Paul Tannery: The Tobacco Engineer Who Changed the History of Math
Have you ever imagined your life would turn out one way… and then it didn’t? Maybe when you were young, you had a dream, you knew exactly what you wanted to become. Perhaps you wanted to be an artist, a scientist, a writer, or a musician. Maybe you imagined yourself discovering something new or creating something that would outlive you. But then life happened. If you can relate, stick around! Have I got a story for you!
So, here is your life. Bills have to be paid. A family needs to be supported. You have a good job, maybe even one that you now thoroughly enjoy, but it’s not the dream you carried with you when you were younger. And you did not let go of that dream.
So now it’s the thing that you do after dinner, and it’s in the books that you read before you go to bed. Eventually maybe next week, maybe next month it will become the thing that progresses into the classes you’re going to take on weekends and evenings and the research that’s going to quietly fill your evenings and your brain while everyone else in the house is scrolling through Instagram.
Perhaps your friends don’t understand it. I have a friend who often asks me, “Oh, you’re still doing the podcast?” As if to allude, “Why are you doing this? What is the point?” And then my brain wanders. I think “Who cares about this?” But obviously you care because you’re listening. We are in the same pickle barrel, or whatever the phrase is! We care about things that our friends question us about. But we keep learning because we love it. It’s not like we’re doing crack cocaine. We are just passionately pursuing an interest. Well, I’m here to tell you that the personal interests that you devote your life to truly matter. And that’s where this story goes.
Imagine spending decades doing what you truly loved outside of your day job, never expecting recognition, never imagining that your greatest contribution to the world would come not from your profession, but from the passion you pursued after work.
This level of passionate effort was the life of Paul Tannery, whose quiet work laid the foundation for math and science history.
First, a quick side quest. When I was in Italy, I had quite an amazing, insanely exciting experience that gave me goosebumps. My husband and I were in Parma, and I had no idea there were so many incredible museums there because I originally went there for the delicious food! So, we visited the Palintine Library, and in the library was a delectable hall of historical books. There were over 1000 books from the 18th and 19th centuries, type setted and published by Giambattista Bodoni who died in 1813. These books included Dante’s Divine Comey, Pietro Giannini’s Opuscula Mathematica, the Iliad and Le Stanze by Angelo Poliziano, published in 1792, and completely printed on silk. It was a grand hall I remember walking down, with shelves towering above me filled with works of history that had been preserved and treasured through wars, fires, and revolutions. I stood there looking up at these books, realizing that I stood in a hallway of voices and thoughts that created the intellectual world that we live in today. And there, in the invisible margins of Diophantine Equations and Ptolomy’s Almagest were echoes of the work done by Hypatia of Alexandria.
The thing about those historical books was that many of those voices were misunderstood. Each one of those gorgeous tomes came from generations of writers, each copying the one before, and gradually transforming history into legend. In the process, facts were embellished, admiration turned to suspicion, and scholarship gave way to myth. And in the case of Hypatia, a celebrated mathematician and philosopher, centuries of retelling often obscured the woman behind the legend.
Until the nineteenth century, most academics accepted those stories. However, Paul Tannery did not.
Today, just a few outside the history of math and science recognize his name. He never discovered a famous theorem. He never founded a school of mathematics. He wasn’t a professor at the Sorbonne or Oxford, nor did he spend his life in the lecture halls of Europe’s great universities.
Instead, every morning he went to work as an engineer in France’s tobacco industry.¹ By all outward appearances, he lived an ordinary professional life. But when the workday ended, another life began. Evenings found him surrounded by Greek manuscripts, philosophical treatises, obscure commentaries, and mathematical texts that most scholars of his day found intimidating. While others pursued leisure, Paul Tannery pursued questions.
Not simply, what did the ancients know? But rather, how do we know what they knew? That distinction would change the history of mathematics.
