Roadmap

The vision

Mathematical Structures is a coherent multi-book series rather than a collection of independent texts — books that share their underlying machinery instead of each rebuilding it. It is being written as several focused books: a Geometric Algebra book, an Elements of Mathematical Structure survey that sets the foundations and methodology, and a Category Theory reference used across the series. Further volumes — geometric calculus and analysis, and eventually texts in physics and engineering built on the same apparatus — sit on the longer horizon.

Progress and plans

Updated July 5, 2026.

Done

• July 2026 — reworked the series into focused books (see the books).
• May–July 2026 — first chapter, Categories, Maps, and Diagrams, drafted and posted as the opening of the Category Theory reference. First draft of this site.

Now — the next 6 to 12 months

The focus is the Geometric Algebra book: working out a substantial chunk of it — the foundational multilinear algebra (tensor and exterior algebra), then the geometric (Clifford) algebra itself, from the essentials into more advanced material. In parallel, Category Theory reference chapters get filled in, since that reference supports the rest of the series.

Expect this to be the shape of the work for a good while — likely the full six-to-twelve-month window, quite possibly longer.

Further out

Beyond that horizon, the plan is to begin a geometric calculus / calculus book and to build out the Elements of Mathematical Structure survey. These are a ways off; the near-term energy is on geometric algebra.