Learning resources, websites, and tools for programming, math, philosophy, and more.

These are links to things I’ve found on the web for everything from math, programming, utilities, research, papers, and videos. This page is mainly for my reference (to keep track of everything I use regularly), but maybe it can save you some time as well.

Online Tools

Search and Information

Wikipedia (random article): You should know this one already!

WolframAlpha: computational knowledge engine (google on steroids)

Understands math, natural language, web queries and more. Seriously just ask it anything. Saves a lot of time and effort instead of having to program and google things.

NumCalc: numerical/scientific web calculator

Useful for quick calculating when you need arbitrary precision, symbolic computation, or special functions quickly.

Content Creation

Runway ML studio

Web-based video editing and content creation studio that uses ML models (check out: Gen-2)

pandoc: free document conversion online, no BS

Useful for quickly converting between markdown, HTML, LaTeX\LaTeX, and other formats in the browser. There’s also a command line version: install pandoc

Interesting Stuff

Math and Science Visualizations

Feature Visualization: How neural networks build up their understanding of images

My Favorite Software

ML/AI Models You Can Use Today Tools and Resources for AI Art 3D-aware style transfer

Utility Libraries

zstd: Fast Compression Algorithm

Math and Science Libraries

PyTorch: Machine Learning Framework

Flexible and easy to use, more generalizable than Tensorflow and better for research. Includes automatic differentiation, GPU support, and a large ecosystem of libraries.

Some extra PyTorch packages I use:

  • PyTorch3D: 3D differentiable rendering and geometry for deep learning
  • DEODR: Another differentiable renderer
  • xFormers: PyTorch implementation of Transformer models

And, if you’re interested in “hacking” PyTorch or writing your own backend, check these out:

OpenCV: Computer Vision Library

Bulky but comprehensive library for computer vision, uses Python bindings.

SOD: An Embedded Computer Vision & Machine Learning Library

Edge computing is awesome! For IoT/embedded needs this is way easier than OpenCV.

MAGMA: Matrix Algebra on GPU and Multicore Architectures

GPU-accelerated library for linear algebra (BLAS & LAPACK) that I worked on, also includes some sparse linear algebra.

libbf: Arbitrary Precision Floating Point Library

GMP: GNU Multiple Precision Arithmetic Library

Arbitrary precision arithmetic library for C, which is very popular but not the best in my opinion.

See also:

FLINT: Fast Library for Number Theory

Symbolic computing library for solving/evaluating number theory problems.

Datasets and APIs

Google Dataset Search

Text Datasets

OpenWebText2, by EleutherAI

Large text database, generated from positive voted Reddit links

Common Crawl dataset - Common crawl of the entire web

Image Datasets

Video Datasets


High quality dataset from Vimeo videos

DeepVideo, with Sports-1M - Sports-1M dataset, scraped from YT

Audio Datasets

3D Datasets

Multi-Modal Datasets

LAION-5B: A new era of open large-scale multi-modal datasets

A new large dataset, used to train Stable Diffusion, but also freely available as subsets for individuals who don’t have 240TB of storage for the full dataset

Also, has lots of good metadata on the considerations that went into it, and the challenges of creating a large dataset

Research Areas

Computer Science

The Art of Computer Programming, by Donald Knuth

Possibly the best book on computer science ever written, deals primarily with algorithms and their implementations

Modern Computer Arithmetic, by Richard Brent and Paul Zimmerman

A useful book for implementing bignum arithmetic, goes into many, many algorithms and special cases. Basically all you need to write your own MPFR/libbf/GMP library

Advanced Programming in the Unix Environment, by Richard Stevens

Heavily recommended for C programming, teaches the C standard library for UNIX OSes. I’ve got the physical book and it’s great for perusing

The Cerberus C Semantics: An in-depth exploration of the C lanauge. If you’re interested in writing compilers and designing new languages, C is a master class in both what can go right and wrong for a language.

Structure and Interpretation of Computer Programs

The Humble Programmer, by Edsger Dijkstra

Dijkstra has (almost) all the correct opinions about programming… A must read!

Design Principles Behind Smalltalk, by Daniel H. H. Ingalls

Smalltalk is incredibly important to understand the languages that came after it, because it was designed with a great purpose and vision.

