Elon Musk famously posited, “We are most likely living in a simulation.” John Archibald Wheeler, who coined the term “black hole,” went even further, stating, “Every physical entity, at bottom, is derived from ‘yes/no’ binary information of question and answer; in other words, all physical things are, at their deepest level, products of information theory, a ‘participatory universe.'”
These perspectives are often predicated on a perceived “fact”: our world can be perfectly explained by mathematics. As Professor C.N. Yang once remarked, “Nature seems to make use of the simple mathematical manifestations of symmetry laws… When you compare the elegance of mathematical reasoning with the complex physical results it yields, a sense of awe for the power of mathematical symmetry laws arises.”
Indeed, mathematics acts like a razor-sharp blade. It slices through the fog of the cosmos, reveals the laws governing stars, and even predicted the existence of black holes. We often declare, “The universe is mathematics,” as if it were the ultimate master key.
Yet, we often overlook that this powerful tool in our hands is not divinely bestowed but man-made. It might merely be a form of self-validation. Its roots lie in our neurons, which operate on an on/off (electric/no electric) basis. This fundamental binary state gives rise to “choices,” leading to our concepts of 0 and 1, and ultimately, to the vast mathematical system we’ve constructed. We use mathematics to define the world and then employ the same tool to verify it. From another perspective, this is akin to “measuring one’s own shadow with a ruler”—the results, of course, will always perfectly align.
Consider the limitations of the human eye: we can only perceive visible light, unable to detect the rich electromagnetic spectrum. We’ve built a vivid world based on what we see, naturally assuming an astonishing congruence between our visual world and reality. Similarly, we readily accept that the remarkable congruence between mathematics and reality is an objective fact—until we discover radio waves.
Mathematics, too, has its “visible spectrum.” To me, the collapse of the wave function during quantum measurement serves as a stark reminder: we still lack a universally accepted mathematical framework that elegantly explains “why observation changes reality.” Isn’t this a resounding slap in the face for the “mathematics is omnipotent” argument? Logically, if there are phenomena mathematics cannot explain, it might suggest that the world isn’t fundamentally constructed from mathematics.
Some might argue, “That just means we haven’t found better mathematical tools yet.” True, when old mathematics hits a wall, new mathematics often emerges. Riemannian geometry paved the way for general relativity, and group theory gave birth to particle physics. But history also tells us that innovation rarely follows a predetermined path; it’s a series of leaps outside our comfort zone. I believe the true challenge isn’t merely about “inventing another mathematics” but about learning to embrace curiosity within uncertainty.
This curiosity stems from a gentle questioning of authority. We revere Euclid, but we must also leave room for non-Euclidean geometries. We worship Boolean logic, yet we need to make space for fuzzy and quantum logic. The business world mirrors this: we’re accustomed to traditional KPI metrics, often overlooking “invisible” creativity. We pursue precision, forgetting the infinite possibilities that might lie beyond its confines.
Mathematics may not be God; it might just be a myth created by humanity. Stripped of its divine robe, mathematics still shines brightly, but its sharp edges are also revealed. How many more phenomena will mathematics fail to illuminate in the future? Can we break free from the constraints of our neurons to explore new cognitive systems? In my view, true courage isn’t believing in the omnipotence of mathematics, but acknowledging the vastness of the unknown and being willing to throw ourselves into it headfirst.