From Physics and Economics to Mathematics: Interdisciplinary Giants and the Mathematical Foundations of Modern Sciences
The journey of transforming from a physicist or economist to a mathematician is not unusual. In fact, this path is exemplified by several prominent figures who have made significant contributions to the fields of mathematics, physics, and economics. Here, we explore some notable individuals who have made this transition successfully.
Notable Translators from Physics and Economics to Mathematics
John von Neumann was originally trained in mathematics and physics, yet he made significant contributions to both. He is celebrated as one of the founders of game theory, which has profound applications in economics. His work in computer science and his involvement in early computing also showcase his interdisciplinary nature.
Hermann Weyl was a prominent figure in both mathematics and theoretical physics. His contributions to quantum mechanics and representation theory significantly advanced the field of mathematics. Weyl’s work highlighted the deep connections between mathematics and physics.
Nicolas Bourbaki is not one individual but a collective pseudonym for a group of mainly French mathematicians, some of whom had backgrounds in physics and engineering. They aimed to reformulate mathematics on an extremely abstract and formal basis. This collaborative effort underscores the importance of interdisciplinary work in advancing mathematical knowledge.
Roger Penrose is a physicist and mathematician renowned for his work in mathematical physics, particularly in general relativity and cosmology. Additionally, his contributions to the foundations of mathematics demonstrate the intricate relationship between these fields.
Marvin Minsky is primarily known for his work in cognitive science and computer science. However, he had a deep background in mathematics and made significant contributions to mathematical theories related to computation and artificial intelligence. This interdisciplinary approach has been critical in advancing both fields.
James Harris Simons is a mathematician and former hedge fund manager. He leveraged his mathematical expertise in quantitative finance, demonstrating the practical applications of mathematics in economics and finance. His transition from mathematics to finance highlights the versatility and applicability of mathematical knowledge.
Theoretical Physics and Mathematics
Theoretical physicists like Albert Einstein and Peter Higgs have produced their groundbreaking results through mathematics rather than experimentation. In fact, theoretical physics can be considered a branch of mathematics. The evolving nature of this relationship is exemplified in books such as Theoretical Physics by Simon_snitzeigt and Theoretical Physics and Its Foundations by Rolf-Peter Horst, which discuss the deep connections between physics and mathematics.
The Mathematical Foundations of Economics
The increasing influence of mathematics on economics is explored in the book How Economics Became a Mathematical Science by E. Roy Weintraub. This book delves into the history and evolution of the use of mathematical models in economic theory, demonstrating how mathematics has become an integral part of economic analysis.
It is important to note that these distinctions between fields such as physics, mathematics, and economics did not exist in the same form as they do today. For instance, Isaac Newton was a physicist, mathematician, and alchemist, as well as an astronomer, chemist, and Biblical scholar. Similarly, Physics, Mathematics, and Beyond by Fumitake Kuma further illustrates the fluid boundaries between these disciplines.
Genius sometimes doesn’t fit into nice little categories. This sentiment is echoed by the many individuals who have made significant contributions in multiple fields. The journey of transforming from physics or economics to mathematics is not only possible but also beneficial, fostering new insights and innovations.