Meet Augustin-Louis Cauchy (1789–1857): the man who walked into calculus
after a century of geniuses had built a machine that plainly worked, and asked the one
question none of them had answered — why? Newton and
He did this, and roughly a thousand other things, at a rate that has never been matched before or since. He was also, by nearly every account from people who knew him, exhausting to work with — a brilliant, devout, stubborn, occasionally maddening man who reshaped mathematics with one hand and, with the other, may have cost two of history's most dazzling young mathematicians their big break. Both stories are true, and neither cancels the other out.
Cauchy arrived in Paris on 21 August 1789 — five weeks after the storming of the Bastille. His father, a minor royal official, went into hiding with the family at their country cottage in Arcueil to avoid the guillotine that was working through anyone connected to the old regime. Food was scarce, safety was not guaranteed, and young Augustin-Louis grew up thin and sickly on a diet that left him permanently frail — friends later blamed his malnourished Terror-era childhood for a lifetime of poor health.
The family's neighbour in Arcueil happened to be the mathematician
Once Cauchy started publishing, he essentially never stopped. Over his lifetime he produced somewhere north of 789 papers — modern counts of his collected works run to nearly thirty large volumes — on calculus, complex analysis, number theory, optics, elasticity, astronomy and probability. He wrote so fast and so often that the French Academy of Sciences, whose journal Comptes Rendus he treated as a personal outlet, introduced a rule capping the length of any single published article. Mathematical folklore still calls it the "Cauchy condition" or the "Cauchy rule," and a version of the page-limit convention survives in academic journals today: a fittingly permanent monument to one man simply writing too much, too well, too fast for anyone else to keep up.
The volume was matched by the depth. Take the idea now named after him: a sequence whose terms eventually get arbitrarily close to each other, not to some pre-known target.
Before Cauchy, "does this sequence converge?" was often answered by guessing the limit and
checking it — hopeless if you have no idea what the limit should be. A
He did the same rigour-first trick to complex analysis, more or less inventing the subject
as a formal discipline. The
The story, as mathematicians tell it: by the 1830s Cauchy was submitting to the Paris Academy's Comptes Rendus so often, and at such length, that he was practically crowding other members out of their own journal. Rather than tell one of France's most eminent scientists to simply write less, the Academy did the polite bureaucratic thing and changed the rules instead — imposing a strict page limit on every submitted article, regardless of author.
It didn't fully work. Cauchy responded to the space limit the way a river responds to a single new dam: he found other channels, publishing overflow material in his own private journals, the wonderfully self-explanatorily named Exercices de mathématiques and Exercices d'analyse, which he simply ran himself so that no editor could tell him no. Few mathematicians in history have needed a bespoke publishing operation just to keep up with their own output.
Cauchy's mathematics was rigorous; so, to a fault, was his conscience — devoutly Catholic and unbendingly royalist, in a France that changed regimes every decade or two and expected its civil servants to swear loyalty to whichever one currently held Paris.
When the July Revolution of 1830 toppled King Charles X and installed Louis-Philippe, every academic post in France required a fresh oath of allegiance to the new government. Cauchy, who regarded the deposed Bourbon king as his rightful sovereign, simply refused to swear it. The refusal cost him every one of his official positions in Paris — his professorships, his standing, his income — and rather than bend, he left the country entirely, going into self-imposed exile. He spent years wandering: first to Switzerland, then to the Italian city of Turin (where the King of Sardinia created a chair in mathematical physics especially for him), and later to Prague, where the exiled Bourbon family had settled and asked him to tutor the young heir to the French throne. It was, by his own account, thankless work — the prince showed little interest in mathematics, and Cauchy's rigid teaching style didn't help.
He did not get his Paris chair back until 1838, and even then only partially — full reinstatement had to wait until 1848, when a new revolution abolished the oath requirement altogether. When Napoleon III's regime reinstated the oath a few years later, Cauchy again refused to take it — and this time was simply allowed to keep his post anyway, a special exemption you can only imagine being granted to the most stubbornly, spectacularly productive employee in the building.
