Awesome Math 
Awesome Math is a curated list of high-quality resources for learning, teaching, and doing mathematics. It covers pure mathematics, applied mathematics, computation, formal proof, and the use of AI in mathematics.
Most resources are free to access. Paid resources may be included when they are widely respected, unusually useful, and hard to replace. Access limits should be stated in the entry.
Read the contribution guidelines before suggesting a resource.
Contents
Start Here
- Khan Academy - Free, self-paced lessons and exercises from arithmetic through calculus and beyond.
- Coursera - University and industry mathematics courses, with access and payment varying by course.
- MIT OpenCourseWare - Free MIT course materials, including notes, assignments, and exams for undergraduate and graduate mathematics.
- edX - University and professional mathematics courses, with audit and paid options varying by course.
- Brilliant - Interactive, problem-based lessons in foundational mathematics, probability, and related quantitative subjects.
- WooTube - Video lessons by Eddie Woo covering secondary-school mathematics with an emphasis on conceptual understanding.
- Mathispower4u - More than 9,000 free, closed-captioned video lessons and worked examples organized from middle-school mathematics through calculus, linear algebra, differential equations, and statistics, by James Sousa.
- Mathigon - Interactive courses, activities, and visual explanations for school and early university mathematics.
- Ximera - Free interactive mathematics textbooks from Ohio State University.
- Almost Fun - Free interactive middle- and high-school mathematics lessons, practice problems, and teacher resources from a nonprofit organization.
- Oxford Mathematics - Lectures and public talks from the University of Oxford, including accessible explanations of advanced topics.
- Math Academy - Paid adaptive platform with diagnostic assessment and mastery-based courses from fourth-grade mathematics through university topics.
- OSSU Math - Free, prerequisite-ordered self-study curriculum modeled on the mathematics requirements of an undergraduate degree.
- Waterloo Open Math - Free university-level courseware with lessons, exercises, and immediate feedback from the University of Waterloo.
Proof and Problem Solving
Video Courses and Series
- Brandon Foltz - Video courses in statistics, probability, and quantitative methods with worked examples.
- StatQuest - Introductory video explanations of statistics, probability, and machine learning.
- 3Blue1Brown - Visual explanations of core mathematics, including calculus, linear algebra, and differential equations.
- NPTEL - University lecture courses from Indian institutes covering mathematics and related technical subjects.
- Numberphile - Popular mathematics videos featuring mathematicians discussing problems, ideas, and curiosities.
- PatrickJMT - Worked-example videos for algebra, calculus, and other introductory college topics.
- Professor Leonard - Full lecture series in precalculus, calculus, and differential equations for college students.
- MIT OpenCourseWare - MIT course recordings and video lectures, including full mathematics courses.
- Mathologer - Visual videos on recreational mathematics and selected advanced topics.
- The Math District - Free guides and videos covering prealgebra, algebra, geometry, trigonometry, statistics, calculus, and technical mathematics.
Questions and Answers
Reference Works
Mathematics Subject Classification 2020 - The standard subject taxonomy maintained by Mathematical Reviews and zbMATH.
Encyclopedia of Mathematics - Reference articles on mathematical concepts, theorems, biographies, and applications.
ProofWiki - Collaborative repository of mathematical definitions, lemmas, and proofs.
nLab - Collaborative research-level notes and expositions in category theory, homotopy theory, mathematical physics, and related areas.
Wolfram Mathworld - Reference articles on mathematical definitions, formulas, identities, and related concepts.
The On-Line Encyclopedia of Integer Sequences - Great compendium of many different integer sequences. Founded 1964 by N. J. A. Sloane.
AIM Open Textbook Initiative - Open mathematics textbooks organized by course and evaluated by the American Institute of Mathematics editorial board.
AMS Open Math Notes - Free course notes, textbooks, and research expositions hosted by the American Mathematical Society.
OpenStax Mathematics - Peer-reviewed, openly licensed textbooks for school and introductory college mathematics from Rice University.
The Princeton Companion to Mathematics - Paid reference edited by Timothy Gowers, June Barrow-Green, and Imre Leader.
Encyclopedia of Distances (4th Edition) - Paid reference by Michel Marie Deza and Elena Deza.
