Cognitive Complementarity in Human–AI Research: A Structured Methodology for Accelerated Problem-Solving

We formalize a structured approach to collaborative research between a human operator and multiple large language models, based on cognitive complementarity: the human provides cross-domain intuition, strategic direction, and tolerance for ambiguity; the AI models provide rapid formal verification, literature coverage, and symbolic computation. The methodology rests on three equally important foundations: the AI models, the interaction protocols, and the human operator — whose cognitive profile, professional background, and willingness to ask the "naïve question" are not incidental but central to the results. Key design principles include: honesty as a non-negotiable design constraint (the models must report errors, not produce agreeable output); multi-model cognitive diversity (five model families — Claude, GPT-4, Gemini, Grok, and Qwen — used as independent validators with distinct analytical tendencies); productive friction (negative results are systematically converted into diagnostic information rather than discarded); and the naïve question as a methodological tool (domain formalism can become an obstacle to resolution — sometimes it is the "stupid" question that unlocks the problem). The methodology is illustrated through a detailed case study tracing a research program on the Riemann Hypothesis from initial (incorrect) unconditional claim through cross-model error identification, conditional correction, discovery of a deeper convolution barrier, honest diagnostic paper, and the construction of an independent spectral program — all within 48 hours. The entire arc is documented with references to the published papers on Zenodo. The methodology is reproducible: it requires no custom model training, no proprietary infrastructure, and no domain-specific AI. It requires structured interaction protocols, intellectual honesty, and the deliberate use of model diversity.