Years later, those same students are laying out bridges, tuning the suspension of a car, or modeling how a skyscraper sways in a gale — still leaning on two short expressions, and rarely sparing a thought for the men behind them. Yet behind the symbols stand two Englishmen who spent much of their lives locked in open hostility, and whose quarrel helped shape which discoveries the world got to keep.

Two Men, One Century

Robert Hooke was born in 1635 on the Isle of Wight. Isaac Newton followed seven years later, in 1642, in a Lincolnshire farmhouse. They came of age during what historians now call the Scientific Revolution — a stretch of decades when old certainties buckled, telescopes disclosed new worlds, microscopes revealed invisible ones, and mathematics was quietly becoming the language of nature.

Hooke and Newton did not merely witness that revolution; they stood near its center. And though each is remembered today for a single equation, both ranged across nearly every science of their age.

The Forgotten Genius

Ask an engineering student what Robert Hooke discovered, and the answer comes back in three words: Hooke’s Law. It is a thin epitaph for so restless a mind.

Hooke improved the microscope and the telescope. He helped survey and rebuild London after the Great Fire of 1666. He designed instruments, puzzled over fossils, and made observations in astronomy. Peering at a sliver of cork through one of his own lenses, he saw a honeycomb of tiny compartments and gave them a name that has never left biology: cells.

His book stunned a continent. Then history filed him under a single law.

His 1665 volume, Micrographia, astonished Europe with its fold-out engravings of fleas and crystals and the compound eye of a fly. For many readers it was the first glimpse of a hidden microscopic world. Hooke’s curiosity seemed to have no floor. And yet posterity has narrowed him to one equation about springs.

The Architect of Mechanics

Newton needs less rescuing. He devised the calculus independently of Leibniz, formulated three laws of motion, explained the orbits of the planets, and bound the heavens and the earth together under a single law of universal gravitation.

His 1687 masterwork, the Philosophiæ Naturalis Principia Mathematica, is routinely called one of the most important books ever written. Few thinkers have reshaped humanity’s picture of nature so completely, or left successors so ready to say, in Newton’s own borrowed phrase, that they had seen further only by standing on the shoulders of giants.

An idea, Newton insisted, is not enough. Science also demands proof.

THE HEART OF THE QUARREL OVER GRAVITY

A Feud Conducted in Letters

It is tempting to imagine Hooke and Newton in separate eras. They were not. Both belonged to the Royal Society; both attended its meetings, traded letters, and pored over each other’s work. What began as collegial scrutiny curdled, over the years, into something closer to enmity.

The first real rupture came in 1672, when Newton presented his experiments on light and color — the claim that white light is a mixture of the spectrum’s hues. Hooke, who had his own theory of light, objected sharply. Scientific disagreement is ordinary and healthy. Personal disagreement is more corrosive. Newton took the criticism to heart, and for years afterward grew reluctant to publish at all. It is sobering to wonder how many ideas stayed locked in his notebooks because of it.

Then Came Gravity

The bitterest dispute concerned gravity itself. Hooke believed he deserved credit for suggesting that the planets are drawn toward the Sun by a force that weakens with distance. Newton allowed that Hooke had, indeed, floated the notion.

But Newton drew a hard line between a suggestion and a demonstration. Hooke had a hunch; Newton supplied the mathematics. Using geometry and his new calculus, he proved that the very law pulling an apple to the ground could also hold the Moon in its orbit and swing the planets around the Sun. That proof changed science forever.

Hooke felt robbed of his due. Newton felt Hooke was claiming ownership of mathematics he had never done. Tellingly, it was in a 1675 letter to Hooke that Newton wrote his most famous sentence — about seeing further by standing on giants’ shoulders — a line some historians read less as humility than as a quiet barb at his rival. The argument never truly ended.

The Irony of It All

Here is the twist the two men never lived to enjoy. They spent years at each other’s throats. Yet today every engineering student, unknowingly, brings them back together at the very first opportunity.

Hooke’s law tells us how an elastic material pushes back when it is stretched or squeezed. Newton’s second law tells us how a force sets mass into motion. Apart, each is powerful. Set one equal to the other — the spring’s restoring pull on one side, the resulting acceleration on the other — and out falls the equation of simple harmonic motion, the seed of vibration analysis, structural dynamics, and much of modern mechanical engineering. The rivals who could not agree in life now collaborate on every blackboard.

Beyond Springs

At a glance, Hooke’s law looks like a fact about coil springs. Its reach is far wider. Wherever engineers analyze elastic deformation — a steel beam bending, reinforced concrete before it cracks, a machine part under load, a vibration isolator absorbing a jolt — Hooke’s insight is quietly at work.

Newton’s second law travels just as far from the orchard. It governs cars and aircraft, satellites and spacecraft, bridges shaken by earthquakes, towers pushed by wind, the joints of a walking robot, even the mechanics of the human body. These two equations are among the first things an engineer learns precisely because they remain among the most useful things an engineer will ever know.

The Missing Face

One small mystery clings to Robert Hooke. Newton’s face is familiar to millions; Hooke’s is unknown. No authenticated portrait of him is known to survive.

