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Dispelling the Mythmakers

Is mathematics an effective way to describe the world?
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Is mathematics an effective way to describe the world?


Mathematics has been called the language of the universe. Scientists and engineers often speak of the elegance of mathematics when describing physical reality, citing examples such as π, E=mc2, and even something as simple as using abstract integers to count real-world objects. Yet while these examples demonstrate how useful math can be for us, does it mean that the physical world naturally follows the rules of mathematics as its “mother tongue,” and that this mathematics has its own existence that is out there waiting to be discovered? This point of view on the nature of the relationship between mathematics and the physical world is called Platonism, but not everyone agrees with it.

Derek Abbott, Professor of Electrical and Electronics Engineering at The University of Adelaide in Australia, has written a perspective piece to be published in the Proceedings of the IEEE in which he argues that mathematical Platonism is an inaccurate view of reality. Instead, he argues for the opposing viewpoint, the non-Platonist notion that mathematics is a product of the human imagination that we tailor to describe reality.

This argument is not new. In fact, Abbott estimates (through his own experiences, in an admittedly non-scientific survey) that while 80% of mathematicians lean toward a Platonist view, engineers by and large are non-Platonist. Physicists tend to be “closeted non-Platonists,” he says, meaning they often appear Platonist in public. But when pressed in private, he says he can “often extract a non-Platonist confession.”

So if mathematicians, engineers, and physicists can all manage to perform their work despite differences in opinion on this philosophical subject, why does the true nature of mathematics in its relation to the physical world really matter? The reason, Abbott says, is that because when you recognize that math is just a mental construct—just an approximation of reality that has its frailties and limitations and that will break down at some point because perfect mathematical forms do not exist in the physical universe—then you can see how ineffective math is.

And that is Abbott’s main point (and most controversial one): that mathematics is not exceptionally good at describing reality, and definitely not the “miracle” that some scientists have marveled at.


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