When people worry about American bridges, they usually picture the worst ones: rusted girders, crumbling concrete, a sign announcing a weight limit. Those bridges exist, and they deserve attention. But the most important number in the latest national assessment of bridge condition is not about the worst bridges at all. It is about the ones in the middle.

The Report Card

Every four years, the American Society of Civil Engineers publishes a Report Card for America’s Infrastructure, grading eighteen categories from aviation to wastewater on a school-style scale. The 2025 edition was, by its own standards, good news. The overall grade rose from C-minus to C, the highest the nation has received since the report card began. Recent federal investment, much of it from the 2021 infrastructure law, was starting to show up in the data.

Bridges received a C, unchanged from 2021. The United States has about 623,000 of them. According to the report, 6.8 percent are in poor condition, down from 7.3 percent a few years earlier. That decline is real progress, and it reflects years of deliberate work by state transportation departments to replace or rehabilitate their most deteriorated structures.

But the same report contained a less comfortable finding. Only 44.1 percent of the nation’s bridges are now rated good. A larger share, 49.1 percent, are rated fair. Fair bridges now outnumber good ones, and the report’s authors flagged that as a trend that will catch up with us.

We are getting better at rescuing bridges at the bottom. We are not keeping enough of them from sliding down.

What the Ratings Mean

The words “good,” “fair” and “poor” are easy to misread, so it helps to know where they come from. Under federal rules, most highway bridges are inspected at least every 24 months. Inspectors rate the major parts of each bridge, typically the deck, the superstructure that carries it, and the substructure of piers and abutments that holds everything up, on a scale from 0 to 9. A bridge’s overall classification is driven by its lowest-rated major component.

A bridge rated “poor” is not necessarily unsafe. It means at least one major component shows significant deterioration, and the bridge will need major rehabilitation or replacement. Unsafe bridges are closed or restricted. A “fair” bridge is structurally sound but showing its age: cracking, some section loss, joints beginning to leak, bearings starting to wear. It is doing its job. It is also on its way somewhere.

Why the Middle Matters

Bridge deterioration is not linear. A new bridge stays in good condition for years, sometimes decades. Then the small problems begin: a deck joint fails and lets salty water drain onto the steel or concrete below; a crack in the deck opens a path for chlorides to reach the reinforcing bar; paint breaks down and rust begins. Each problem, left alone, speeds up the others. A bridge that drifts into fair condition can fall into poor condition much faster than it fell out of good.

The economics follow the same curve. Preservation work on a fair bridge, such as sealing a deck, replacing joints, repainting steel or patching concrete before the damage spreads, is relatively cheap. Rehabilitating a poor bridge costs far more. Replacing one costs more still, and it means detours, closures and years of disruption for the people who depend on it. The ASCE has estimated the backlog of bridge investment need at around $191 billion.

For decades, many agencies funded bridges using what engineers sometimes call a “worst first” approach: fix the bridges in the worst shape, because those are the ones most visibly at risk. It is an understandable instinct, and politically it is easy to defend. But it means money flows to the most expensive problems while the cheaper, preventable ones are left to grow. Federal law now requires states to maintain risk-based transportation asset management plans that look ahead over ten years, partly to push agencies toward preservation. Writing a plan is easier than funding it.

A dollar spent on a fair bridge buys years. A dollar spent on a poor bridge mostly buys time.

What Failure Looks Like

Bridge collapses in the United States are rare, and when they happen, the causes vary. On August 1, 2007, the I-35W bridge over the Mississippi River in Minneapolis fell during the evening rush hour, killing 13 people. Investigators traced the collapse to undersized gusset plates, a design error compounded by added weight over the years, rather than ordinary deterioration. In March 2024, the Francis Scott Key Bridge in Baltimore collapsed after being struck by a container ship, a failure of protection against vessel impact rather than of condition.

The Fern Hollow Bridge in Pittsburgh was different. On the morning of January 28, 2022, the steel frame bridge collapsed into a ravine, sending a bus and several cars down with it. Remarkably, no one was killed, though several people were injured. The bridge had been rated in poor condition for years. Federal investigators later pointed to corrosion and section loss in key structural members, and to a long failure to act on repeated inspection findings.

Fern Hollow is the uncomfortable lesson in this story. The deterioration was documented. The inspections were done. What failed was the step between knowing and fixing.

