Mathematical documents as a working environment
PlanetMath organizes mathematical explanations written and discussed by a community. Its needs include rendering notation, linking concepts, revising entries, and helping readers find prerequisites. Planetary explored an extensible platform for those activities. The authors’ 2012 work-in-progress paper explicitly describes PlanetMath as an operating system for mathematics and Planetary as its kernel.
The paper reports a mixture of established PlanetMath functions and work on a replacement platform. Its implementation discussion includes LaTeXML rendering, semantic linking, and services around mathematical documents. The proposed learning environment should be read as a development goal, not as a completed feature list.
A reader’s path through mathematics
Consider a reader encountering a theorem whose proof assumes compactness. A useful document system connects the term to its definition, prerequisites, examples, and discussion. A formal proof system has another responsibility: establish that the particular compactness hypothesis needed by a theorem holds. These activities can support one another, but a link to a definition does not discharge a proof obligation.
The comparison with Axeyum
Axeyum’s artifact pages connect statements to evidence and dependencies. Its research vision also concerns choosing and executing further mathematical work. Planetary is a precedent for the shared document and service environment around such work. The cited paper does not establish an equivalent to Axeyum’s producer-contract and kernel-admission design.
For Axeyum, the design lesson is to preserve the connection between readable explanation and exact mathematical records. A revised statement should retain its identity and evidence history. A reader should be able to tell which statement version an explanation describes.
The operating-system phrase names a responsibility worth investigating. PlanetMath’s prior use means the phrase itself cannot establish novelty. MMT and MathHub address the related question of how mathematical meaning can support services across documents and systems.