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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,
K. Vela Velupillai wrote of The unreasonable ineffectiveness of mathematics in economics.^{[2]}^{[3]} To him "the headlong rush with which economists have equipped themselves with a half-baked knowledge of mathematical traditions has led to an un-natural mathematical economics and a non-numerical economic theory." His argument is built on the claim that
At the same time, however, Sergio M. Focardi and Frank J. Fabozzi have written of The reasonable effectiveness of mathematics in economics.^{[5]} Acknowledging that "economic science is generally considered less viable than the physical sciences", and that "sophisticated mathematical models of the economy have been developed but their accuracy is questionable to the point that the present [i.e.2007–08] economic crisis is often blamed on an unwarranted faith in faulty mathematical models," they nevertheless claim that
Roberto Poli of McGill University delivered a number of lectures entitled The unreasonable ineffectiveness of mathematics in cognitive sciences in 1999. The abstract is:
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.^{[8]}
Quantum mechanics, Electromagnetism, Energy, Astronomy, Thermodynamics
Macroeconomics, Microeconomics, Adam Smith, Game theory, Utility
Genetics, Biochemistry, Protein, Cell biology, DNA replication
Monash University, Australian National University, University of Cambridge, National Taiwan University, Queensland University of Technology
Science, Psychology, Isaac Newton, Literature, Philosophy of science
Mathematics, Philosophy of mathematics, Foundations of mathematics, Alan Turing, Physics
Philosophy of science, Mathematics, Computer science, Philosophy of mathematics, Foundations of mathematics