Josh Anderson wrote;
It makes sense to say that basic mathematics was developed to describe things in the everyday world. We can understand the origin of things like counting and addition and how to calculate area. However, as Wigner goes on to argue, this simple explanation fails to account for so much of what we see.
The work of professional mathematicians often involves incredible ingenuity and extraordinary feats of logic. Some theorems and proofs take years to work out. And yet, astonishingly, many of the most brilliant and insanely abstract concepts turn out to model real-world phenomena perfectly. They fit like a lock and key.
Consider for a moment just how extraordinary this is. We have this set of things our minds seem to have produced in an abstract, non-physical realm of ideas. And we have another category or set of things we’ll call “things the universe does.”
Then, as history unfolds, we discover that there is an exact correspondence between various mathematical concepts and the “things the universe does.” There’s a kind of remarkable overlap between what’s going on in our minds and what’s going on out there. And very often, the math was worked out long before we went looking out in the world for a fit.
To quote Wigner, “It’s difficult to avoid the impression that a miracle confronts us here.”
This is remarkable. The things the universe appears to be doing at the level of physics are mirrored in the mathematical realm. The universe, it seems, is behaving in accordance with the products of the mind.
Is mathematics something humans invented?
If you answer yes, how did something that is purely an artifact of mind get out there in the wild? How does it make it into the very fabric of the external world?
Around every corner in physics, we find concepts no one thought would ever show up in the familiar world. But they do. Crazy, non-intuitive principles and things no one ever dreamed would leave the pages of mathematics journals to turn out to be exactly what is needed to describe what the world is doing.
You could almost put this into a syllogism:
Premise one: Mathematical entities are the products of the mind.
Premise two: The universe behaves according to mathematical entities.
Conclusion: Therefore, the universe behaves according to the products of the mind.
But maybe we’ve got this all wrong. Maybe mathematical entities are not actually produced by our minds. Yet, if we change our story and accept that mathematics is somehow really out there, really existing in a humanity-independent way, we still have not managed to escape from this conclusion. In fact, if it’s discovered and not invented, the mystery is even more profound.
Now we have this realm of abstract ideas and relationships, an infinite logical landscape to which we have direct access to through our minds. And yet, while non-physical, somehow, this realm guides the behavior of things in the physical world.
It seems inescapable. Something mind-like is running the world, providing the framework, the tracks for physical reality to run on.
Einstein himself struggled to explain how this could be: “How is it that mathematics, being after all a product of human thought, is so admirably appropriate to the objects of reality? Is human reason then, without experience, merely by taking thought, able to fathom the properties of real things?”
If anyone in history had a right to comment on this issue, it was Einstein. He, relying more or less entirely on thought experiments, was able to unlock some of the best-kept secrets of the universe. He himself found this astonishing, saying famously, “The most incomprehensible thing about the world is that it is comprehensible.” Why should what’s really out there have corresponded meaningfully to what was going on in his mind?
Einstein spoke reverently, even religiously, of the experiences he had in beholding the “radiant beauty” that shone forth when he sought to peer into the mysteries of the universe. He was satisfied, he said, with a sense of the “marvelous structure of existence” and his “humble attempt to understand even a tiny portion of the Reason that manifests itself in nature.”
Speaking of mathematics in particular, he wrote:
“Pure mathematics is, in its way, the poetry of logical ideas. …In this effort toward logical beauty, spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.”
The more you think about it, the more remarkable it becomes. How is it that, with little more than some deep reflection, a man sitting alone in a Swiss patent office was able to grasp the most profound secrets of space and time? What does it say about the universe that pure thought is able to disclose many of its deepest enigmas?
The philosopher David Wood brings this into sharp focus:
“Before you knew that the universe is governed by elegant mathematical equations, would you have had reason to await that? Would you expect the universe to be like that? Of course not. Mathematics is a language. The universe operates according to language. This should not be at all surprising for those who believe in God. It should be horrifying to atheists because that is the last thing you should expect.”