The Quiet Work

Very little of what keeps bridges standing makes the news. It is the inspector climbing under a deck in February with a hammer and a flashlight. It is the maintenance crew sealing joints before winter. It is the engineer arguing, in a budget meeting, for repainting a steel bridge that looks fine to everyone else in the room. None of it is dramatic. That is the point.

New tools are starting to help. Drones can reach parts of bridges that once required lane closures and snooper trucks. Sensors can monitor strain, vibration and corrosion continuously. Data from decades of inspections can be used to forecast which bridges are likely to slip from fair to poor next, so that money reaches them first. These technologies do not replace inspection or judgment, but they can make both more targeted.

The Real Question

The national bridge story of the past decade is a genuine success, and the people who produced it deserve credit. The share of bridges rated poor has been falling steadily.

But a bridge inventory is not a snapshot. It is a moving population, aging every year. The bridges built in the great highway expansion of the 1950s, ‘60s and ‘70s are now old enough to need serious attention, and many of them sit in that large middle group. Whether today’s fair bridges become tomorrow’s poor ones depends on decisions being made now, in budgets that rarely make headlines.

The worst bridges are the ones we see. The ones that will decide the next report card are the ones that still look fine.

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On the first day of a large introductory chemistry or calculus course at many American universities, some version of the same speech is given. Look to your left. Look to your right. By the end of the semester, one of you will not be here.

The line is delivered as a warning, sometimes as a challenge, occasionally as a point of pride. It reflects an idea that runs deep in science and engineering education: that the early courses are supposed to be hard, that their difficulty serves a purpose, and that the students who leave were never going to make it anyway. Students call these courses “weed-out classes.” Faculty rarely use the term in public, but many recognize it.

The trouble is that the idea rests on an assumption that, when researchers have looked closely, has not held up well.

How Many Leave

The best-known national figure comes from the U.S. National Center for Education Statistics, which followed students who began college in 2003–04 for six years. About 28 percent of students pursuing a bachelor’s degree entered a STEM field at some point. By 2009, 48 percent of those STEM entrants had left. Roughly half of the leavers switched to a non-STEM major. The rest left college without any degree at all.

For students in associate’s degree programs, the loss was larger still: 69 percent of STEM entrants had left the field.

Those numbers are now old, and the landscape has shifted since. But the pattern they describe has been remarkably stable over decades of study. An earlier analysis found that 44 percent of freshmen who entered college in 1987 intending to major in a STEM field had switched out by 1991. The share of freshmen who say they want to study STEM has long sat well above the share of degrees that actually go to STEM graduates. Something in between is draining the pipeline.

The students who stayed and the students who left often described the same problems. What differed was not their ability.

The Twist in the Data

Here is the part of the NCES report that gets quoted less often. STEM was not unusual. Attrition in humanities, education and health sciences was actually higher, between 56 and 62 percent. Business and the social sciences were roughly comparable to STEM. Students leave majors all the time, in every field.

That finding cuts two ways. On one hand, it suggests that the STEM exodus is not some unique catastrophe. On the other, it undermines the usual justification for weed-out culture. If students leave every field at similar rates, then the extra difficulty of introductory science and math courses is not obviously doing the special sorting work it is claimed to do. And STEM loses students in a particular way: many of those who leave are capable, high-achieving students who arrived with strong preparation and genuine interest.

What the Leavers Said

The most influential study of why students leave science is a book called Talking About Leaving, published in 1997 by the sociologists Elaine Seymour and Nancy Hewitt. They interviewed hundreds of students at several universities, including both those who switched out of science, math and engineering and those who stayed.

Their most cited finding is that about 90 percent of the students who switched out described poor teaching as a concern. But the more revealing finding was quieter. Many of the students who stayed described the same problems: overloaded curricula, impersonal lectures, a competitive grading culture, faculty who seemed uninterested in undergraduates. The persisters and the leavers were not cleanly separated by ability. Many of those who left were as capable as those who stayed. What often differed was how they responded to an environment both groups found discouraging.

If that is true, then the weed-out course is not functioning as a fair test of who can do science. It is functioning, at least in part, as a test of who will tolerate a particular style of teaching.

The Evidence on Teaching

There is now strong evidence that the style of teaching matters a great deal. In 2014, a team led by the biologist Scott Freeman published a meta-analysis in the Proceedings of the National Academy of Sciences covering 225 studies of undergraduate science, engineering and math courses. They compared traditional lecturing with “active learning”: classes where students work problems, discuss in small groups, answer questions in real time, and get frequent feedback.

