For most people, the word "calculus" triggers a kind of academic vertigo. It marks the spot where the intuitive world of numbers hardens into a thicket of dry, mechanical symbols — a gatekeeper meant to be endured rather than a window meant to be looked through. We remember it as a series of hurdles. Steven Strogatz, a professor of applied mathematics at Cornell, remembers it as an epic.
Strogatz is what you might call a mathematics mensch. Despite his world-class credentials, he still describes himself as the "weakest math major" of his Princeton years, watching classmates solve problems at a speed he couldn't match. That humility is what makes him such an effective translator of the subject. Whether he's walking the hills of Ithaca dictating chapters to his dog, Murray, or trading ideas on the Into the Impossible podcast, Strogatz treats mathematics as a matter of human history and feeling, not formula. For him, calculus isn't a textbook subject. It's the language of God.
The Dialect of the Universe
The modern story of calculus turns on an unlikely meeting between two masters of very different crafts: physicist Richard Feynman and novelist Herman Wouk. While researching the Manhattan Project for a novel, Wouk — a man steeped in literature and faith — sat down with Feynman. As the conversation wound to a close, the physicist asked a piercing question: did Wouk know calculus? When Wouk admitted he didn't, Feynman gave him advice that would haunt the novelist for decades:
"You better learn it. It's the language God talks."
Wouk became a stand-in for every curious reader who has ever hit that wall. He took Feynman's advice seriously, and failed anyway — first with Calculus Made Easy, then in an audited high school class, falling behind both times.
The takeaway: that failure is what elevates calculus from a school subject to something closer to a revelation. If the universe is written in mathematics, Strogatz argues, calculus is the dialect of change — the grammar you need to read gravity's pull, a fluid's turbulence, or the flicker of a quantum particle. Learn it, and you're not memorizing formulas. You're listening to the universe speak in its native tongue.
Time Is the Emotional Dimension
There's a strange asymmetry in how we respond to art and music. In a conversation with physicist Robbert Dijkgraaf, Strogatz turned this over: a handful of notes can move a listener to tears, while the Mona Lisa — for all its genius — rarely does.
The difference, he suggests, is geometric. Painting occupies space; music occupies time. A canvas can be taken in all at once, but a melody unfolds note by note, forcing you to experience it at the exact pace its composer intended.
The takeaway: if that's true, then time — not space — is the emotional dimension. Music moves us because it's inseparable from memory, loss, and the irreversible flow of a life. We can wander freely through space, revisiting any point we like. Time offers no such freedom. We are not tourists in it; we're passengers.
The Scientist's Moral Obligation
Strogatz argues that researchers have both a moral and a strategic reason to master communication. Morally, because the public funds their work and deserves to understand it. Strategically, because the scientists who can explain themselves are the ones whose ideas survive.
He reaches for a baseball metaphor: we train scientists to hit home runs — the technical breakthrough, the hard result — but nobody teaches them how to run the bases. The "soft skills" of storytelling and clarity are treated as optional, even though they're what actually get an idea across the plate. At Cornell, Strogatz runs a Mathematical Communication Seminar where PhD students dissect everything from Fields Medal addresses to YouTube explainers, hunting for what makes an idea land.
The takeaway: clear communication isn't about dumbing science down. It's closer to a survival trait. A researcher who can't make their work legible to a lay audience will eventually lose the grants, the recognition, and the public trust that keep the whole enterprise funded. Clarity isn't a courtesy — it's a precondition for progress.
The Infinity Principle: A Beautiful Fiction
At the center of Strogatz's worldview sits what he calls the Infinity Principle — the trick that makes the impossible solvable. Take a complex, smoothly changing problem, like a planet's orbit. Slice it into infinitely many, infinitesimally small pieces. At that scale, curves flatten into straight lines and variables behave like constants. Solve the trivial problem at that tiny scale, then stitch the answers back together to recover the whole.
He contrasts this with Feynman's rival candidate for the universe's foundational idea — the Atomic Hypothesis, the notion that everything is built from indivisible parts. The irony is sharp: the Atomic Hypothesis is probably true. The Infinity Principle almost certainly isn't — reality, at its smallest scale, may not be smooth or infinitely divisible at all. It's a beautiful fiction.
The takeaway: the fiction works anyway, and works spectacularly. Even though the universe is likely discrete at bottom, treating it as continuous is what lets us predict motion with staggering precision. Consider: it takes only about 60 digits of pi to measure the entire observable universe down to the Planck scale. Calculus turns an admitted lie about the world into a tool sharp enough to feel like magic.
Why AI Still Lacks the Human Edge
Strogatz calls himself a materialist — he doesn't think humans are made of anything more mysterious than the "star stuff" that also builds a silicon chip. Still, he points to three things that currently separate human insight from artificial intelligence:
- Embodiment. We have direct physical interfaces to the world — vibrating eardrums, sensitive fingertips — that let us feel reality rather than just process data about it.
- Desire. Machines calculate, but they don't want to understand. There's no restlessness driving them toward a question.
- Origination. An AI can master chess or Go with dazzling, even "swashbuckling" style — but it didn't invent either game. It optimizes within rules someone else wrote.
The takeaway: calculation has already become a machine's job. Insight — the ability to ask why something is true, not just confirm that it is — remains, for now, a distinctly human one. A machine can solve the equation. It doesn't yet feel the beauty of the answer.
The "Cards Face Up" Philosophy
Strogatz's advice to the next generation comes down to a phrase he lives by: cards face up. It's a commitment to transparency — in life and in mathematics — that strips out the gamesmanship common to high-level academia. He borrows Mark Twain's line on the subject:
"If you tell the truth, you don't have to remember anything."
In the classroom, he tempers that with a rule from mathematician Mark Kac: tell the truth, and nothing but the truth — but not the whole truth all at once.
The takeaway: this is intellectual economy, not evasion. Simplifying for a student isn't the same as lying to them, and managing complexity so a beginner isn't drowned in it is simply good teaching. Honesty, done well, is also efficient — it frees the mind from maintaining a facade and redirects all of that energy toward the actual work of understanding.
Conclusion: The Method of Exhaustion
We may never grasp infinity in our bones — it's a concept that has always provoked as much dread as awe. But through what Archimedes called the method of exhaustion — squeezing a problem from every side until the truth has nowhere left to hide — we've learned to operate with the infinite well enough to build a modern world out of it. Calculus lets us chart the stars, and it anchors us, at the same time, in a universe defined by ceaseless change.
As artificial intelligence closes in on our calculating abilities, the question worth sitting with is this: is the desire to understand our last uniquely human trait? And if the universe really is written in a language of change — are we willing to learn the alphabet?
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