The Reasonable Ineffectiveness of Mathematics By Derek Abbott (2013)

http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6600840

This paper contradicts the idea often used to bolster Platonism, that mathematics’ “unreasonable effectiveness” (Eugene Wigner) proves something about the existence of mathematical objects.

Hamming resigned himself to the idea that mathematics is unreasonably effective. These four points are: 1) we see what we look for; 2) we select  the kind of mathematics we look for; 3) science in fact answers comparatively few problems; and 4) the evolution of man provided the model.

[…} The following is anecdotal and is by no means a scientific survey. However, in my experience of interacting with mathematicians, physicists, and engineers, I would estimate that about 80% of mathematicians lean to a Platonist view.2 Physicists, on the other hand, tend to be closeted non-Platonists. An ensemble of physicists will often appear Platonist in public, but when pressed in private I can often extract a non-Platonist confession.

Engineers by and large are openly non-Platonist. Why is that?

This paper questions the ‘effectiveness’ of mathematics, raising a pragmatic viewpoint on complex numbers and highlighting the role of selection in generating pleasant fractals, before examining applications of mathematics to show that it isn’t always fit for purpose.

The reader is now asked to entertain strong non-Platonism, where all physical laws are tainted with anthropocentrism and all physical models have no real interpretative value. The interpretive value of physics is purely illusory. After all, a beam of light passing through a slit knows nothing of Fourier transforms; that is an overlaid human construct.

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