Maths is a Pain in the Physics
By Jim Redgewell
Introduction: When Models Become Masters
Physics is supposed to be about understanding the natural world. Yet somewhere along the line, it seems we’ve forgotten that. While mathematics has always been a crucial tool in the physicist’s kit, today it often feels like mathematics has taken over—as if equations are reality, and if we can write the math, we can stop asking the questions.
But as I argue here, and as many of the greatest minds in science have warned: math should serve understanding, not replace it.
The Authority of Mathematics—and Its Limits
There’s no question that mathematics works. It models planetary motion, predicts quantum behavior, and underlies technologies we use every day. But it’s not the whole picture. Mathematics is a language—a powerful one—but it is not the same as meaning.
Albert Einstein made this distinction clear when he said:
“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
—Albert Einstein (Wikiquote)
In other words, the more mathematically perfect a system is, the less likely it is to fully describe messy, unpredictable reality.
Einstein himself relied on intuition, physical reasoning, and mental models—what we might call "common sense"—to discover the theory of relativity. Mathematics came afterward, as a way to express what he already understood conceptually.
Feynman, Sex, and the Problem of Symbol Worship
No one combined mathematics and intuition better than Richard Feynman. Yet Feynman was highly critical of those who believed that manipulating symbols was the same as grasping physical truth.
His famously irreverent quote captures it perfectly:
“Physics is to math what sex is to masturbation.”
—Richard Feynman (Goodreads)
Feynman loved equations—but he loved understanding more. In his Lectures on Physics, he emphasized visual models, experimental thinking, and questioning assumptions over blindly following formalism (source).
When Mathematics Goes Rogue: The Case of String Theory
One of the clearest examples of math overtaking physics is string theory. Elegant? Certainly. Mathematically rich? Incredibly so. But testable? Not yet—and maybe never.
The theoretical physicist Peter Woit has been one of its most vocal critics. In his book Not Even Wrong, he argues that string theory represents a shift from science to speculative mathematics. It is not falsifiable in the Popperian sense and thus risks drifting out of the domain of empirical science. (Book site)
Lee Smolin, another prominent physicist, echoed this concern in The Trouble with Physics, warning that a generation of physicists is being trained to value mathematical beauty over physical insight (source).
Reclaiming Physical Meaning
So what do we do? Abandon math? Of course not. The challenge is to bring balance back to the relationship between mathematics and meaning.
We need to recover what used to be called “natural philosophy”—the effort to understand nature conceptually, not just model it numerically.
This doesn’t mean dumbing things down. It means re-grounding physics in questions:
-
What is a particle?
-
Why does time dilate?
-
What is space, really?
These questions aren’t answered by math alone—they require interpretation, physical reasoning, and yes, a good dose of common sense.
Toward a Physics of Understanding
The next era of physics should not just chase new equations. It should chase meaning.
The great theoretical physicist Carlo Rovelli has said:
“The best theories are not only predictive—they are explanatory.”
—Carlo Rovelli (source)
To that end, we must demand more than math. We must demand that our theories tell us why something happens, not just how to calculate it.
Let’s return to a physics where a child can ask “why is the sky blue?”—and get an answer that means something.
Conclusion: A Call for Conceptual Clarity
Mathematics is a powerful servant but a dangerous master. When physics becomes obsessed with mathematical purity and elegance, it risks losing its heart.
Let’s not forget: the point of physics is to make sense of the world. And that means more than equations—it means asking the right questions, building mental pictures, and staying rooted in reality.
As I’ve argued:
Math should serve understanding, not replace it.
That, to me, is the most important equation of all.
No comments:
Post a Comment