Even if you have heard about Smalltalk, READ THIS. Unfortunately, if you just believe the common view that “Smalltalk is an object oriented language” you have fallen victim to the propaganda. The best contributions of Smalltalk are the fact that the objects send messages to each other, and that atomistic communication between objects is actually the benefit of OOP. To quote the paper: “Purpose of Language: To provide a framework for communication”.

All OOP languages that came after but don’t implement message passing are failing to realize the true benefit of OOP.

Blub Paradox, by Paul Graham

You can’t trust the opinions of the others, because of the Blub paradox: they’re satisfied with whatever language they happen to use, because it dictates the way they think about programs.

Codata in Action

My favorite explanation of how codata can actually be used. Essentially, it works as encoding control flow and order on top of normal data. I think this is something new programming languages need to use as it is lazier and easier to reason about in many cases.

I’m surprised this came from Microsoft… One of the few times they have positively affected programming.

GOTO Considered Harmful, by Edgar Dijkstra

Why goto statements (i.e. unstructured control flow) are bad. It’s so important to understand this, because even allowing low-level unstructured control flow inhibits the ability for optimizers and static analyzers to do their job. Not to mention the ability of programmers to reason about the code.

On a meta-note, this paper established the “X considered harmful” title meme, which is still used today.

Structured Programming with goto statements, by Donald Knuth

Great history about the goto debate, with a lot of interesting anecdotes and analogies to the world of mathematics. Although Knuth was probably in the wrong here (at least, in our modern view) in suggesting goto has valid uses, it’s refreshing to hear a different perspective on the matter.

Notation as a Tool of Thought, by Kenneth Iverson

Important work by a Turing award winner that explores how notation and language can affect our thinking. So often overlooked is the fact that “ugly” or otherwise “bad” syntax is conducive to worse quality code, and conversely that “pretty” syntax can lead to better code.

All syntaxes are not created equal! We should strive for syntaces that are easy to read and write, and that are easy to reason about.

Theory of Sets, Types, and Categories

Algebraic Subtyping (thesis), by Stephen Dolan

A long, grueling tour of algebraic subtyping, but there are a lot of good nuggets in there. Also great to get acquainted with the notation

Cogent: uniqueness types and certifying compilation

Great end-to-end example about the theory of uniqueness types

Types, Abstraction, and Parametric Polymorphism, by John Reynolds

A great theory paper explaining distinctions between “types”, “sets”, and some of the problems with common conceptions we have about programming and math. A must-read for anyone making a new programming language, so as to not repeat the mistakes of the past and thinking with a mathematical mindset.

An Expirement with Inline Substitution, Rice University

Results are dated, but a good example of a historical note where inlining did not aid in perforance. Of course, nowadays it is absolutely required due to the more abstract nature of programming

Programming Languages and Compilers

LISP 1.5 Programmer’s Manual

Polyhedral Compilation

Graphene: An IR for Optimized Tensor Computations on GPUs

Diesel: DSL for Linear Algebra and Neural Net Computation on GPUs

Example of a language geared at numerics-heavy compilation (focusing on neural networks). I actually ended up working with the authors of this paper as part of my NVIDIA internship

PolyJIT: Polyhedral Optimization Just in Time

Application of JIT techniques with polyhedral compilation

slides: Polyhedral Compilation as a Design Pattern for Compiler Construction

ML/AI Research

GLM-130B: NLP Model for Text Generation

Better than GPT-3 at most things, available in different sizes, and free to download and use

GPT 3: NLP Model for Text Generation

State of the art in text generation, at 176 billion parameters this model is just too large to run yourself. You can run it using OpenAI’s API to GPT-3

Here’s a walkthrough of GPT architecture. This is the best overall explanation I’ve seen

Real-ESRGAN: Image Super Resolution

For image super resolution (just say: AI, enhance and zoom image!), this is the best deployed general solution I’ve seen

RIFE: Real-Time Intermediate Flow Estimation for Video Frame Interpolation

For video frame interpolation (just say: AI, increase frame rate fluidly!), this is the best downloadable model out there. This is kind of controversial because different models do different things better but I like RIFE the best

I use hzwer/Practical-RIFE, which promises better aesthetics and is easier to use

