A Cartographic Study Guide

Navigating the Mathematics of Geometric AI

A structured learning path for engineers with Haskell and category theory background, mapping the mathematical terrain from foundational calculus to advanced differential geometry and probabilistic inference.

4

Learning Phases

From foundational refreshers through core disciplines to advanced synthesis, each phase builds on the last.

12

Topic Waypoints

Each topic includes key concepts, curated resources (Brilliant, Khan Academy, MIT OCW, YouTube), and Haskell connections.

Engineer-First

Every topic bridges to your Haskell and category theory background, making abstract math concrete through code.

The Journey

Learning Phases

1
Phase 1

Foundational Mathematics

Rebuilding the Basics

2
Phase 2

Core Disciplines

The Heart of Geometric AI

Core Disciplines
3
Phase 3

Probabilistic Foundations

Connecting Geometry to Inference

Probabilistic Foundations
4
Phase 4

Haskell & Category Theory

Leveraging Your Strengths

Haskell & Category Theory

Expedition Plan

Study Strategy

This journey will be challenging but incredibly rewarding, allowing you to appreciate the intricate theoretical tapestry of the Geometric AI.

1

Start with Foundations: Begin with Multivariable Calculus, Linear Algebra, and Differential Equations. Focus on the concepts directly relevant to the Geometric AI document.

2

Progress to Core Disciplines: Move to Differential Geometry, Variational Calculus, Ricci Flow, and Quasicrystals. These are conceptually more challenging.

3

Integrate Probabilistic Concepts: Study Graphical Models, Variational Inference, and Information Geometry. Understand how they connect to the geometric ideas.

4

Leverage Haskell: For each mathematical concept, try to think about how you would represent it in Haskell. If possible, implement small examples or use relevant libraries.

5

Revisit the Geometric AI Document: As you learn new concepts, re-read the relevant sections of the Geometric AI document. The connections will become clearer.

6

Focus on the “Bridges”: Pay special attention to the areas where the document explicitly links different fields (e.g., Fisher Information Metric as the bridge, CBFE minimization as curvature flow).

7

Conceptual Understanding First: Don’t get bogged down in every single proof. Aim for a strong intuitive and conceptual understanding before diving into formal details.