* Combinatorics: MacMahon is best known for his work in combinatorics, a branch of mathematics dealing with counting and arranging objects. He developed powerful techniques for enumerating and analyzing combinatorial structures like partitions, permutations, and compositions.
* Symmetric Functions: He made significant contributions to the theory of symmetric functions, a crucial tool in representation theory and other areas of mathematics.
* Mastermind: He is credited with inventing the classic logic puzzle "Mastermind" (although he initially called it "Pigs in Clover").
* Other Areas: MacMahon's contributions extended to other fields like algebraic geometry, probability, and statistical mechanics.
His Legacy:
MacMahon's work continues to influence mathematicians today. His insights into combinatorics and symmetric functions have had a profound impact on diverse fields like computer science, physics, and engineering.
Note: There are no notable mathematicians named "Percy" besides Percy Alexander MacMahon. If you have another name in mind, please provide it for a more accurate response.