Can AI Do Formal Demography? Why Vaccinating the Oldest Saves Both the Most Lives and the Most Years of Life

Can AI contribute to formal demography? We report an experiment in which an AI model, Claude, was asked to explain and then simplify the proof of an earlier result: that vaccinating the oldest against COVID-19 saves both the most lives and the most years of life, because the years saved per person treated rise with age. The model proposed a new proof that is shorter, more intuitive, and somewhat more general than the original, built from a known life-table identity and the definition of convexity. It states the condition for the result as the convexity of the reciprocal of the hazard, which can be checked from the hazard alone and holds for most familiar parametric models, and it yields a lower bound on life expectancy whenever that condition is met. Prompted by a further question, the model also gave an exact form of the condition, showing how far convexity can be relaxed. The model traced these identities and related results in earlier literature. An edited record of the sessions is provided, and complete transcripts are available on request. The exercise suggests that AI can revisit established results, make them easier to understand, and prove valuable generalizations.