On The Main Challenges And New Perspectives On Generating Robust Benchmark Datasets For Large Language Models In Modern Advanced Mathematics

Large language models write fluent prose yet still struggle with verifiable, compositional reasoning in advanced mathematics; we address this gap with a compact, cognitively grounded protocol that mirrors how mathematicians think. Our framework instantiates seven human--inspired dimensions--concept formation, dualization, negative knowledge, transfer, and more--via meta--prompts drawn from active research problems, not toy exercises, and audits full solution traces for faithfulness and invariant control. Under identical conditions, we benchmark four state--of-the--art systems and observe a global breaking degree of more than ninety percent on stress tests. In general terms, error forensics reveal systematic failures in lemma synthesis, long--horizon planning, premise selection, and counterexample search. From these findings we suggest the systematic integration of the aforementioned new tactic to enhance concrete levers--rationale SFT, process supervision with process reward models, and stepwise preference learning--that directly target step--level correctness. We further outline an Artificial Mathematical Intelligence (AMI) agenda to model concept creation and proof discovery along these lines. Together, the protocol and interventions chart a reproducible path toward the systematic design of genuinely creative mathematical reasoning in LLMs and related IA--based systems.