Rigor and Antiformalism in Mathematics

Definitions and mathematical statement

Supplied discussion question (2012). How can the apparent tension between the modern demand for rigor and criticism of formalism be explained?

The supplied record presents this as a philosophical and historiographical question about mathematical practice. It does not specify definitions of rigor or formalism, identify the criticisms in question, delimit a historical period or community, or give a criterion for an adequate explanation. Consequently, no precise mathematical proposition, domain of quantification, or formal system is determined by the supplied evidence.

The registry labels the item open, but also assigns the statement status unrecoverable. Its supplied verification note characterizes the workshop material as a historical, pedagogical, or methodological discussion prompt rather than an unresolved mathematical proposition; no separate clean statement is supplied. The question above is therefore retained as a discussion target, with these qualifications, rather than converted into a conjecture.

Short English statement

Explain the apparent tension between demands for rigor and criticism of formalism in mathematics. The supplied record treats this as a historical and philosophical discussion question; its terms and explanatory criteria are insufficiently specified for a precise mathematical assertion.

Sources

• Local UnsolvedMath registry, supplied record with permanent ID $30001976$, title Rigor and Antiformalism in Mathematics, source problem code catalogue entry, in the Oberwolfach Reports Open Problems collection. The recorded proposed year is 2012; no individual proposer is identified.
• Explicit Versus Tacit Knowledge in Mathematics (2012), Oberwolfach Reports, pp. 131--210, DOI 10.4171/owr/2012/04. Supplied source URL and literature reference labeled "original Oberwolfach report": https://doi.org/10.4171/owr/2012/04. The supplied background describes these reports as documenting mathematical workshops and their open-problem discussions.
• Supplied literature assessment, checked 2026-08-21: status open; the item is characterized as a philosophical historiographical question about rigor and formalism, not a resolved mathematical assertion, and as remaining open as extracted. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment. The supplied curation requests independent verification of time-sensitive status and cited claims.