A collection of books, textbooks, articles, essays, and other media. Hyperlinked titles indicate the source material is freely available online.

math ~ applied math ~ category theory ~ applied category theory ~
stats ~ math/culture ~ biology/foundations ~ biology/perspectives ~ physics ~ programming languages ~ language models ~ cellular automata ~ misc/webtoys
(as a spreadsheet)

    ↥ math

  1. A Short Course on Spectral Theory by William Arveson (2001).
  2. Linear Algebra Done Right by Sheldon Axler (1996) - see his webpage.
  3. Linear Algebra Abridged by Sheldon Axler (2016).
  4. Ideals, Varieties, and Algorithms by David A. Cox, John B. Little, and Don O’Shea (2007).
  5. Abstract Algebra by David S. Dummit and Richard M. Foote (1991).
  6. Naive Set Theory by Paul Halmos (1960).
  7. Algebraic Geometric by Robin Hartshorne (1977).
  8. Algebraic Topology by Allen Hatcher (2002) - webpage.
  9. Introduction to Lie Algebras and Representation Theory by James E. Humphreys (1972).
  10. Algebra by Serge Lang (1965).
  11. The collected works of F. W. Lawvere (1961-2017).
  12. Introduction to Smooth Manifolds by John M. Lee (2000).
  13. Equilibrium points in n-person games by John Nash (1950).
  14. Linear Algebra and its Applications by Gilbert Strang (1988).
  15. Dynamical zeta functions and the distribution of orbits by Mark Pollicot (2021).
  16. Principles of Mathematical Analysis (AKA “Baby Rudin”) by Walter Rudin (1953).
  17. Real and Complex Analysis by Walter Rudin (1966).
  18. Linear Algebra Done Wrong by Sergei Treil (2004).
  19. Homotopy Type Theory by The Univalent Foundations Program (2013).

    ↥ applied math

  20. Product-form stationary distributions for deficiency zero chemical reaction networks by David F. Anderson, Gheorghe Craciun and Thomas G. Kurtz (2018).
  21. Quantum Techniques for Reaction Networks by John C. Baez (2013).
  22. Discovering governing equations from data by sparse identification of nonlinear dynamical systems by Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz (2016).
  23. Modern Koopman Theory for Dynamical Systems by Steven L. Brunton, Marko Budišić, Eurika Kaiser, and J. Nathan Kutz (2021).
  24. Toric Differential Inclusions and a Proof of the Global Attractor Conjecture by Gheorghe Craciunv (2015).
  25. Sampling Theory in Fourier and Signal Analysis: Foundations by J. R. Higgins (1996).
  26. Weak SINDy: Galerkin-Based Data-Driven Model Selection by Daniel A. Messenger, David M. Bortz (2020).
  27. Differential Equations and Dynamical Systems by Lawrence Perko (1991).
  28. Physics Informed Deep Learning, Part I: Data-driven Solutions of Nonlinear Partial Differential Equations and Part II: Data-driven Discovery of Nonlinear Partial Differential Equations by Maziar Raissi, Paris Perdikaris, and George Em Karniadakis (2017)
  29. Nonlinear Dynamics and Chaos by Steven H. Strogatz (1994).

    ↥ category theory

  30. An Introduction to n-Categories by John C. Baez (1997).
  31. Physics, Topology, Logic and Computation: A Rosetta Stone by John Baez and Michael Stay (2009).
  32. Nine short stories about geometric higher categories by Christoph Dorn (2023).
  33. Decorated Cospans by Brendan Fong (2015).
  34. Seven Sketches in Compositionality by Brendan Fong and David Spivak (2018).
  35. Higher Topos Theory by Jacob Lurie (2010).
  36. Categories for the Working Mathematician by Saunders Mac Lane (1971).
  37. Category Theory for Programmers by Bartosz Milewski (2014).
  38. Category Theory in Context by Emily Riehl (2016) - check out her bibliography.
  39. Categorical logic from a categorical point of view by Michael Shulman.
  40. The Galois connection between syntax and semantics by Peter Smith (2010).
  41. Propositions as Types by Philip Wadler (2014).

    ↥ applied category theory

    (does this count as applied math? no one will tell me)

  42. A Compositional Framework for Reaction Networks by John C. Baez and Blake S. Pollard (2017).
  43. Structured Cospans by John C. Baez and Kenny Courser (2019).
  44. Compositional Modeling with Stock and Flow Diagrams by John Baez, Xiaoyan Li, Sophie Libkind, Nathaniel Osgood, and Evan Patterson (2022).
  45. Compositional game theory by Neil Ghani, Jules Hedges, Viktor Winschel, and Philipp Zahn (2016).
  46. Graph Neural Networks are Dynamic Programmers by Andrew Dudzik and Petar Veličković (2022).
  47. Backprop as Functor: A compositional perspective on supervised learning by Brendan Fong, David I. Spivak and Rémy Tuyéras (2017).
  48. Some Notions of (Open) Dynamical System on Polynomial Interfaces by Toby St. Clere Smithe (2021).

    ↥ stats

  49. Statistical Inference by George Casella and Roger L. Berger (1989).
  50. Topology and Data by Gunnar Carlsson (2008).
  51. EigenGame: PCA as a Nash Equilibrium by Ian Gemp, Brian McWilliams, Claire Vernade, Thore Graepel (2020). Blogpost by DeepMind.
  52. Statistical Learning Theory by Vladimir Vapnik (1989).

