Mathematical Thinking DPF
A pattern language for constructing mathematical objects, operations and arguments, using their results, and developing the next useful question.
- Author: Anatoly Levenchuk, with AI-assisted development and review
- Version: 20 September 2026
- Status: Eternal alpha: a growing repertoire of methods for mathematical work.
- License: © 2026 Anatoly Levenchuk. Original framework text: Creative Commons Attribution 4.0 International (CC BY 4.0). Cited sources retain their own terms.
- Publication: FPF ecosystem repository
Begin with the working question. If you have not yet identified its mathematical contribution, use Readme entry MP-FRAME. Use the Table of Contents to find a relevant pattern, then open its Problem frame, Solution, worked cases and checklist. Readme follows connected mathematical work; Preface explains the methods and when to revise a construction.
The reference code MATH names this DPF. Its numbers are stable pattern addresses; § shows position in this edition. References such as B.5.RA and C.29.1 name patterns in FPF. Use those patterns when the cited question arises.
When a mathematical result changes a working method, Method Engineering DPF provides two further methods: ME.7 helps resolve a proposed composition of methods; ME.12 helps locate an inconsistency between a method, its descriptions, the work performed and its supporting means.
Open the cited publications for those pattern bodies. When using another edition, revisit your conclusion if a cited operation or condition has changed.
To cite this edition: Anatoly Levenchuk, Mathematical Thinking DPF, FPF ecosystem repository. Include the version date shown above.