websites

wikis and the like

• The Stacks Project
• The nLab
• Kerodon – An online resource for homotopy-coherent mathematics
• The Automorphic Project – An open source textbook and reference work on automorphic representations

• The Clowder Project – An online resource for category theory and mathematics

• Foundations of Relative Category Theory
• Joyal’s CatLab
• GroupProps
• ProofWiki

books and resources

• The Electronic Library of Mathematics
• Euclid’s Elements with Coloured Diagrams and Symbols
• Analysis Situs (FR)
• EGA & SGA, SGA IV
• The TeXromancers
• Tim Hosgood’s translations
• Livres en accès libre (FR)
• Kedlaya’s notes on prismatic cohomology and class field theory,
• Milne’s notes on… many things
• Visual Algebra textbook
• Category theory: online lecture notes, etc.
• LibGen and Sci-Hub. Use Tor Browser to access restricted websites in your country
• Awesome books that are free: Cohomology of Number Fields (v2.3), The Rising Sea (Feb. 24), Grimoire d’Algèbre Commutative
• Shelah’s Archive

databases

number theory

• The L-Functions and Modular Forms Database
• Number fields, polynomials, Galois groups:
  • GaloisDB - A Database for Number Fields [paper]
  • PARI/GP - A database of Galois polynomials and number fields
• Dessins d’enfants and Belyĭ maps:
  • Belyĭ maps (LMFDB) [paper]
  • Dessins d’enfants with field of moduli (Guillot)
  • Plane trees and Shabat polynomials (Bétréma-Zvonkin)
  • Granboulan’s thesis
• Inverse Galois problem for small simple groups (Zywina)
• manYPoints – Table of Curves with Many Points
• A database of databases (Number Theory Tables)

other databases

• Group theory:
  • ATLAS of Finite Group Representations
  • Abstract Groups (LMFDB)
  • Group Names
• π-Base: topological properties and (counter)examples
• The OEIS for Integer Sequences
• The Knot Atlas
• Optimal Packings
• House of Graphs
• SmallCategories
• The Digital Library of Mathematical Functions
• DaRT - The Database of Ring Theory
• Catalogue of Mathematical Datasets
• The \(M_{g,n}\) bucket list , Le Superficie Algebriche, Fanography and Cubic 4-folds, Hyperkähler varieties, Grassmanians, Map of Grothendieck topologies for schemes, and basically everything by Pieter Belmans.

blogs

• Terence Tao
• John Baez
• Jordan Ellenberg
• Persiflage
• Why is this nontrivial? (FR)
• Cihan Posts Theorem (Twitter account)
• neverendingbooks (static version)
• Joel David Hamkins (also has a substack)
• LocalCharts
• n-Category Café

Cool Twitter thread about \(G\)-sets

Proof of the second-incompleteness theorem via the proof speed-up phenomenon by Joel David Hamkins (on Twitter)

A good Twitter thread about the absolute Galois group of ℂ(T) by David Madore, who also has these excellent blog posts:

• Le topos effectif
• Un joli problème paradoxal de théorie de l’information
• Nombres ordinaux : j’ai lu ce thread quand j’étais au lycée, ça m’a hanté de fascination
• and many more…

Join Mathstodon!

youtube

• 3Blue1Brown
• Mathologer, for example this proof of quadratic reciprocity
• Aleph 0, for example this video on class groups
• Peak Math
• Math-Life Balance
• Dr. V
• Quanta Magazine
• Numberphile, in particular Magic Square of Squares (a sweet introduction to arithmetic geometry by Anthony Várilly-Alvarado), Eating Curves for Breakfast (an introduction to algebraic curves by Isabel Vogt)
• Certainly not to everyone’s taste, but I liked Math Curator Zanachan’s series on class field theory, its history and reciprocity laws.

Great videos: Abel’s theorem, Regular Polyhedra, Counting Points on the E₈ lattice, Gareth Jones explains Dessins d’enfants

En français:

• El Jj
• Voyages au pays des maths
• Scientia Egregia, dont cette superbe vidéo sur Riemann-Roch et celle-ci sur les « distributions formelles »
• Thomaths
• Maths*
• Micmaths et en particulier sa vidéo sur le nœud de Conway
• Le Myriogon et ses bonus
• Philippe Caldero, qui présente souvent des petites pépites avec le sourire. Petite sélection:
  • Théorème de progression arithmétique de Dirichlet (version faible)
  • Un scoop sur Cayley-Hamilton?
  • Loi de réciprocité d’Artin [1] [2] [3] [4]
• Physique : Science étonnante, Passe-sciences

Talks I enjoyed watching:

• Conférence surprise (FR): A talk by E. Ghys about a funny problem in real algebraic geometry
• Grothendieck-T. theory by P. Lochak
• Homology of Hurwitz spaces by O. Randal-Williams
• BSD and Estimates for Class Groups of Number Fields by J. Tsimerman

Non-mathematical YouTube gems:

• Tom7 (who has many incredible videos)

formalization stuff

• XenaProject
• The 1Lab for cubical type theory
• TypeTopology
• Lean Zulip
• Dedukti
• The Four Color Theorem in Coq, The Independence of the Continuum Hypothesis in Lean, \(\pi_4(\mathbb{S}^3)\) in HoTT/Cubical Agda, Feit-Thompson in Coq, Liquid Tensor Experiment
• Fermat’s Last Theorem: n = 3 in Lean, n ∈ {3, 4} in Isabelle

misc

• A fun rabbithole to fall into: Part 1, Part 2 and Part 3.
• Tie Knot Generator
• Coherence Diagrams for a Tetracategory
• The Map of the Universe (according to model theorists)
• Erdős problems by Thomas Bloom

conference lists

• Number Theory Conferences
• Kedlaya’s list of conferences in arithmetic geometry
• Noncommutative Algebraic Geometry

tools

• TeXpresso: live rendering/incremental compilation for (La)TeX
• q.uiver: draw commutative diagrams easily
• IPE: make figures
• My own tex2unicode script
• TeXpaste
• Desmos, WolframAlpha, SageCell

games

• The Natural Number Game
• My own Seven Trees in One game
• Conway’s \(M_{13}\) puzzle (blog post) (arXiv)
• Taquin sur \(M_{24}\)
• Infinite Chess: (play the game), (mate in ω²), (talk by A. Tsevas about mate in ω²), (Evans-Hamkins)
• Infinite Hex (talk by I. Törmä), Infinite Wordle, Infinite Games Workshop
• Funny NP-hardness proofs: Mario, Candy Crush, Tetris, Wordle
• Pan-Galactic Division / Division by Four: as someone who spent some time being fascinated by the original division by three article, I feel weird about such a simple algorithm existing!

music

• Ian Ring’s Amazing Scale Finder
• Sevish’s Scale Workshop
• IMSLP
• Fun music-theory channels on YouTube: 12tone, 8-bit music theory, David Bruce, Nahre Sol, Partoche (FR), Yogev Gabay, Addy D.

other

• Free Foucault
• Language Science Press: awesome linguistic books in open-access!