    ↥ math/culture

  53. Proofs from THE BOOK by Martin Aigner and Günter M. Ziegler (1998).
  54. The Ideal Mathematician by Philip David and Reuben Hersh.
  55. The Responsibility of the Scientist Today by Grothendieck (1970).
  56. There Are Too Many B.A.D. Mathematicians by Melvin Henriksen (1993).
  57. Mathematics at Göttingen under the Nazis by Saunders Mac Lane (1995).
  58. The Mathematical Coloring Book by Alexander Soifer (2009).
  59. On proof and progress in mathematics by Bill Thurston (1994).

    ↥ biology/foundations

  60. Molecular Biology of the Cell by Bruce Alberts, Dennis Bray, Julian Lewis, Martin Raff, Keith Roberts, and James D. Watson (1983).
  61. Neuroscience: Exploring the Brain by Mark F. Bear, Barry W. Connors and Michael A. Paradiso (1995).
  62. Biology by Neil A. Campbell (1987).
  63. Principles of Biochemistry by Albert L. Lehninger (1970).
  64. Ecology: Concepts and Applications by Manuel C. Molles and Anna Sher (2002).
  65. Mathematical Biology by J. D. Murray (2002).

    ↥ biology/perspectives

  66. Silent Spring by Rachel Carson (1962).
  67. The Problem of Biological Individuality by Ellen Clarke (2011).
  68. The Selfish Gene by Richard Dawkins (1976).
  69. A Sand County Almanac by Aldo Leopold (1949) - excerpt.
  70. Technological Approach to Mind Everywhere by Michael Levin (2022).
  71. The Dialectical Biologist by Richard Levins and Richard Lewontin (1985).
  72. Open-endedness: The last grand challenge you’ve never heard of by Kenneth O. Stanley, Joel Lehman and Lisa Soros (2017).

    ↥ physics

  73. Nanosystems: Molecular Machinery, Manufacturing, and Computation by K. Eric Drexler (1992).
  74. Introduction to Electrodynamics by David J. Griffiths (1981).
  75. Introduction to Quantum Mechanics by David J. Griffiths (1995).
  76. Modern Quantum Mechanics by J. J. Sakurai and Jim Napolitano (1985).
  77. Classical Mechanics by John R. Taylor (2004).
  78. The Everything-is-a-Quantum-Wave Interpretation of Quantum Physics by Vlatko Vedral (2023).

    ↥ computer science

  79. Introduction to Coalgebra: Towards Mathematics of States and Observation by Bart Jacobs (2016).
  80. Thoughts on Flash by Steve Jobs (2010). Wikipedia.
  81. Gödel, Escher, Bach by Douglas Hofstadter (1979).
  82. The Death of a Technical Skill by John J. Horton and Prasanna Tambe (2020).
  83. Artificial intelligence meets natural stupidity by Drew McDermott (1976).
  84. Why AI is Harder Than We Think by Melanie Mitchell (2021) - check out her website.
  85. Purely Functional Data Structures by Chris Okasaki (1999).
  86. [Designing Voice User Interfaces: Principles of Conversational Experiences by Cathy Pearl (2016).
  87. Software Foundations by Benjamin C. Pierce et al. (2011).
  88. How To Become A Hacker by Eric Steven Raymond.
  89. Proof Repair by Talia Ringer (2021).
  90. Reinforcement Learning: An Introduction by Richard S. Sutton and Andrew G. Barto (2018).

    ↥ programming languages

  91. The Rust Programming Language by Steve Klabnik and Carol Nichols (2010).
  92. Learn You a Haskell for Great Good! by Miran Lipovača (2011).

    ↥ language models

  93. On the Dangers of Stochastic Parrots: Can Language Models Be Too Big? 🦜 by Emily M. Bender, Timnit Gebru, Angelina McMillan-Major, and Shmargaret Shmitchell (2021).
  94. Discovering Latent Knowledge in Language Models Without Supervision by Burns et al. (2022).
  95. Training Compute-Optimal Large Language Models by DeepMind (2022).
  96. Language Model Cascades by Dohan et al. (2022).
  97. Dissociating language and thought in large language models: a cognitive perspective by Mahowald et al. (2023).
  98. Talking About Large Language Models by Murray Shanahan (2022).

    ↥ cellular automata

  99. Finding life in the shadows by David H. Ackley and Elena S. Ackley (2018). Conference talk.
  100. Digital protocells with dynamic size, position, and topology by David Ackley (2018).
  101. Learning sensorimotor agency by Gautier Hamon, Mayalen Etcheverry, and Bert Wang-Chak Chan (2022).
  102. Differentiable Self-organizing Systems by Alexander Mordvintsev et al. (2020) - “Growing Neural Cellular Automata” is the first post in the series.
  103. Particle Lenia by Alexander Mordvintsev, Eyvind Niklasson, and Ettore Randazzo (2022).
  104. Conway’s game of life is a near-critical metastable state in the multiverse of cellular automata by Sandro Reia and Osame Kinouchi (2014).
  105. Lenia: Biology of Artificial Life by Bert Wang-Chak Chan (2018). Website.
  106. Lenia and Expanded Universe by Bert Wang-Chak Chan (2020).

    ↥ misc/webtoys

  107. Complexity Explorables - cool simulations of nonlinear dynamical systems.
  108. Shadertoy - community of people writing shaders that run in browser. Beautiful and mathematical!
  109. Neural Patterns - web-based implementation of discrete reaction diffusion equations in the form u(t+1) = f(k⋆u(t)). Epilepsy warning.
  110. AsciiMath - converts Latex to Ascii. I use this a lot.
  111. Braids by Ester Dalvit. Four-part animated video series on the braid group.
  112. Space Engine a 3d universe sandbox that contains many known celestial objects and procedurally generates the rest.
  113. 30 Weird Chess Algorithms - YouTube.
  114. Game of life time dimension tower in Minecraft
  115. SHRDLU in Action - early attempt at embodied LLMs.