About fifty (50) years ago, Nobel Prize Winner Eugene P. Wigner reflected on the "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". In his paper, Wigner makes the following two points:
- Mathematical concepts are ubiquitous, they result in unexpected connections and are able to accurately describe the phenomena under investigation.
- Why mathematical concepts work is not understood, thus it is unclear whether or not theories based on these concepts are unique.
What is the Principal Focus and Role of Mathematics?
According to Nobel Prize Winner Eugene Wigner, the principal focus of mathematics should be on the invention of entirely new concepts, rather than the further development of existing concepts. Physics, says Wigner, is focused on discovering the “laws of nature” and since the universe is complex and unpredictable, that such “laws of nature” should even exist is not self-evident. Even more amazing to Wigner is that such “laws” only depend on a small set of manageable conditions; it is a miracle that people are actually able to discover these “laws”.
The principal role of mathematics in physics is not simply to evaluate already established theories (applied mathematics). Since “the laws of nature are written in the language of mathematics”, to Wigner, mathematical concepts are instrumental in the formulation of the laws of physics; Wigner further emphasizes that mathematical concepts are not chosen for their conceptual simplicity, but rather for their amenability to brilliant arguments.
Is the Language of Mathematics "the Correct Language"?
According to Eugene Wigner, the physicist’s use of mathematics to formulate the laws of physics can be described as “somewhat irresponsible”; the physicist assumes a mathematical concept is applicable simply because no other alternatives are available. Although the physicist’s approach may be “somewhat irresponsible”, Wigner acknowledges that the mathematical formulations in physics are often amazingly accurate descriptions of the phenomena under investigation. For Wigner, this only further substantiates the notion that mathematics is indeed “the correct language”.
Eugene Wigner acknowledges that the limitations of empirical laws are unknown and that fundamentally, “we do not know why our theories work so well”. Inevitably, we should be grateful for the language of mathematics. To Wigner, whether we attain the “ultimate truth” or resign ourselves to “the permanence of conflicting theories” will be determined solely by our willingness to go after more “miracles”.
Reference
Wigner, Eugene P., "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", Communications on Pure and Applied Mathematics, Vol. 13, 001-14, 1960.
Rehan Choudhary - Rehan's education is as follows: 1. BS Chemical Engineering 2. BA Economics 3. MBA He has worked for prestigous Fortune 100 ...
Join the Conversation