Historical Proposal for Concrete Infinitesimal Analysis

Definitions and mathematical statement

Research proposal and limits of formulation. The supplied record asks: "Can infinitesimal analysis be given a rigorous yet concrete foundation using a calculus based on historical geometric insights?" Its accompanying verification describes the intended direction as historical and foundational research on machine-based calculus.

The record does not specify a mathematical meaning for "concrete," the historical geometric constructions or machines to be used, or the scope of "infinitesimal analysis." It supplies no underlying domain, axioms, admissible operations, class of functions, notion of infinitesimal, boundary conditions, or criteria by which a proposed foundation would satisfy the request. Consequently, neither definitions of the intended objects nor a precise quantified existence statement can be recovered without adding substantive hypotheses.

The question is therefore retained as a foundational research proposal, with its target unresolved. The supplied statement status is unrecoverable; the accompanying verification explicitly says that this is not a sufficiently specified mathematical conjecture or construction problem and that no separate clean statement is promoted. This draft does not replace the proposal with an invented formalization.

The supplied classification is partially_solved. The supplied literature assessment says that tractional and constructive approaches provide rigorous partial formalisms, while no generally accepted concrete foundation based on the proposed historical constructions has been completed. These are supplied curation claims, not independently verified mathematical facts or a precise description of which parts have been solved.

Short English statement

The proposal asks whether historical geometric and machine-based approaches can support a rigorous, concrete foundation for infinitesimal analysis. The source does not define the intended constructions or success criteria, so a precise mathematical problem cannot be recovered. Its supplied partially solved label and literature assessment require independent review.

Sources

• Local UnsolvedMath registry, permanent ID 30003682, title Historical Proposal for Concrete Infinitesimal Analysis, source code catalogue entry, collection Oberwolfach Reports Open Problems. The project registry locations are data/unsolvedmath/problems.json and the supplementary catalog/problems.json; this draft uses the supplied complete record. No individual proposer is supplied. The recorded proposed year is 2017.
• Supplied source citation: Mathematical Instruments between Material Artifacts and Ideal Machines: Their Scientific and Social Role before 1950 (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/58, pp. 3471--3560. https://doi.org/10.4171/owr/2017/58. The background attributes the collection to Oberwolfach workshop reports and their open-problem discussions; no passage within this page range is identified for the proposal.
• Supplied literature source, labeled "OWR Report 58/2019": https://ems.press/content/serial-article-files/46722. Its relationship to the source citation above is not established by the supplied record.
• Literature assessment checked at 2026-08-21: supplied dated curation, not independently verified. It reports partial formalisms from tractional and constructive approaches and the absence of a generally accepted completed concrete foundation based on the proposed historical constructions. The background expressly calls this a dated literature triage derived from supplied OWR curation and requests independent verification of time-sensitive status and cited claims.