Basics of Algebra, Topology, and Differential Calculus - Jean Gallier (University of Pennsylvania).
Multivariable Calculus - G. Cain, J. Herod (Georgia Tech).
Wikibooks - Community-authored collection of open mathematics textbooks and instructional books.
Online Mathematics Textbooks - Index of freely available mathematics textbooks maintained at Georgia Tech.
Trigonometry - Michael Corral.
The Math Behind Artificial Intelligence - Tiago Capelo Monteiro (freeCodeCamp).
Broad Course Notes
- Evan Chen - MIT. 2012 ~ 2018. Covers Combinatorics, Number Theory, Honors Algebra, Set Theory, Real Analysis, Graph Theory, and more.
- Dexter Chua - Harvard. 2013 ~ 2018. Covers Analysis, Probability, Linear Algebra, Complex Analysis, Numerical Analysis, Statistics, Optimization, Algebraic Topology, Quantum Field Theory, and more.
General Mathematics
- Paul's Online Math Notes - Free notes, examples, and practice problems for algebra, calculus, and differential equations, by Paul Dawkins at Lamar University.
- UBC CLP Calculus Textbooks - Free textbooks, problem books, and source files for a four-course university sequence in differential, integral, multivariable, and vector calculus.
Foundations and Logic
Logic
- Introduction to Logic - Michael Genesereth, Eric J. Kao (Stanford University).
- An Introduction to Formal Logic - P.D. Magnus (University at Albany).
- forall x: Calgary (An Introduction to Formal Logic) - P.D. Magnus and Tim Button, remixed by Aaron Thomas-Bolduc and Richard Zach (Open Logic Project).
- Computability - An introduction to recursive function theory - Nigel Cutland (University of Hull).
- Language, Proof, and Logic, Second Edition - Paid textbook by Dave Barker-Plummer, Jon Barwise, and John Etchemendy.
- Mathematical Logic - Helmut Schwichtenberg.
- Mathematical Logic - Stephen G. Simpson (Pennsylvania State University).
- Formal Logic - Miguel Palomino.
- Predictive Arithmetic - Edward Nelson.
- Proofs and Concepts: the fundamentals of abstract mathematics - Joy Morris, Dave Morris.
- Mathematical Reasoning: Writing and Proof - Ted Sundstrom.
- Logic and Proof - Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn.
- QED - an interactive textbook - Terence Tao.
- Open Logic Textbook - collaborative effort, main contributors listed here.
Set Theory
Type Theory
Category Theory
- Lean - Open-source interactive theorem prover and programming language based on dependent type theory, used for formal mathematics and software verification.
- mathlib - Community-maintained mathematical library for Lean 4, with formalized theories, proof tactics, programming infrastructure, and generated documentation.
- Mathematics in Lean - Free textbook with examples and exercises for mathematicians learning Lean 4 and mathlib.
- Theorem Proving in Lean 4 - Free official textbook on dependent type theory, propositions, tactics, inductive types, type classes, and constructing verified proofs in Lean 4.
- Natural Number Game - Interactive Lean 4 game that introduces theorem proving through guided exercises about natural numbers.
- Isabelle - General-purpose interactive theorem prover with higher-order logic and set-theory environments for formalizing mathematics and computer science.
- Archive of Formal Proofs - Refereed collection of Isabelle proof libraries, examples, and scientific developments maintained against current Isabelle releases.
- Rocq Prover - Open-source interactive theorem prover and dependently typed programming language for mechanized mathematics and verified software.
- Mathematical Components - Rocq libraries and tools for large-scale formalized mathematics, including substantial developments in algebra and analysis.
- Metamath - Minimal formal language and proof verifier with explicit, inspectable proofs built from simple foundations.
- Courses Using Lean - Maintained, filterable index of university courses that teach Lean or use it for mathematics, logic, programming, and formal verification.
- Lean-related Conferences and Events - Maintained calendar and archive of conferences, workshops, and tutorials about Lean, mathlib, and formalized mathematics.
Algebra
- Elementary Algebra 2e - Free one-semester textbook from OpenStax with web and PDF editions, worked examples, practice exercises, chapter reviews, and answer keys.
