Unreasonable ineffectiveness of mathematics

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The unreasonable ineffectiveness of mathematics is a catchphrase, alluding to the well-known article by physicist Eugene Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". This catchphrase is meant to suggest that mathematical analysis has not proved as valuable in other fields as it has in physics.

For example, I. M. Gelfand, a famous mathematician who worked in biomathematics and molecular biology, as well as many other fields in applied mathematics, is quoted as stating,

Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology. ^[1]

K. Vela Velupillai wrote of the ineffectiveness of mathematics in economics.^[2]^[3]

Roberto Poli of McGill University delivered a number of lectures entitled The unreasonable ineffectiveness of mathematics in cognitive sciences in 1999. The abstract is:

My argument is that it is possible to gain better understanding of the "unreasonable effectiveness" of mathematics in study of the physical world only when we have understood the equally "unreasonable ineffectiveness" of mathematics in the cognitive sciences (and, more generally, in all the forms of knowledge that cannot be reduced to knowledge about physical phenomena. Biology, psychology, economics, ethics, and history are all cases in which it has hitherto proved impossible to undertake an intrinsic matematicization even remotely comparable to the analysis that has been so fruitful in physics.) I will consider some conceptual issues that might prove important for framing the problem of cognitive mathematics (= mathematics for the cognitive sciences), namely the problem of n-dynamics, of identity, of timing, and of the specious present. The above analyses will be conducted from a partly unusual perspective regarding the problem of the foundations of mathematics.^[4]

Jeremy Gunawardena has investigated the unreasonable ineffectiveness of mathematics in computer engineering. He delivered a seminar on the topic in 1998 at the University of Sydney [1].