Top mathematicians say LLM is strong in computing but weak in creativity, and AI lacks creative thinking.

Large language models (LLMs) excel at mathematical calculations, but have significant limitations in truly original thinking. Mathematicians Timothy Gowers and Peter Sarnak respectively pointed out that LLM is good at combining known methods and exploring multiple operation paths, but it lacks the intuition to select a few effective paths in a huge search space. DeepMind researcher Tom Zahavy also holds a similar view and attributes the bottleneck to the insufficient ability of "manipulative abduction", that is, the inability to invent new basic hypotheses that lack linguistic precedents. Strong in calculation but weak in creativity Gowers believes that although the current model can quickly integrate existing mathematical techniques and try a variety of problem-solving directions, it cannot intuitively lock in a few productive routes when faced with a vast search space. Sarnak added that AI can derive results from existing theories, but if it starts from basic problems, it often cannot develop the abstract concepts that support major proofs. The bottleneck is the ability to guess. In his paper "LLMs Can't Jump," Zahavy focused on the limitations of LLM on "manipulative guessing"—the ability to invent new basic assumptions. This ability requires breaking away from existing language patterns. He believes that world models may provide a breakthrough direction, but it is still difficult for current models to overcome this obstacle. Competency Controversy Continues These evaluations fuel a broader discussion of whether LLM is truly becoming more comprehensive, or whether it is simply an increase in benchmark test scores in familiar problem areas. The views of mathematicians provide an important reference for the assessment of AI capabilities, showing that even with powerful computing power, creative thinking is still a key area that LLM has failed to break through.