Abstract Algebra
Linear Algebra
Group Theory
Ring and Field Theory
Commutative Algebra
- The CRing Project - Open-source work-in-progress textbook introducing commutative algebra for readers with elementary abstract algebra, with an emphasis on foundations for algebraic geometry.
- Commutative Algebra Notes - Free graduate course notes by Mel Hochster, from an introductory course through advanced topics such as Cohen-Macaulay rings, multiplicities, and étale maps.
Representation Theory
Number Theory
Algebraic Number Theory
Analytic Number Theory
Combinatorics and Discrete Mathematics
- Basic Combinatorics - Carl G. Wagner (University of Tennessee).
- Applied Combinatorics - Mitchel T. Keller, William T. Trotter.
- Discrete Mathematics: An Open Introduction - Free fourth-edition undergraduate textbook by Oscar Levin, with inquiry activities, more than 750 exercises, solutions and hints, and coverage of proofs, graph theory, counting, sequences, and discrete structures.
- Notes on Combinatorics - Peter J. Cameron.
- Analytic Combinatorics - Philippe Flajolet, Robert Sedgewick.
- generatingfunctionology - Herbert Wilf.
- A=B - Marko Petkovšek, Herbert Wilf, and Doron Zeilberger on algorithms for proving hypergeometric identities.
Graph Theory
Geometry and Topology
Differential Geometry
Algebraic Geometry
General Topology
Algebraic Topology
Analysis
Real Analysis
Complex Analysis
Functional Analysis
Operator Theory
- Lecture Notes on Operator Algebras - Free graduate notes by John M. Erdman on Hilbert-space operators, Banach algebras, spectral theory, C*-algebras, compact operators, and K-theory.
Harmonic Analysis
Measure Theory
Differential Equations and Dynamical Systems
Ordinary Differential Equations
Partial Differential Equations
Ergodic Theory and Chaos
- Chaos: Classical and Quantum - Maintained technical webbook on dynamical systems, periodic orbits, deterministic chaos, statistical mechanics, and quantum chaos.
Probability and Statistics
Probability
Stochastic Processes
Statistics
- Lecture Notes on Statistical Theory - Undergraduate notes by Ryan Martin on estimation, likelihood, hypothesis testing, and Bayesian statistics, with some R examples.
- Introduction to Statistics and Data Analysis for Physicists - Gerhard Bohm, Günter Zech.
- Lectures on Statistics - Free text by William G. Faris covering inference, Bayesian methods, regression, principal components, and linear models.
- Theory of Statistics - Advanced, actively revised text by James E. Gentle on probability, statistical models, estimation, testing, and asymptotic theory.
- Theory of Statistics - Graduate notes by Joseph C. Watkins on measure-based probability, decision theory, estimation, testing, and hierarchical models.
- UCLA Statistical Methods and Data Analytics - Tutorials and examples for R, Stata, SAS, and SPSS.
- NIST Handbook of Statistical Methods - Resource on practical statistics directed towards scientists and engineers.
- Statistical Thinking for the 21st Century - Russell A. Poldrack.
- Odds and Ends: Introducing Probability & Decision with a Visual Emphasis - Jonathan Weisberg.
- Seeing Theory - Daniel Kunin, Jingru Guo, Tyler Dae Devlin, and Daniel Xiang.
- Statistics Done Wrong - Alex Reinhart.
- All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman.
- OpenIntro Statistics - Free introductory textbook for college courses and self-study, with datasets, labs, slides, videos, exercises, and accessible PDFs.
Statistical Learning
Algebraic Statistics
Numerical and Computational Mathematics
Numerical Analysis
- Introduction to Numerical Analysis - Undergraduate notes by Doron Levy on root finding, interpolation, approximation, numerical differentiation, and quadrature.
- Numerical Analysis (Second Edition) - Free second-edition textbook by L. Ridgway Scott on the theory and practice of numerical methods.
- Lectures in Basic Computational Numerical Analysis - Archived University of Kentucky textbook by J. M. McDonough, focused on computational methods for differential equations.
- Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods - Specialized notes by Alfred Schmidt and Arsen Narimanyan on adaptive finite element methods.