The results were striking. Students in traditional lecture courses were about 1.5 times more likely to fail than students in active-learning courses. Average failure rates were roughly 34 percent under lecturing and 22 percent with active learning. Exam performance improved as well. The authors noted that if the experiments had been medical trials, the control condition might have been stopped early for the benefit of the patients.

That finding does not mean every lecture is bad or that every active-learning class is good. Implementation matters, and doing it well takes faculty time and institutional support. But it does mean that a large share of failure in introductory courses is not simply a property of the students. It is partly a property of the course.

If a medical treatment cut failure rates by a third, we would not call the old treatment rigorous. We would call it outdated.

Who Pays the Price

The costs of weed-out culture are not distributed evenly. Students who arrive without strong high school preparation, without family members who have navigated college, or without the financial cushion to retake a course are more likely to be pushed out by a single bad semester. First-generation students, students from under-resourced schools, and students who are the only person like them in a room of three hundred all face extra friction. When the course is designed to lose a third of its students, those are often the students it loses.

That matters for more than fairness. Engineering and science need people who will design water systems for small towns, keep bridges standing, write safe software and run laboratories for decades. Every capable student who leaves because of how a first-year course was taught is a loss the profession pays for later.

What Rigor Should Mean

None of this is an argument for easy courses. Engineering is hard because the world is hard: loads are uncertain, materials are imperfect, and mistakes can hurt people. Students need to be held to high standards, and some will discover that the field is not for them. That is normal and healthy.

But there is a difference between a course that is rigorous and a course that is designed to lose people. A rigorous course sets high expectations and then gives students what they need to meet them: practice, feedback, chances to fail cheaply and improve. A weed-out course sets high expectations and treats the resulting casualties as proof of its standards.

The universities that have moved away from weed-out culture have not lowered the bar. They have redesigned the path toward it, with active learning, peer support, early warning systems and faculty who are rewarded for teaching well. The results, where they have been studied, are encouraging.

The old first-day speech assumed that one in three students did not belong. A better version would say something different: this course is hard, and it is our job to help you through it. Look to your left and to your right. Our goal is for all three of you to be here in May.

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Stand beneath the Eiffel Tower and look up at the first platform. Running around the frieze, in gold letters more than half a meter tall, are 72 names. Gustave Eiffel chose them himself: French scientists, engineers and mathematicians who had distinguished themselves since the Revolution of 1789. Lagrange is there. So are Laplace, Cauchy, Fourier, Navier and Poisson, names every engineering student eventually meets in an equation.

All 72 are men. One name that belonged among them, perhaps more than most, was missing. The tower is a lattice of iron plates and members whose behavior under load depends on the theory of elasticity, and one of the first people to attempt a mathematical theory of how elastic surfaces bend and vibrate was a woman named Sophie Germain.

A Girl in Her Father’s Library

Marie-Sophie Germain was born in Paris in 1776, into a comfortable family. Her father was a prosperous merchant who later became involved in revolutionary politics. In 1789, when she was thirteen, the Revolution made the streets of Paris dangerous, and she spent long days confined to the house. She found her way to her father’s library.

There, the story goes, she read an account of the death of Archimedes. When Roman soldiers stormed Syracuse, the old mathematician was so absorbed in a geometric figure drawn in the sand that he ignored a soldier’s command, and was killed for it. Sophie wondered what kind of subject could hold a person so completely. She decided to find out.

Her parents disapproved. Mathematics was not considered a suitable pursuit for a girl, and they tried to stop her. According to accounts handed down from her family, they took away her candles and let the fire go out in her room so she could not study at night. She waited until the house was asleep, wrapped herself in blankets, and worked by candles she had hidden. Eventually her parents gave up.

The École Polytechnique did not admit women. So she borrowed the identity of a man who had dropped out.

Monsieur LeBlanc

In 1794 the École Polytechnique opened in Paris, designed to train the engineers and scientists the new republic needed. Women were not admitted. But the school made lecture notes available, and students were invited to submit written observations to their professors.

A former student named Antoine-Auguste LeBlanc had left Paris, and the school apparently had not noticed. Sophie obtained the notes under his name and began submitting work as “Monsieur LeBlanc.” One of the professors reading it was Joseph-Louis Lagrange, among the greatest mathematicians alive. He noticed that LeBlanc, who had been a poor student, had suddenly become remarkable. He asked to meet him.

