Why was the classification of finite simple groups a major mathematical project?

The classification of finite simple groups was a major mathematical project because these groups serve as the fundamental building blocks of group theory. Much like prime numbers are the atoms of arithmetic, simple groups are the irreducible components into which all finite groups can be decomposed.12

The project gained significant momentum following a 1963 breakthrough by Walter Feit and John Thompson, who proved that all non-Abelian finite simple groups have an even number of elements. This result provided a vital structural handle for mathematicians to begin a systematic search for all such groups.12

The endeavor was monumental, spanning decades and involving the collective contributions of hundreds of mathematicians whose work filled thousands of pages. Completed in the early 1980s, the classification revealed a complex landscape, including the discovery of exotic structures like the "Monster" group, which operates in 196,883 dimensions. It remains a landmark example of a large-scale, collaborative mathematical achievement that lacks a single, simple systematic description.12