- Numerical Analysis for Engineers - University of Waterloo course with lectures, assignments, projects, and MATLAB material on numerical methods for engineers.
- Advanced Linear Algebra: Foundations to Frontiers - Online text by Robert van de Geijn and Margaret Myers on algorithms for advanced numerical linear algebra.
- Fundamentals of Numerical Computation - Online textbook by Tobin Driscoll and Richard Braun with Julia, MATLAB, and Python editions covering core numerical methods for linear systems, approximation, root finding, ODEs, and PDEs.
Optimization, Operations Research, and Control
- Convex Optimization - A free textbook with slides, exercises, code, and course material by Stephen Boyd and Lieven Vandenberghe.
- Nonlinear Optimization - Free graduate MIT course covering analytical and computational methods for unconstrained and constrained optimization.
- CVXPY - Open-source Python modeling language for convex, geometric, quasiconvex, and related optimization problems.
Control Theory
Mathematical Physics
Interdisciplinary Mathematics
Mathematics for Computer Science
- Mathematics for Computer Science - Free MIT OpenCourseWare course with an open textbook, videos, notes, problem sets, and exams on proofs, discrete structures, counting, graphs, modular arithmetic, and discrete probability.
- Algorithms and Complexity - H. Wilf.
- Lecture Notes on Optimization - Pravin Varaiya.
- Information Theory, Inference, and Learning Algorithms - David J. C. MacKay.
- The Chaos Textbook: Mathematics in the age of the computer - Glenn Elert.
Mathematics for Machine Learning
- Mathematics for Machine Learning - Free textbook on the linear algebra, geometry, calculus, probability, and optimization needed to study machine learning.
- Deep Learning: Foundations and Concepts - Free-to-read online textbook by Christopher M. Bishop and Hugh Bishop, with a probability-based treatment of modern deep-learning models and methods.
- Mathematics of Machine Learning - Free graduate MIT course on the mathematical and statistical foundations of machine learning, with lecture notes, assignments, and problem-set solutions.
- Probabilistic Machine Learning - Introductory and advanced books by Kevin Murphy, with free draft PDFs, code, figures, exercises, and teaching resources.
- Information Theory - Free graduate MIT course on entropy, source and channel coding, rate distortion, Gaussian channels, feedback, and multi-user information theory.
- Essential Coding Theory - Free graduate MIT course on error-correcting codes, Hamming spaces, and the algebraic and complexity aspects of coding theory.
- Error Correction Zoo - Maintained reference database of classical, quantum, and hybrid error-correcting codes, with definitions, relationships, and references.
Mathematical Finance
Mathematical Biology
Signal Processing
Mathematical Practice
AI for Mathematics
This section covers AI-assisted theorem proving, formalization, and mathematical discovery. Resources that teach the mathematics used in machine learning appear under Mathematics for Machine Learning.
- LeanDojo v2 - Open-source framework and benchmark data for training, evaluating, and deploying AI-assisted theorem provers for Lean 4.
- miniF2F - Cross-system benchmark of formalized olympiad, high-school, and undergraduate problems for evaluating automated theorem provers.
- AlphaGeometry - Open research implementation combining learned guidance with symbolic deduction for olympiad geometry problems.
- First Proof Project - Independent project that publishes research-level problems, evaluation methods, solutions, and expert commentary for assessing AI systems in mathematics.
- Math AI Seminar - University of Washington research seminar on formalization, theorem proving, mathematical AI, and machine-learning applications in mathematics, with a multi-year event archive.
- b=M²L - Barcelona Mathematics and Machine Learning colloquia on the interaction between mathematics and machine learning, with multi-year editions and recorded talks.
- AI for Mathematics and Theoretical Computer Science - Simons Institute and SLMath workshop archive with recorded talks on proof assistants, automated reasoning, machine learning, and mathematical discovery.
- Mathematics and AI - University of Washington Fall 2025 graduate course with public slides, Lean examples, projects, and readings on machine learning, formalization, autoformalization, mathematical discovery, and ethics.
- AI-Assisted Mathematical Discovery - Open thirteen-week course with notes, notebooks, exercises, and case studies on coding agents, machine learning, language models, reinforcement learning, and experimental mathematical research.
