# Algebra and groups

- kind: region

Symmetry and structure. The largest collaborative proof in history lives here, along with problems that have been open since Galois.

Mathematics Subject Classification: 08, 12, 13, 15, 16, 18, 20, 22.

## Problems

- [Solving the quintic by radicals](/wiki/Problem:quintic-insolvability.md) (refuted)
- [Classification of finite simple groups](/wiki/Problem:classification-finite-simple-groups.md) (solved)
- [Inverse Galois problem](/wiki/Problem:inverse-galois.md) (open)
- [Burnside problem](/wiki/Problem:burnside-problem.md) (refuted)

Part of [Mathematics](/wiki/Continent:mathematics.md).

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