Mathematical research drives scientific discovery, and recent advances in AI for mathematics have shown that language-model agents can solve challenging problems and develop substantial mathematical proofs. Yet much of today's AI-for-mathematics work centers on obtaining a final answer. This emphasis leaves the exploration behind a result difficult for researchers to understand, while long-running investigations face fragmented context and the risk of unsupported claims propagating across reasoning steps. We present Euler, a human-centered mathematical research system built around a shared, structured representation of the research process. Euler organizes mathematical statements, assumptions, proof dependencies, alternative approaches, failed attempts, and verification evidence into connected research graphs. This representation allows researchers to trace how results are developed and supplies agents with persistent, task-relevant knowledge for planning, collaboration, and verification across sessions. Researchers can also select a graph node linked to a saved team state, revisit the agents' earlier reasoning, and explore alternative directions through continued interaction. We illustrate Euler's capabilities through three mathematical research case studies and describe the implemented system and its software validation.

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