- Symbolab - Online solver with step-by-step solutions, graphing, calculators, and practice tools. Some solution steps and study features require a paid plan.
- Desmos - Browser-based graphing calculator with geometry, tables, statistics, and classroom activities.
- Wolfram Alpha - Computational knowledge engine for evaluating expressions, plotting functions, and answering structured queries. Some advanced features require a paid plan.
- Maxima - Free computer algebra system for symbolic and numerical calculations, plotting, and scripting.
- SymPy - Python library for symbolic algebra, calculus, equation solving, matrices, and code generation.
- SageMath - Free mathematics software combining computer algebra, numerical computation, geometry, statistics, and visualization through Python.
- MathFlow - C# math expression library with symbolic computation (differentiation, simplification, equation solving).
- GeoGebra - Interactive mathematics suite for geometry, graphing, algebra, spreadsheets, statistics, and calculus.
- Macaulay2 - Research system for algebraic geometry and commutative algebra with specialized computational packages.
- Singular - Computer algebra system for polynomial computations in commutative algebra, algebraic geometry, and singularity theory.
- GNU Octave - Free environment for numerical computing, linear algebra, plotting, and MATLAB-compatible scripts.
- Magma - Subscription-based computer algebra system for research in algebra, number theory, algebraic geometry, and combinatorics.
- Maple - Paid computer algebra and numerical mathematics system for symbolic computation, visualization, and programming.
- MATLAB - Paid numerical computing environment by MathWorks.
- Wolfram Mathematica - Paid technical-computing system for symbolic and numerical mathematics, visualization, programming, and data analysis.
- Free Math - Free, open-source software for recording, organizing, and reviewing digital mathematics homework without solving the problems automatically.
- RunMat - Runtime for MATLAB-syntax array math with automatic CPU/GPU execution.
History and Mathematics Education
- MacTutor History of Mathematics Archive - University of St Andrews archive of mathematician biographies, histories of mathematical topics, timelines, institutions, and related reference material.
- NRICH - Free curriculum-linked problems, investigations, articles, and teacher guidance from the University of Cambridge for learners aged 3 to 18.
Community and Further Reading
Journals and Magazines
- Quanta Magazine - Features latest research breakthroughs in an accessible style for non-experts.
- Bulletin of the American Mathematical Society - Expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic.
- Notices of the American Mathematical Society - Publicizes activities of the Society and features surveys, reports, news, announcements, and opinions on industry trends, academia, and research.
- European Mathematical Society Magazine - The Magazine features announcements about meetings and conferences, articles outlining current trends in scientific development, reports on member societies, and many other informational items.
- Mathematics Today by Institute of Mathematics and its Applications - News, opinions, and articles related to mathematics, so the reader stays updated.
- Crux Mathematicorum by Canadian Mathematical Society - Challenging problems for secondary and undergraduate students, including an Olympiad Corner.
- Chalkdust Magazine - Independent magazine for mathematically curious readers, with free expository articles, interviews, puzzles, and downloadable issues.
Blogs
- BetterExplained - Maintained by Kalid Azad.
- ILoveMaths - Mathematics lessons and activities for Indian classes 6 to 12.
- 3Blue1Brown - Animated explanations of mathematics by Grant Sanderson.
- Math Is Fun - Lightweight lessons and reference pages for school mathematics.
Meetings and Conferences
- MathsJam - Monthly local recreational mathematics and puzzle meetups, plus an annual gathering in the United Kingdom.
- Talking Maths in Public - Biennial conference for mathematics communicators in the United Kingdom.
- Bridges - Annual conference on mathematical connections in art, music, architecture, and culture.
- Theoretical Computer Science - Curated resources on computation, complexity, logic, algorithms, cryptography, and related mathematics.
- Scientific Computing - Curated software for numerical analysis, scientific computing, meshing, solvers, and visualization.
- Optimization - Courses, books, notes, and software across mathematical optimization and operations research.
- Interactive Mathematics - Tools and libraries for building interactive mathematical explanations and explorations.
- AI for Mathematics - Research index covering AI-assisted mathematical reasoning, discovery, formal proof, and related datasets. Individual entries require independent review.
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