Lagrange was surprised to find a young woman. To his credit, he was also supportive, and he became something of a mentor.

A few years later, Germain used the same pseudonym to write to Carl Friedrich Gauss in Germany, sending him her own ideas in number theory. Gauss, who was famously sparing with praise, took her seriously and wrote back. The disguise ended in 1806, when Napoleon’s army occupied Gauss’s home city of Brunswick. Remembering Archimedes, Germain feared for his safety, and asked a French general who was a family friend to make sure no harm came to him. When the general explained who had sent him, Gauss was confused. He had never heard of a Sophie Germain. She wrote to explain. Gauss’s reply expressed astonishment and admiration that a woman had overcome so many obstacles to reach the hardest parts of the subject.

The Problem of the Singing Plates

Around 1808, a German physicist named Ernst Chladni came to Paris with a striking demonstration. He sprinkled sand on a thin metal plate and drew a violin bow along its edge. As the plate vibrated, the sand danced away from the moving regions and settled along the still lines, forming intricate, symmetrical patterns. Different notes produced different figures.

The patterns were beautiful, and nobody could explain them mathematically. Napoleon was intrigued, and the Paris Academy of Sciences announced a prize for a mathematical theory of the vibrations of elastic surfaces that agreed with experiment. Many of the leading mathematicians of France judged the problem too difficult, or thought the mathematics of their day was not up to it.

Germain was the only person to submit an entry in the first round. It was rejected; her reasoning contained errors, which was not surprising for someone who had never received formal training in the calculus of variations. The deadline was extended. She tried again and received an honorable mention. She tried a third time. In 1816, at the age of 39, she won.

She was the first woman to win a prize from the Paris Academy of Sciences. She did not attend the ceremony; women were not welcome at its sessions unless they were the wives of members. When the Academy did not publish her winning memoir, she paid to publish it herself, in 1821.

What She Got Right, and What Others Fixed

Germain’s theory was not complete. Some of her assumptions, particularly about the conditions at the edges of a plate, were later shown to be wrong. Gustav Kirchhoff corrected them in 1850, and the classical theory of plate bending that engineers learn today owes as much to him and to later mathematicians as it does to her.

But she asked the right question, framed it in mathematical terms, and pushed it far enough that others could finish it. That matters more than it sounds. Plate theory is how engineers analyze bridge decks and floor slabs, ship hulls and aircraft skins, steel gusset plates and concrete walls. Every time a structural engineer checks how a flat element bends under load, they are working in a field she helped open.

She asked the right question, and pushed it far enough that others could finish the answer.

She also left a lasting mark on pure mathematics. Her work on Fermat’s Last Theorem was among the most important progress on the problem in the early nineteenth century. Mathematicians still study “Sophie Germain primes”: prime numbers p for which 2p + 1 is also prime.

An Ending, and a Late Correction

Germain never married. She developed breast cancer and died in Paris in 1831, at 55. Gauss had persuaded the University of Göttingen to award her an honorary degree, but she died before it could be conferred. Her death certificate, as it is often told, recorded her not as a mathematician but as a rentière, a woman of independent means.

When the Eiffel Tower opened in 1889, she had been dead for nearly sixty years, and her name was not among the 72. In 1913, an American writer pointed out the omission and suggested the obvious reason: she was a woman.

The correction has taken a long time. In January 2026, the city of Paris unveiled a list of 72 women scientists whose names are to be engraved in gold on the tower’s first level, alongside the original men. Sophie Germain is among them. The work is expected to be completed by 2027.

Why an Engineer Should Care

It is easy to read Germain’s story as a story about exclusion, and it is that. But it is also a story about how engineering knowledge actually gets built. Her first attempt failed. Her second was only partly right. Her final theory had flaws that someone else fixed decades later. None of that made her contribution smaller. It made it normal. Almost every useful theory in engineering arrived the same way: incomplete, contested, and improved by many hands.

The difference is that most people who make that kind of contribution are allowed into the room where the work is discussed. Germain was not. She had to borrow a man’s name to get the lecture notes, and she could not attend the ceremony for her own prize.

The next time you calculate the deflection of a slab or the stress in a plate, it is worth remembering that one of the people behind the theory had to study it by hidden candlelight. Her name is finally going up on the tower. It belonged there all along.

