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The BrokenMath benchmark (NeurIPS 2025 Math-AI Workshop) tested this in formal reasoning across 504 samples. Even GPT-5 produced sycophantic “proofs” of false theorems 29% of the time when the user implied the statement was true. The model generates a convincing but false proof because the user signaled that the conclusion should be positive. GPT-5 is not an early model. It’s also the least sycophantic in the BrokenMath table. The problem is structural to RLHF: preference data contains an agreement bias. Reward models learn to score agreeable outputs higher, and optimization widens the gap. Base models before RLHF were reported in one analysis to show no measurable sycophancy across tested sizes. Only after fine-tuning did sycophancy enter the chat. (literally)
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Real, but easy, example: factorialFactorial is easy enough to reason about, implement, and its recursive, which