What's Next?

What's Next

You have implemented the core machinery of differential geometry in Python — from function composition to Riemann curvature and geodesics. Here are natural next steps:

  • General Relativity — Apply what you built to the Schwarzschild metric (spacetime around a black hole). Compute geodesics in Schwarzschild coordinates to see light bending and orbital precession.
  • Gauge Theory — The connection and curvature you implemented are the mathematical heart of Yang-Mills theory and the Standard Model of particle physics.
  • The Original Book — Read Functional Differential Geometry by Sussman and Wisdom. The Scheme code maps directly to your Python implementation.
  • SICM — Structure and Interpretation of Classical Mechanics by the same authors applies functional programming to classical mechanics with the same philosophy.
  • Differential Forms — Deepen your understanding of exterior algebra, Stokes's theorem in full generality, and de Rham cohomology.

Further Reading

  • Functional Differential Geometry by Sussman & Wisdom (MIT Press) — The source for this course. Free PDF at groups.csail.mit.edu.
  • Gravitation by Misner, Thorne & Wheeler — The comprehensive reference for general relativity, with extensive use of differential geometry.
  • Differential Geometry, Gauge Theories, and Gravity by Göckeler & Schücker — Bridges differential geometry and physics.
  • Geometry, Topology and Physics by Nakahara — Graduate-level treatment connecting geometry to quantum field theory.
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