A Survey on Mathematical Methods and Their Impact on Modern Science

Mathematics has been described as the "language of science" for many years, with mathematics forming the cornerstone of many of the greatest scientific advances. In this paper, there is given a comprehensive outline of the diversified mathematical methods involved in modern science and their extended impacts on subjects of physics, biology, computer science, and economics. Throughout the paper, the focus lies on the mathematical modeling, numerical analysis, optimization, and statistical methods to advance knowledge and tackle complex real-life problems. Moreover, we deal with the challenges and opportunities of introducing new mathematical techniques into modern science.