Archimedes had his hand in many things, a lot of which are still applicable today. Check out the link below for everything you ever wanted to know about his research.
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Archimedes conducted research in various fields, including mathematics, physics, and engineering. He made significant contributions to geometry, algebra, and calculus. His principles of buoyancy and lever mechanics, known as Archimedes' Principle and the Law of the Lever, are still used today in various engineering applications. Additionally, his discoveries in mathematics laid the foundation for many modern scientific and technological advancements.