Shared Conceptual Foundations of Mathematics

Definitions and mathematical statement

The source does not define a core Conceptual Foundations of Mathematics, specify the philosophical approaches under consideration, or give a criterion for a concept to be acceptable within an approach. With those qualifications unresolved, the supplied question is:

Can there be a core Conceptual Foundations of Mathematics consisting of concepts acceptable across several philosophical approaches?

The cleaned statement asks whether such a common core can be developed across several major philosophical approaches. The original statement does not include the restriction to major approaches. Neither formulation specifies whether the approaches are fixed in advance or may be selected together with the core, what substantive content the core must contain, or what would establish feasibility. Consequently, the supplied evidence supports this conceptual feasibility question but does not determine a precise mathematical existence statement.

Short English statement

Can mathematics have a common conceptual foundation acceptable across several philosophical approaches? The intended approaches, the required content of the common core, and the meaning of acceptability remain unspecified.

Sources

• Local UnsolvedMath registry, permanent ID 30003657, title Shared Conceptual Foundations of Mathematics, source problem code catalogue entry, collection Oberwolfach Reports Open Problems.
• Supplied source citation: Mathematical Logic: Proof Theory, Constructive Mathematics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/53, pp. 3121--3183. https://doi.org/10.4171/owr/2017/53. The background describes these reports as documenting mathematical workshops and their open-problem discussions.
• Supplied literature source and attribution context: "Oberwolfach Report 53, Aczel talk," https://doi.org/10.4171/owr/2017/53. The registry lists proposed year 2017 but supplies no proposer in its proposer field; attribution to a specific proposer is therefore unresolved.
• Literature assessment dated 2026-08-21: the supplied curation labels the problem open, describes the proposal as a feasibility question, and reports finding no subsequent mathematical resolution. This is supplied dated curation, not an independently verified literature assessment. The supplied background requests independent verification of time-sensitive status and cited claims.