The French mathematician Évariste Galois is primarily known for his work in which?

Évariste Galois is primarily known for his work in Galois Theory. This branch of mathematics revolutionized the understanding of field theory and algebraic equations. Galois Theory is concerned with the study of field extensions and their corresponding algebraic equations, providing a deep understanding of the relationship between polynomial equations and their solutions. Galois developed this theory at a young age before his untimely death at 20, leaving behind extensive manuscripts that were later published and significantly contributed to the development of abstract algebra and mathematical physics. Through his profound insights, Galois opened up new paths for future mathematicians, allowing them to solve equations that were previously considered unsolvable.