Now the hardest part of the story. In the 1820s, a young Norwegian mathematician named Niels Henrik Abel travelled to Paris and submitted a paper to the Academy of Sciences — a genuinely revolutionary result, now called Abel's theorem, on integrals of algebraic functions. Cauchy was one of the two referees assigned to review it. The paper sat, unread and unreported, for years. Abel left Paris disillusioned, sick and unrecognised, and died of tuberculosis in 1829 at just twenty-six — two days, as it happens, before a letter arrived offering him the professorship that might have saved his life. The lost manuscript was only rediscovered and finally published, to general astonishment, years after his death.
A few years later it happened again, with an even younger mathematician: Évariste Galois, the teenage prodigy who would go on to found what is now called group theory, submitted a memoir on the solvability of equations to the Academy — with Cauchy again among those responsible for handling it. That manuscript, too, disappeared from the review process without a report ever being filed. Galois's own life spiralled through political imprisonment and heartbreak before ending, at twenty, in a duel in 1832 — the night before which, according to legend, he stayed up scribbling his mathematical testament by candlelight, sensing he would not survive until morning. His work, like Abel's, was only fully appreciated by the mathematical world after he was gone.
Two of the most original mathematical minds Europe ever produced, both dead before thirty, both with breakthrough papers that passed through Cauchy's hands and came out the other side unread. It is one of the great "what could have been" double tragedies in the history of science — and Cauchy's name sits at the centre of both.
It's tempting — and the internet loves this version — to cast Cauchy as the arch-villain who jealously buried the work of two brilliant rivals. The real picture, as historians who have gone through the Academy's records now see it, is messier and, in its own way, sadder.
There is no good evidence that Cauchy plagiarised or suppressed either paper out of jealousy or malice. What the record does show is a man drowning in his own productivity: Cauchy was, at the time, the single busiest mathematician in Europe, refereeing an enormous backlog of submissions on top of writing his own avalanche of papers, teaching, and — for good measure — dealing with the political upheavals of his exile years. Losing or simply never getting around to a manuscript fits a pattern of chronic administrative overload rather than a plot. He was, by several contemporary accounts, notoriously careless with other people's papers generally, not uniquely cruel to Abel and Galois in particular.
That context matters, but it doesn't erase the outcome. Carelessness at the top of a field has real victims, and Abel and Galois paid for Cauchy's overload with the recognition — and in Abel's case, arguably, the medical care and financial security — that might have come from a report filed on time. The fair verdict sits between the myth and a full pardon: not villainy, but a very human failure of an inhumanly busy man, with consequences that were anything but small.
Cauchy's Catholicism was not a quiet, private matter — it spilled into every corner of his public life, and it is a large part of why so many of his contemporaries found him exhausting. He was an active member of charitable religious societies, gave generously and personally to the poor, and used his position and prestige to campaign for causes such as relief for famine-stricken Ireland. None of that was performative: colleagues who found him maddening in committee meetings also, often in the same breath, described him as personally generous and sincere in his beliefs.
The trouble was where the sincerity spilled over. Cauchy had a habit of turning ordinary scientific meetings of the Academy into occasions for religious argument, lecturing colleagues on faith and morals whether or not anyone had asked, and he treated theological certainty with exactly the same absolute confidence he brought to a theorem — which is a wonderful trait in mathematics and a considerably more difficult one to sit across a table from. Even mathematicians who admired his work without reservation, and there were many, tended to describe him personally with a wince. He was, in short, a man who could be rigorously, unimpeachably right about almost everything and still be the person nobody wanted to get stuck next to at dinner.
Strip away the biography and Cauchy's mathematics is everywhere a modern student turns.
His definition of the limit — the ancestor of the
He also, not incidentally, more or less invented the modern textbook lecture course in analysis. His Cours d'analyse (1821), written for his students at the École Polytechnique, was the first time limits, continuity, series convergence and the derivative were laid out for a general student audience with real definitions rather than intuitive appeals to "quantities becoming small." Generations of textbooks, this Primer's own treatment of calculus included, are descendants of that one course.
Put the two halves of the man side by side and the contradiction is the point: a mathematician who insisted that every step of an argument be nailed down with total precision, and a person whose stubborn, unbending certainties — about a king, about a creed — cost him a decade of his career and, quite possibly, cost two of the brightest mathematicians of his century the recognition they needed while they were still alive to use it.
The full story (with far fewer jokes) is on Wikipedia: Augustin-Louis Cauchy — Wikipedia. For the two lost manuscripts, see the articles on Niels Henrik Abel and Évariste Galois.