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Every civil engineering student meets him in a fluids course, usually in the second or third week. The instructor sketches a pipe that narrows in the middle, draws a few arrows, and writes a line that looks almost too tidy to be true: pressure, plus the energy of motion, plus the energy of height, stays constant along a streamline. Where the fluid speeds up, its pressure falls. Where it slows, the pressure returns.

It is called Bernoulli’s principle, and it is everywhere. It sizes the culverts under our highways and the spillways on our dams. It explains why a Venturi meter can measure flow without a single moving part, and how a Pitot tube on an aircraft’s nose reads airspeed. Water engineers lean on it so often that they stop noticing it, the way a carpenter stops noticing a level.

Few of them know that the man who published it was thrown out of his family home for doing well, or that his father later tried to claim the idea as his own.

A Family Business in Mathematics

The Bernoullis were a family of refugees before they were a family of mathematicians. Protestant merchants from Antwerp, they had fled religious persecution in the Spanish Netherlands and eventually settled in Basel, Switzerland, where they traded spices and kept their heads down.

Then, in a single generation, the family began producing mathematicians the way other families produce lawyers. Jacob Bernoulli helped found probability theory and discovered the constant we now call e. His younger brother Johann became one of the first great masters of calculus, a teacher to Leonhard Euler and, quietly, the source of much of the first calculus textbook ever printed. Over three generations the family produced eight mathematicians of note.

They were brilliant. They were also, by most accounts, impossible. Jacob and Johann spent years attacking each other in print, each insisting the other had stolen or bungled a solution. It was a family in which talent was abundant and generosity was not.

Johann’s father had tried to force him into business. Johann then did exactly the same thing to his own son.

A Son Steered Away

Daniel Bernoulli was born in 1700 in Groningen, in the Netherlands, where his father held the chair of mathematics. From early on he showed the family gift. Johann’s response was to try to keep him away from it.

Mathematics, Johann told him, did not pay. Daniel should become a merchant. The irony is hard to miss: Johann’s own father had once tried to push him into commerce, and Johann had fought it bitterly. Now he did the same thing to his son. Daniel resisted, and the two settled on a compromise that suited neither. Daniel would study medicine, and his father would teach him mathematics on the side.

It turned out to be a useful detour. Daniel’s medical thesis was on respiration, and his interest in how blood moves through the body fed directly into his later thinking about how fluids move through pipes. In 1725 he accepted a post at the new Academy of Sciences in St. Petersburg. He was lonely there, and wrote home saying so. His father’s solution was to send one of his best students to keep him company: a young Swiss named Leonhard Euler. The two became close friends and, for a few years, the most productive pair of mathematicians in Europe.

The Prize That Broke a Family

In 1734 the Paris Academy of Sciences, the most prestigious scientific body in Europe, announced the winners of its annual prize. That year the question concerned the orbits of the planets. The prize was split between two entries. One came from Johann Bernoulli. The other came from his son.

Most fathers would have been proud. Johann was furious. He could not tolerate being ranked as his son’s equal, and he banned Daniel from the family house. Daniel would go on to win the Paris prize many more times over his career. His father never forgave him for the first one.

Hydrodynamica, and Hydraulica

For years Daniel had been working on a book about how fluids move: water flowing through pipes, the force of a jet, the pressure on the walls of a vessel, the efficiency of pumps and machines for raising water. He finished the manuscript before leaving St. Petersburg, and after long delays it was printed in 1738 under the title Hydrodynamica. It was the first book to treat flowing fluids as a unified subject, and it is the reason the field still carries that name. In one chapter, almost in passing, Daniel modeled a gas as countless tiny particles colliding with the walls of their container, an idea that would become the kinetic theory of gases a century later.

Then Johann did something that still startles historians. He wrote his own book on the same subject, called it Hydraulica, and put a date of 1732 on it. The book drew heavily on his son’s work. The false date was meant to suggest the reverse: that the father had written it first, and the son had borrowed.

The deception did not hold. Colleagues recognized what had happened, and Johann’s reputation suffered for it. But the damage to the relationship was permanent. Daniel tried to reconcile. His father refused, and carried the grudge until his death in 1748.

The father had the talent to write his own masterpiece. What he lacked was the ability to let his son have one.