For centuries a rumor persisted that Newton, in his years of power at the Royal Society, destroyed Hooke’s likeness out of spite. Modern historians find little to support the story; the portrait was more likely lost to ordinary neglect than to malice. A painting once hopefully identified as Hooke turned out, on closer study, to depict another natural philosopher entirely. And so one of the founders of modern science looks out at us from behind a blank frame — present in every laboratory, absent from every wall.

A Legacy Without Heirs

Neither man married; neither left children. In the ordinary sense, both family lines simply stopped. And yet each achieved something exceedingly rare. Three centuries after their deaths, millions of students still learn their ideas by heart.

Their true descendants are intellectual: every scientist, engineer, and inventor who has built on their foundations. Few inheritances outlast an equation that keeps on explaining the world.

Why an Engineer Should Care

Engineering is often taught as a catalogue of formulas to be trusted and applied. History offers a useful correction: every formula began as a question. Someone looked at the world a little differently. Someone doubted the accepted answer. Someone failed, and failed again, and kept going in the face of criticism.

Hooke and Newton were not saints. They competed, they sulked, they claimed and counter-claimed. And still, between them, they laid the foundations of modern mechanics. Perhaps that is the quiet lesson underneath the equations: progress is rarely the gift of a lone genius. It is built, argument by argument, by people who inspire and provoke and occasionally infuriate one another. That is how knowledge grows.

The next time you meet F = ma or F = −kx, pause a moment. These are more than equations. They are reminders that behind every discovery is a human story — curiosity and stubbornness, rivalry and reconciliation, and the long, relentless pursuit of understanding. Perhaps that is the truest lesson of engineering itself.

❦

Did you know that the two scientists behind some of the most important equations in engineering were fierce rivals?

Or that one of history’s greatest mathematicians was forced to flee his home because of religious persecution?

Or that several of the people who changed science forever left no descendants—but their ideas continue to shape our world centuries later?

I’m excited to announce a new article series:

The Giants Behind the Equations

Each article will explore the life, struggles, friendships, rivalries, failures, and discoveries of the scientists and mathematicians who built modern engineering.

This series is for:

• High school students

• College students

• Engineers

• Teachers

• Anyone who loves science and history

🎓 Student Challenge

To celebrate the launch, I’m offering a $100 prize for one outstanding high school student.

To enter:

1. Read one article from the series.

2. Write a thoughtful reflection (500–1,000 words) answering:

   • What surprised you most?

   • What did you learn?

   • How did the scientist’s story change the way you think about mathematics, physics, or engineering?

3. Submit your reflection before the deadline.

The winning entry will receive $100 and may be featured (with the student’s permission) in a future edition of this newsletter.

My goal isn’t just to teach equations.

My goal is to inspire the next generation of scientists, engineers, and curious thinkers.

Because behind every great equation is an even greater story.

A 2025 survey by the Digital Education Council found that 86 percent of students worldwide use AI in their studies, with more than half using it weekly. A separate UK study put the figure at 92 percent, up from 66 percent a year earlier. In the United States, Inside Higher Ed reported in mid-2025 that 65 percent of students reach for a chatbot every week. Another survey found that 88 percent of students had used AI on a test or assignment in 2025, compared with just over half a year before. The exact number depends on who is counting, but the trend line is vertical.

The technology has moved faster than the institutions trying to absorb it. As of spring 2025, only 28 percent of American colleges and universities had a formal policy on student use of AI. Another third said they were still developing one. Nearly a third of students said they did not know when they were allowed to use the tools in class. Some professors prohibit them, some require them, and some say nothing at all, leaving students to read the room.

For supporters, the picture is one of overdue modernization. AI tutors do not get tired, do not run out of office hours, and can rephrase a concept until a struggling student finally hears it. Adaptive platforms can spot a student falling behind weeks before a midterm reveals the problem. Universities including Arizona State, the University of Texas at Austin, Columbia, and the entire California State University system have struck deals with OpenAI to put ChatGPT in the hands of every student. Three out of four college-aged Americans say they want to use AI in their education and careers, and roughly half of recent graduates report they do not feel they have enough AI skill for the jobs they are applying to. By this reading, a college that refuses to engage with AI is a college failing to prepare its students for the economy they are graduating into.

For skeptics, the picture is darker. The same surveys that show booming adoption also show that 60 percent of college students believe AI is diminishing the value of a degree. More than half describe using it on assignments as a form of cheating, even as they keep using it. Researchers studying students who lean heavily on the tools without guidance report weaker writing skills, less original thinking, and a growing dependence that resembles the way calculators once eroded mental arithmetic. The American Association of University Professors has warned that AI is being absorbed into teaching and research with minimal oversight. The worry is not only that students will cheat. It is that students who never wrestled with a difficult paragraph, who never sat in front of a blank page and worked their way out, will leave college without the kind of mind a college education was supposed to build.

A strange middle ground has emerged in the meantime. Even students who do not use AI describe a kind of unease, what some have called a constant surveillance over their writing. They edit their drafts to sound less polished, less coherent, more identifiably human, because they know their professors are watching for the opposite. Faculty, in turn, hesitate to accuse anyone, because detection software is unreliable and the cost of a false accusation is high. Trust on both sides of the seminar table is thinner than it used to be.

