To have a basic understanding of how accurate and loyal this universe is to math, we could visualize our solar system. Back in 1905, scientists discovered that the orbit of Uranus and Neptune was not following Newton’s Gravitational laws, and using mathematical expressions, predicted that there must be some other heavenly body that was influencing their orbit. In 1930 Clyde Tombaugh used the method of comparative plating of astronomical photographs also known as the blink comparator technique. The calculations were made precise to a point where we could even tell where to point our telescope in order to find that heavenly body. And thus, Pluto was discovered. Recently, Peter Higgs took the standard model of particle physics, equations that combine Quantum theory with an understanding of relativity, and predicted that if we build a machine (a Hadron collider), we’ll be able to come up with new particles. Einstein predicted using Mathematics that Gravitational waves existed which was experimentally proven recently. So, in a sense, the Universe has always been the language of Mathematics, and we’ve only learned to recognize the alphabet of it recently.Sunny Labh, “Why Mathematics Is the Ultimate Language of the Universe” at Medium (October 15, 2022)
It’s a real universe but its underpinnings are immaterial.
Shades of Eugene Wigner (1902–1995) and “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” (1960): “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.”
But now… is mathematics invented or discovered? That’s a big question:
Some mathematical ideas are so fundamental that even if you didn’t discover them, someone else would have. Mathematics is the language of science and its structures are innate to nature. Even if the universe were to disappear tomorrow, the eternal mathematical truths would still exist. It is upon us to discover it, understand its functioning and build on our knowledge to find solutions to the physical event we seek to control.
Many mathematicians support this view. They have discovered many eternal truths, independent of the mind that found them. For example, there is no highest prime number, and the number pi when expressed in decimals can go on forever.
Math manifests itself in nature and holds answers to many universal questions. One such example where math can be found in nature is The Golden Ratio.Ketaki Bepat, “Is Mathematics An Invention Or A Discovery?” at ScienceABC (October 29, 2021)
We certainly do live in a designed universe in the sense that it is anything but a mere jumble of numbers.
You may also wish to read: Yes, you can manipulate infinity in math. The hyperreals are bigger (and smaller) than your average number — and better! (Jonathan Bartlett)