Repository | Book | Chapter

Since the outset of modern physical science, its close relationship to mathematics has distinguished it from other natural sciences. Once a science has reached a certain stage of formalisation, it always applies mathematics, but no science finds itself more frequently in the vanguard of genuinely mathematical developments than physics. The cases of general relativity and quantum mechanics are paradigmatic for what Eugene P. Wigner once called "the unreasonable effectiveness of mathematics in the natural sciences' In both cases, the basic equations of the theory made major use of mathematical structures discovered shortly before: Non-Euclidean geometry and matrix-valued differential equations. Since the early 1980s, however, the rapidly growing and extremely fertile interaction between string theory and differential geometry has inverted the direction of inspiration. Theoretical physicists constantly reveal genuinely mathematical results and propound beautiful mathematical structures undreamed of before. In this sense, Arthur Jaffe, a renowned mathematical physicist and editor of the discipline's leading journal, has recently proposed to modify Wigner's famous dictum into the "unreasonable effectiveness of theoretical physics in mathematics "²

DOI: 10.1007/978-94-017-0769-5_10

Full citation: