Your brain is a manifold. Here is the syllabus.

What it does This repository is an awesome-list that catalogs textbooks, lectures, surveys, and software at the intersection of pure mathematics and neural computation. It covers the geometry of representations in biological brains and deep networks, organizing resources across group theory, differential geometry, topology, and geometric machine learning. The curation is a collaborative effort driven by the Symmetry and Geometry in Neural Representations research community.

The interesting bit Rather than siloing math and machine learning, the list places Spivak’s differential geometry tomes next to surveys on equivariant convolutional networks and topological deep learning. It is built on the premise that understanding neural representations—whether cortical or computational—requires fluency in manifolds, symmetry, and curvature.

Key highlights

• Extensive pure math foundations: Lie groups, algebraic topology, Riemannian geometry, and information geometry
• Applied bridges to ML: geometric deep learning, manifold optimization, and symmetry-aware architectures
• Resources for computational neuroscience alongside the formal mathematics
• Community-maintained via an active Slack workspace with open PR contributions
• Includes datasets and specialized software libraries, not just papers

Caveats

• Explicitly labeled a “collaborative work-in-progress,” so depth varies by section
• At least one bibliographic entry appears truncated in the README source
• Contains no original code or implementations—purely a signposting resource

Verdict Worth bookmarking if you are a researcher or advanced student trying to backfill mathematical foundations for geometric ML or theoretical neuroscience. Not the place to find copy-paste code or quick tutorials.