There’s a certain romance in the age-old debate: mathematics or physics? For me, the choice is clear. Mathematics, with its pristine elegance and unyielding logic, reigns supreme. Physics is fascinating, no doubt—it grapples with the universe, models reality, and gives us tangible advancements. But mathematics is the language, the bedrock, the eternal truth behind it all.
Physics asks, "How does the world work?" Mathematics asks, "What must be true?" And that distinction is everything.
When contemplating the philosophical depths of mathematics and the role of proofs, it reinforces the essence of what makes mathematics superior. Physics relies on experimentation, approximation, and the physical world—an ever-changing canvas. Mathematics, on the other hand, builds from axioms, through pure deduction, into a towering structure of truths that exist independent of the universe itself.
There is an undergraduate fantasy of mathematics: a solid bedrock of axioms leading to incontrovertible truths. While the practice of mathematics may not live up to this ideal perfectly, it still strives for something far more eternal than physics. Physics must revise its models when new evidence arises. Mathematics, once proved, is unshakable.
Take Euclidean geometry, for instance—axioms laid down thousands of years ago still hold in their domain. When mathematicians developed non-Euclidean geometries, they didn’t discard the old; they simply extended the language of truth. Physics, meanwhile, can be upended by a single experiment. Newton’s laws of motion were considered sacrosanct until Einstein redefined the playing field. What happens when another Einstein comes along?
Then there’s the question of proof. Mathematics is about knowing. Proofs are the crown jewel of mathematical thought. They aren’t just ways to show something is true—they’re ways to understand why it’s true. Physics can give you predictions, but mathematics gives you insight.
AI in mathematics further underscores this difference. Tools like Lean, which rigorously verify proofs, reflect mathematics’ commitment to precision. Lean insists on clarity—refusing to accept anything less than absolute logic. This kind of rigour doesn’t exist in physics, where approximations and empirical validations are often enough.
Some may argue that AI threatens the very nature of mathematics, automating proofs and leaving us to wonder: what’s left for human mathematicians? But this fear only highlights the superiority of mathematics. It’s not about the mechanics of solving problems but about uncovering deeper truths. Even with AI, mathematics retains its philosophical core.
And this is where physics stumbles. Without proof, mathematicians might end up like physicists, throwing out "any old nonsense" and letting machines sort it out. It’s a playful jab, but it rings true. Physics is always at the mercy of the physical world—a world we don’t fully understand and probably never will. Mathematics, in contrast, is self-contained, self-sufficient, and, dare I say, divine.
This isn’t to say that physics isn’t incredible—it undoubtedly is. But it’s dependent on mathematics, not the other way around. Physics needs mathematics to express its theories, but mathematics doesn’t need physics to exist. Even in a universe with no matter, no forces, no time, mathematics would remain. The primes would still be infinite, π would still be irrational, and Euler’s identity would still hold its breathtaking beauty.
For me, that’s why mathematics is superior. It’s not tied to the whims of the universe—it transcends it. While physics tries to explain what is, mathematics reveals what must be. And in that certainty, mathematics stands alone.
So yes, I’m team mathematics. Always have been, always will be. Physics may dazzle with its applications, but mathematics is where the real magic lies.
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