What did Johann Peter Gustav Lejeune Dirichlet do for math?

Johann Peter Gustav Lejeune Dirichlet was a prominent 19th-century mathematician known for his contributions to number theory, mathematical analysis, and mathematical physics. He is best known for the Dirichlet principle in analysis, which led to the formulation of Dirichlet boundary conditions in partial differential equations. Additionally, he made significant advancements in the understanding of prime numbers, particularly through Dirichlet's theorem on arithmetic progressions, which states that there are infinitely many primes in any arithmetic sequence where the first term and the common difference are coprime. His work laid the groundwork for modern number theory and influenced many future mathematicians.