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This preprint is an informal test of whether a language model can do mathematical research: Claude reproduced, simplified, and generalized a proof about COVID-19 vaccine prioritization by age. The result is a shorter proof and a relaxed convexity condition, but the evidence is a single edited session record, transcripts are only available on request, and the work is not peer-reviewed. For AI readers, the useful signal is the workflow, which is AI-assisted derivation checked against existing literature, not a demonstrated breakthrough. Health conclusions should not be drawn from it without expert review.
Can AI Do Formal Demography? Why Vaccinating the Oldest Saves Both the Most Lives and the Most Years of Life
arXiv:2611.03500v1 Announce Type: new Abstract: 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.
Important: e-prints posted on arXiv are not peer-reviewed by arXiv; they should not be relied upon without context to guide clinical practice or health-related behavior and should not be reported in news media as established information without consulting multiple experts in the field.
Title:Can AI Do Formal Demography? Why Vaccinating the Oldest Saves Both the Most Lives and the Most Years of Life
Abstract: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.
Artificial Intelligence (cs.AI); Populations and Evolution (q-bio.PE)
arXiv:2611.03500 [cs.AI]
(or arXiv:2611.03500v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2611.03500 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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