How are Mathematics and Reality related?
“Are mathematics the universe’s “Mother Tongue?” from phys.org
“Of course, when we talk about reality we are also talking about consciousness, or the human window on reality.
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.”
“An abstract object is an object that exists outside of spacetime, or, being more careful, a non-spatiotemporal object, that is, an object that exists but not in spacetime. In any event, such objects are non-physical,non-mental and acausal. The belief in such objects is called Platonism, and the disbelief anti-Platonism. A mathematical object is just an abstract object that would ordinarily be thought of as falling in the domain of mathematics, for example a number, a function or set. Finally, mathematical Platonism is the view that there exists mathematical objects, and mathematical anti-Platonism is the view that there do not exist such objects…”
– read more about mathematical Platonism/non-Platonism