The "enormous theorem" — one of the greatest achievements in the history of mathematics. Over 50 years, more than 100 mathematicians produced a proof spanning tens of thousands of pages to answer a single question: what are all the finite simple groups? Explore the answer through 21 interactive demonstrations, from the prime-order cyclic groups to the Monster and its mysterious moonshine connections.
See also: Group Theory for the foundational axioms and structure these groups inherit, Representation Theory for the irreducible representations of simple groups, and Lie Groups for the infinite families of groups of Lie type.
The atoms of algebra — groups with no proper normal subgroups
Z/pZ and composition series — factoring groups into simple pieces
Why A_n is simple for n ≥ 5 and what that means for polynomials
Matrix groups over finite fields — the 16 infinite families
From the Mathieu groups to the Monster — the exceptions that prove the rule
50 years, 100+ mathematicians, 10,000+ pages — the enormous theorem
The Monster meets modular functions — the most surprising connection in mathematics