of the clearest cases yet of AI systems contributing genuinely new theoretical computer science, and would push researchers to re-examine hundreds of ETH-dependent results.

Until then, the claims sit in limbo between breakthrough and error, and independent verification will decide which.

Meanwhile, TechRadar reports a reminder that AI's rising profile cuts both ways: security researchers at Push Security found scammers using fake OpenAI, Anthropic, and SpaceX event invitations — offering free ChatGPT Pro subscriptions or Grok Heavy access — to phish Microsoft and Google credentials via the Kali365 and VoidProxy phishing-as-a-service platforms.

As AI's prestige grows, so does the volume of noise, hype, and fraud orbiting it.