Mathematical Research Methodology

Frame and refine a math research question, choose tactics (prove vs compute vs simulate), keep a tight research diary.

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Mathematical research methodology

  • State the question precisely before anything else: domain, hypotheses, unknown, success criterion.
  • Catalogue what is known (cite theorems, papers) and what is unknown explicitly.
  • Pick a tactic: a proof attempt, a computer-algebra reduction, or a numerical experiment — and say why that tactic.
  • Keep a running research diary under /agent-filesystem/research/<slug>/diary.md with one entry per session: question, attempts, dead ends, next step.
  • Re-evaluate after every dead end: is the question wrong, the tactic wrong, or the regime wrong?

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