Mathematics

A map of mathematics to learn before formalizing intelligence: analysis, logic, category theory, and the foundations crisis.

· Updated Apr 27, 2024

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Before diving into formalizing intelligence, you need a solid grasp of:

  • Analysis & Topology (for mathematical rigor)
  • Linear Algebra (for AI, neural networks)
  • Probability & Statistics (for learning and inference)
  • Information Theory (for cognition, compression, and intelligence)
  • Dynamical Systems & Chaos (for modeling brain-like systems)
  • Category Theory & Logic (for abstraction and AI reasoning)
  • Computability & Complexity → "Computational Complexity" – Christos Papadimitriou
  • Optimization → "Convex Optimization" – Stephen Boyd & Lieven Vandenberghe
  • Statistical Learning → "Pattern Recognition and Machine Learning" – Christopher Bishop
  • Neural Networks & Deep Learning → "Deep Learning" – Ian Goodfellow, Yoshua Bengio, Aaron Courville
  • Theoretical Neuroscience → "Theoretical Neuroscience" – Peter Dayan & Larry Abbott
  • Mathematical Theories of Intelligence → "Universal Artificial Intelligence" – Marcus Hutter
  • Alternative Computation → "Hypercomputation: Computing Beyond the Church-Turing Barrier" – Apostolos Syropoulos
  • Category Theory & AI → "Category Theory for the Sciences" – David Spivak
  • Physics of Cognition → "The Physics of Life" – Adrian Bejan

Currently doing

  • reading mathematics for the non mathematician
  • Course intro to mathematical thinking
Quote

One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts.

  • Albert Einstein

Study Plan

Readings

History

Foundations

Pure Mathematics

  • Number System & Theory
  • Algebra
  • Partition Theory
  • Group Theory
  • Graph Theory
  • Combinatorics
  • Order Theory
  • Measure Theory
  • Geometry
  • Trigonometry
  • Fractal Geometry
  • Topology
  • Differential Geometry
  • Complex Analysis
  • Chaos Theory
  • Dynamical Systems
  • Analysis
  • Calculus
    • Infinite Powers

Applied Mathematics

  • Mathematical Physics
  • Bio mathematics
  • Mathematical Chemistry
  • Control Theory
  • Numerical Analysis
  • Game Theory
  • Economics
  • Probability
    • Decision Theory
  • Statistics
  • Optimization
  • Cryptography
  • Computer Science

Resources

Appendix