Escaping the Cognitive Well: Efficient Competition Math with Off-the-Shelf Models

A new inference pipeline using off-the-shelf models has achieved state-of-the-art results on International Mathematical Olympiad-style math problems while slashing costs from thousands of dollars to roughly 31 USD per question, according to research posted on arXiv in 2026 [1][2]. The system, described in a paper by Xingyu Dang and colleagues, attained 67.1 percent performance on the IMO-ProofBench Advanced benchmark using Gemini 3.0 Pro [1][2]. That result more than doubles the success rate of the next best publicly accessible pipeline, the authors report, and does so at a fraction of the cost [2]. Earlier efforts to match gold-medal IMO performance with publicly available models required large-scale inference that ran to approximately 3,000 USD per problem [1][2]. The pipeline targets a failure mode the researchers call the Cognitive Well — a cycle in which a solver-grader system iteratively refines a solution that both components wrongly judge to be correct [2]. To escape that trap, the method uses conjecture extraction: candidate lemmas are isolated from generated solutions and independently verified alongside their negations in a fresh environment, a step the authors term context detachment [2]. Reasoning models, a class of large language models trained for multi-step logical tasks, have shown superior performance on mathematics and programming benchmarks compared to standard LLMs [5]. The new pipeline extends that capability without requiring custom-trained math models, relying instead on general-purpose systems [2]. The International Mathematical Olympiad has long served as a benchmark for advanced problem-solving. Founded in 1959, the competition has inspired cultural depictions such as the 2014 film "X+Y," which followed a teenage prodigy navigating the IMO [4]. In artificial intelligence research, IMO-level mathematics has become a prominent testbed since the AI boom of the 2020s, when generative AI and transformer architectures drove rapid advances in language model capabilities [6]. The arXiv paper, titled "Escaping the Cognitive Well: Efficient Competition Math with Off-the-Shelf Models," was first submitted in February 2026 and revised in June 2026 [1][2]. The authors note that at the time of evaluation, their pipeline represented the state-of-the-art on PB-Adv among both public and unreleased models [2].