What the Equation Actually Says

Strip away the family drama and the idea is beautifully simple. A moving fluid carries energy in three forms: the pressure it exerts, the energy of its motion, and the energy it has because of its height. Along a smooth path, and if friction is ignored, the total stays the same. Squeeze the flow through a narrow section and it must speed up to get the same volume through. Because more of its energy is now in motion, less is left as pressure.

It is worth adding an honest footnote. Bernoulli’s principle is often used to explain why airplanes fly, usually with a story about air “needing” to travel faster over the curved top of a wing. That story is incomplete at best. The principle is real, and pressure differences do produce lift, but the full explanation involves how the wing turns the air downward as well. Even the most famous equations get misused when we want a simple story.

In engineering practice, the equation is a starting point. Real pipes have friction, real channels have turbulence, and real pumps lose energy. Engineers add correction terms for all of it. But the skeleton of almost every hydraulic calculation, from a storm drain to a hydroelectric penstock, is still the balance Daniel Bernoulli wrote down in the 1730s.

A Life Beyond the Quarrel

Daniel lived to 82. He returned to Basel, where he held chairs in anatomy, botany, physiology and finally physics, which is roughly the career of three ordinary scholars folded into one. He used mortality data to argue, with early statistics, that inoculation against smallpox would save lives, at a time when the practice was still controversial. He worked on vibrating strings, on probability, and on the problem of how people value risk, an idea economists still cite today.

He never married and had no children. Like Hooke and Newton, he left his inheritance in equations rather than in descendants.

Why an Engineer Should Care

There is an old temptation in engineering education to treat great names as statues: Bernoulli’s equation, Euler’s buckling load, as if the ideas arrived fully formed from people who had nothing else going on. The Bernoullis are a useful corrective. These were people with families and grudges, ambitions and insecurities. One of the most important books in the history of fluid mechanics was written by a man whose own father tried to discredit it.

There is a quieter lesson too. Johann Bernoulli was a great mathematician, and nothing in his own record needed his son’s work to prop it up. His mistake was treating knowledge as a contest in which one person’s success meant another’s loss. Daniel’s book did not diminish his father. It extended him. That is how knowledge is supposed to work.

The next time you write the Bernoulli equation on a page, remember that it carries a family’s name, and a family’s wound. Behind the tidy line of symbols is a young man who was told mathematics would not pay, did it anyway, and gave the world a principle that still moves its water.

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But the machinery of accountability now operates in a world that academic procedures were not designed for. An allegation can leave the confines of an editorial office or university committee and travel across social media in hours. Documents are circulated. Screenshots accumulate. Strangers offer judgments. A complicated professional record can quickly collapse into a single accusation.

The accused person, meanwhile, is still a person.

That observation is not an argument for overlooking misconduct. Nor should concern about mental health become a shield against legitimate scrutiny. The more difficult proposition is that both responsibilities must be held at once: protecting the integrity of scholarship and protecting the dignity, and sometimes the safety, of the people caught in its disciplinary processes.

Arday’s story makes that tension difficult to ignore.

It is tempting after a tragedy to reconstruct a person’s private suffering from the outside, assigning meaning to events that may have been far more complicated than they appeared. We should resist doing that here. Unless supported by evidence, we cannot know precisely what Arday was thinking, what burdens he was carrying or how he understood the controversy surrounding him.

What we can ask is whether our institutions are prepared for the human consequences when professional scrutiny becomes public disgrace.

That question extends far beyond one researcher.

Academic life attaches unusual weight to reputation. A career assembled over decades can depend on publications, appointments, grants and the confidence of one’s peers. Misconduct allegations can therefore threaten not merely employment but the identity around which someone has organized much of adult life.

The appropriate response cannot be to stop investigating wrongdoing. It should be to build systems capable of doing something harder: investigating rigorously without treating humiliation as part of the punishment.

A journal can retract a paper without dehumanizing its author. A university can investigate misconduct while ensuring that someone facing potentially career-ending allegations knows how to obtain confidential psychological support. Researchers can expose questionable work without encouraging harassment. Journalists and commentators can report allegations while distinguishing accusation from established fact.

These distinctions may seem procedural until a human being is in crisis.

Academic integrity and human compassion are sometimes presented as competing values. They should not be. A system confident enough to investigate wrongdoing should also be mature enough to recognize that accountability has boundaries.

The scientific record deserves protection.

So do the people whose names appear in it.

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.