A periodic table of finite simple groups: 18 infinite families and 26 sporadics
burny_tech · x · 2026-10-28
axiommathai shared an infographic laying out the classification behind the "Enormous Theorem": finite simple groups are the building blocks of finite groups, like primes are for whole numbers.
- Infinite families: cyclic groups Cp, alternating groups An, plus 16 groups of Lie type (6 classical, 10 exceptional, including the Tits group).
- 26 sporadic groups: from the Mathieu, Janko, Conway, and Fischer families down to the Monster, with 8.08×10^53 elements.
There are no others — the full classification rendered as a clean "periodic table of finite symmetry."
More from Research
- A Bayesian take on P vs NP: likelihood ratio 10:1 favors P=NP — jessi_cata · 2026-10-28
- Karpathy's GitHub repos as a free LLM learning path: micrograd to nanochat — lmoroney · 2026-10-28
- AI Science vs. Human Science: An Essay Inspired by Thurston's Math Philosophy — hugo_larochelle · 2026-10-28
- Top econometricians publish paper on how their LLMs wrote it — lihua_lei_stat · 2026-10-28
- Frontier models hit 73.3% on SpatialBench 10 months after release, near 75% ceiling — kenbwork · 2026-10-28
- Minimal PyTorch project implements transformer autograd by hand for learning custom backward passes — ifaposto · 2026-10-28