Benefits of a shared formal vocabulary for statistics

Establish whether building a shared formal vocabulary for well-established statistical theory broadens the discipline’s capacity to develop, communicate, and teach statistical theory.

Background

The paper observes that Mathlib provides a standardized, machine-checked corpus whose formalized results can be reused by later developments, whereas statistics lacks a comparable statistics-specific layer. It proposes a community-built library containing formalized statistical definitions, axioms, and theorems.

The claimed benefits of such a shared vocabulary are not established by the five case studies. The authors explicitly present them as a conjecture, making the question of whether the proposed infrastructure produces broader disciplinary benefits an unresolved issue.

References

We conjecture that building a shared formal vocabulary for the well-established statistical theory corpus would widen the discipline's capacity to develop, communicate, and teach its theory.

— Statistical Theory in the Age of Machine-Assisted Mathematics: Rethinking How Theory Is Made and Taught  (2609.04481 - Coretto, 3 Sep 2026) in Section 2, “Proof Assistants for the Theoretical Statistician”