Mathematical research involves the exploration and study of mathematical concepts, theories, and problems. Researchers aim to develop new mathematical ideas, prove existing theories, or find solutions to unsolved problems. This work can range from pure mathematics, which focuses on abstract concepts, to applied mathematics, which uses mathematical methods to solve real-world issues. Researchers often collaborate with others in academia or industry, sharing their findings through publications and conferences. Notable mathematicians, such as Andrew Wiles, who proved Fermat's Last Theorem, have made significant contributions to the field. Overall, mathematical research plays a crucial role in advancing knowledge and understanding in mathematics.