Leading mathematicians Timothy Gowers and Peter Sarnak have criticised large language models for lacking the creative intuition required to generate genuinely new ideas. While these systems demonstrate significant capability in combining known methods and traversing established search paths, they fail to select the few productive routes necessary for breakthroughs in complex problem spaces. Gowers notes that current models struggle with the vastness of mathematical inquiry because they cannot mimic the human ability to discard unproductive directions early. Sarnak adds that AI can derive results from existing theory but cannot develop the new abstractions needed to underpin major proofs when starting from elementary questions.
Tom Zahavy, a researcher at DeepMind, supports this view in his paper “LLMs Can’t Jump,” identifying the bottleneck as an inability to perform manipulative abduction. This term describes the capacity to invent new foundational assumptions without any prior linguistic precedent. The assessment suggests that while world models might offer a path forward, current tools remain limited to improving performance on benchmarks and familiar problem spaces rather than expanding versatility. The debate continues over whether these systems are becoming truly versatile or simply refining their grasp of known data.
- Current models excel at combining existing methods but lack intuition for new routes
- Zahavy defines the limitation as an inability to invent foundational assumptions without precedent
- Experts question if improvements represent true versatility or just better benchmark performance