I also use nihui/rife-cnn-vulkan, which runs on Apple Silicon and has a nice interface (although you’ll have to use FFMPEG in addition)

HIFIC: High-Fidelity Generative Image Compression

This model can be used to get insane results in image compression (much better than JPEG)

PyTorch implementation, since TensorFlow is so 2019

AIVC: Artificial Intelligence-based Video Coding

Although not as much of a upgrade as HIFIC is for images (relative to existing codecs), this is still interesting research as we wait for a superior one to emerge…

Check out the interactive slides

NNCP: Lossless Data Compression with Neural Networks

Neural networks typically aren’t easily made into lossless compressors, but this implementation gives state-of-the-art results (albeit with slow compression speed) for text compression

Consistent Video Depth Estimation

Magenta Colab Notebooks: ML music resources

LAVIS: A one-stop library for language-vision intelligence

This library can do anything from image captioning to image classification to image generation. It’s great to quickly integrate into your own projects

bRigNet: Automatic neural net 3D character rigging in Blender

Check out the code here: pKrime/brignet

Deep Motion Editing: deep learning for 3D character motion

Motion style transfer, retargetting, and more 3D animation features

torch-ngp: Neural Graphics Primitives

Awesome Neural Rendering (curated)

ACT-1: Transformer for Actions

A very ambitious research/product that aims to create a transformer that “can do anything a human can do in front of a computer”

This is a first of it’s kind that I think will end up being the primary way we interact with computers in the future. Seriously this thing is cool AF!

WebGPT: Improving the Factual Accuracy of Language Models through Web Browsing

Interesting article about WebGPT, a model meant to surf the web to answer questions

Training Compute-Optimal Large Language Models (Chinchilla), by DeepMind/Google

Chinchilla, better and smaller than GPT-3. Also, this paper has a great introduction that explains broad ideas in ML/AI. Notable for also considering compute efficiency (LLMs are getting expensive, so this is becoming more important)

Video Diffusion Models

Soon-to-be-outdated, but an interesting paper about using diffusion models for video generation

Infinite Nature: Perpetual View Generation of Natural Scenes from a Single Image

Basically an infinite 3D fractal zoom into landscapes, works fairly well

Dream Fusion Paper: Text-to-3D using 2D Diffusion

Interesting proof of concept of using diffusion models to generate 3D scenes from text, with no 3D data or training required! Uses optimization like DeepDreaming, unlike typical ML models which train then use inference

Deep Positron: A Deep Neural Network Using the Posit Number System


The Elements

Written by Euclid around 300BC, this book is a good introduction to the basics of mathematics starting with the basics of geometry

In my opinion, this should be the first mathematics textbook for schools to use. It’s ridiculous that most schools to teach students geometry without using Euclid’s work. Anything to overpay the private companies that produce US textbooks, I guess…

Prime Numbers and the Riemann Hypothesis

Very useful book, for people of all backgrounds (not just mathematicians) that explains prime numbers, number theory, and the Riemann Hypothesis. Gives multiple formulations, diagrams, and explanations. My favorite book on my favorite problem in all of mathematics (so far)!

On the Number of Primes Less Than a Given Magnitude

Possibly the most influential (and yet still underrated) paper in all of mathematics, I highly recommend this paper. Check out my blog post on the Gamma/Zeta function implementations

Counterexample To Euler’s Conjecture on Sums of Like Powers

One of my favorite papers, although not particularly explanative. A computer-assisted dis-proof of one of Euler’s conjectures

Fast constant-time GCD computation and modular inversion

Machine Learning-Aided Numerical Linear Algebra: Convolutional Neural Networks for the Efficient Preconditioner Generation

And associated talk/slides

The FBHHRBNRSSSHK-Algorithm For Multiplication in Z_{2}^{5x5} is Still Not The End of the Story

Deep Programming Lore

TempleOS: a truly impressive operating system written by a lone schizophrenic developer, according to his perceived “revelations from God”

the case of Terry Davis is tragic, but the story of his life and work is fascinating and important to understand. Due to his online presence, he may be one of the best-documented schizophrenia cases in history.

Paul Le Roux: a South African programmer who became a cartel boss, arms dealer, and drug trafficker. Creator of the well-known Encryption for the Masses (E4M) program.