What the technology actually does to learning may depend less on the technology and more on how it is used. AI can help a student think harder, or it can spare them from thinking at all. The evidence suggests both are happening, often inside the same classroom, sometimes inside the same student. The institutions that have responded most thoughtfully have not banned the tools and have not embraced them uncritically. They have tried to teach students to argue with AI, to fact-check it, to treat it as a sparring partner rather than a ghostwriter. That is harder than writing a policy.

The deeper question the technology forces is one universities have spent a long time not asking. What is a college education actually meant to produce? If the answer is a credential, AI is mostly a shortcut, and the credential will eventually mean less. If the answer is a mind capable of doing the work the credential implies, then the question of how, and how much, to lean on the machine is the most important one being argued on American campuses right now.

Most campuses are not yet ready to argue it. The students, in the meantime, have already decided.

Across the country, students are voting with their feet. In fall 2025, community college enrollment rose 3.0 percent over the previous year, more than double the growth rate at public four-year universities and a sharp contrast to private four-year schools, which lost ground, according to the National Student Clearinghouse Research Center. Total postsecondary enrollment in the United States now stands at roughly 19.4 million students, and two-year institutions are driving the recovery.

The shift is not a blip. Since fall 2023, undergraduate enrollment overall has climbed 5.7 percent, but community colleges have outpaced every other sector with a 9.6 percent jump. For a sector that lost more than a third of its enrollment between 2010 and 2022, the turnaround is striking.

The clearest reason is money. The average published tuition at a public two-year college sits around $4,050 a year, compared with roughly $9,400 at a public four-year university and considerably more at private institutions. Throw in housing, and the gap widens further. Most community colleges don’t offer dorms, and most students live at home. With average student loan balances for borrowers now hovering near $38,000, families that once treated community college as a backup are reading the math more carefully.

But cost alone doesn’t explain the surge. The composition of who is enrolling, and what they are studying, tells the rest of the story.

Certificate programs have become the engine of growth. These short, career-focused credentials cover fields like welding, nursing assistance, HVAC, and information technology, and enrollments in them at community colleges have climbed 28 percent in just four years, with 752,000 students now pursuing them. Trade-aligned majors are surging in tandem: mechanic and repair technologies are up more than 10 percent, engineering technologies more than 8 percent, and health professions more than 10 percent. Meanwhile, computer and information science enrollment is contracting at two-year and four-year schools alike, a quiet warning shot for a field once treated as a guaranteed paycheck.

The students themselves are a more varied group than the stereotype suggests. Adult learners, those returning to school in their late twenties and beyond, have continued to grow, up another 4.5 percent this fall. So has dual enrollment, the practice of high schoolers taking community college courses for credit, which accounted for nearly 40 percent of community college growth alone. Eighteen-year-old freshmen, the traditional bread and butter of four-year recruiters, are increasingly walking into two-year classrooms instead.

Higher education researchers point to a convergence of forces. The sticker shock of four-year tuition has reached a tipping point in the public imagination. Skepticism about the value of a bachelor’s degree, particularly in liberal arts fields with uncertain job markets, has grown. Employers, struggling to fill skilled trades and healthcare positions, have leaned into partnerships with community colleges that funnel graduates directly into work. And a wave of state-level “promise” programs, which cover tuition for in-state students at two-year institutions, has lowered the bar to entry in places from Tennessee to Oregon.

None of this means community colleges have arrived without baggage. Completion rates remain a persistent challenge: many students who enroll never finish a credential, and those who do often struggle to transfer credits cleanly to a four-year school. Even at a fraction of university prices, debt is still a reality for some, particularly at colleges in higher-cost regions, and default rates among community college borrowers are higher than at four-year institutions, in part because many leave without the degree that would have boosted their earnings.

There is also a demographic cliff looming over all of higher education. The number of American 18-year-olds is projected to drop sharply through the 2030s, a delayed consequence of falling birth rates after the 2008 recession. Every sector will feel that squeeze. But community colleges, with their flexibility, older student base, and workforce ties, may be best positioned to weather it.

What is happening right now looks less like a temporary recovery and more like a referendum. Quietly, school by school, decision by decision, Americans are rendering a verdict on the four-year university and the bargain it has asked families to accept for the better part of a century.

There are two ways to read that verdict. The first is that the country is finally getting honest. Higher education had drifted into something bloated and overpriced, a luxury good marketed as a necessity, and a generation of students is correcting the market by walking toward something cheaper, faster, and tied to real work. By this reading, the rise of the community college is the sound of common sense returning to a system that had lost it.

The other reading is harder. The four-year university, for all its excesses, was also where Americans went to be exposed to ideas outside their hometowns, to study things that did not pay immediately, to become the kind of citizens a democracy depends on. If a growing share of young people are skipping that experience because they cannot afford it or no longer trust that it will pay off, the country may be losing something it will not miss until it is gone.

Which reading is right may depend less on the data than on what Americans decide college is supposed to be for. That conversation has barely started. The enrollment numbers, meanwhile, keep climbing.