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

stats ~ math/culture ~ biology/foundations ~ biology/perspectives ~ physics ~ programming languages ~ language models ~ cellular automata ~ misc/webtoys

(as a spreadsheet)

## ↥ math

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

- Product-form stationary distributions for deficiency zero chemical reaction networks by David F. Anderson, Gheorghe Craciun and Thomas G. Kurtz (2018).
- Quantum Techniques for Reaction Networks by John C. Baez (2013).
- Discovering governing equations from data by sparse identification of nonlinear dynamical systems by Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz (2016).
- Modern Koopman Theory for Dynamical Systems by Steven L. Brunton, Marko Budišić, Eurika Kaiser, and J. Nathan Kutz (2021).
- Toric Differential Inclusions and a Proof of the Global Attractor Conjecture by Gheorghe Craciunv (2015).
- Sampling Theory in Fourier and Signal Analysis: Foundations by J. R. Higgins (1996).
- Weak SINDy: Galerkin-Based Data-Driven Model Selection by Daniel A. Messenger, David M. Bortz (2020).
- Differential Equations and Dynamical Systems by Lawrence Perko (1991).
- 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)
- Nonlinear Dynamics and Chaos by Steven H. Strogatz (1994).
## ↥ category theory

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

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

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

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

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

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

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

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

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

- The Rust Programming Language by Steve Klabnik and Carol Nichols (2010).
- Learn You a Haskell for Great Good! by Miran Lipovača (2011).
## ↥ language models

- 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).
- Discovering Latent Knowledge in Language Models Without Supervision by Burns et al. (2022).
- Training Compute-Optimal Large Language Models by DeepMind (2022).
- Language Model Cascades by Dohan et al. (2022).
- Dissociating language and thought in large language models: a cognitive perspective by Mahowald et al. (2023).
- Talking About Large Language Models by Murray Shanahan (2022).
## ↥ cellular automata

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

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