I’ve always admired people who quietly devote themselves to truth. Not because they’re seeking fame. Not because they’re trying to prove themselves right. But because they believe that evidence matters.
During my own research while writing Hypatia: The Sum of Her Life, I kept returning to scholars who had taken the time to separate historical fact from centuries of repetition. Again and again, Paul Tannery’s name appeared in the footnotes.
At first, I assumed he was simply another nineteenth-century historian whose work had been superseded by modern scholarship. I couldn’t have been more mistaken.
The more I read, the more I discovered a man whose intellectual habits felt surprisingly modern. He questioned accepted narratives, examined primary sources, and deeply learned the mathematics he was studying. And the part that gets me is that he treated the people of antiquity not as legends, but as human beings deserving of careful understanding.
This methodology may sound obvious today. However, it wasn’t obvious in the late nineteenth century. History, especially the history of science and math, was still finding its footing as an academic discipline. Many scholars were content to repeat what earlier historians had written. Ancient texts were often approached more as literary curiosities than as living records of intellectual achievement. Additionally, before the nineteenth century, math was frequently presented as a sequence of isolated discoveries rather than as a conversation spanning millennia.
But Tannery believed there was a better way. He approached history almost as if he were solving a mathematical proof. Every assertion required evidence. Every conclusion had to follow logically from the sources. Every contradiction demanded investigation rather than a convenient explanation, which is an approach that mathematicians understand instinctively.
Mathematicians don’t assume the answer. We prove it.
And I truly believe that this way of thinking came naturally for Tannery because the traditions of academia didn’t confine him.
An Engineer with an Unexpected Future
When we look back on the lives of remarkable people, it is tempting to imagine that they always knew exactly where they were headed. We picture them as children with a clear sense of purpose, following a straight path toward the work for which history would eventually remember them. Paul Tannery’s life tells a different story.
Born on December 20, 1843, in Mantes-sur-Seine, France, Tannery displayed an early aptitude for math and science. His academic ability earned him admission to the prestigious École Polytechnique in Paris, one of France’s most demanding institutions and a training ground for many of the nation’s finest engineers, scientists, and civil servants. At the École Polytechnique, students received a rigorous education in mathematics, physics, mechanics, and engineering, subjects that emphasized precision, logical reasoning, and disciplined analysis. Those habits of mind would remain with Tannery for the rest of his life.[1]
Like many talented young Frenchmen of the nineteenth century, Tannery pursued a practical, highly respected career after graduation. Rather than pursuing an academic position, he entered the École d’Application des Tabacs (known as the School of Tobacco Application), where engineers were trained to serve in the French government’s tobacco administration. Today, that career choice may seem unusual, but in nineteenth-century France, the manufacture and sale of tobacco was a state monopoly. Managing the industry required skilled engineers who could oversee production, improve manufacturing techniques, and administer large industrial operations. Government service offered financial security, intellectual challenge, and the opportunity to contribute to one of France’s most important public enterprises.[2]
Over the years, Tannery worked in several cities, including Tonneins (TU-NEENS) and Paris, steadily advancing through the ranks of the administration. His colleagues knew him as a capable engineer and administrator whose work demanded careful planning, attention to detail, and analytical thinking. Yet beneath the surface, another story was unfolding. His position as an engineer paid his salary, but it was his curiosity that began building his legacy.
When his workday ended, Tannery did not leave his intellectual curiosity at the office. Instead, he returned home to books. He read widely in philosophy, ancient history, mathematics, astronomy, and classical literature. Unlike many scholars who specialized in a single discipline, Tannery became fascinated by the connections between fields. He wanted to understand not only what ancient scientists had discovered but also how those discoveries emerged, how ideas evolved, and why certain branches of knowledge flourished while others disappeared.
The turning point for Tannery came through the writings of the French philosopher Auguste Comte.
Comte argued that human knowledge develops through historical stages and that every scientific discipline has its own history of growth and transformation. Science, in Comte’s view, was not simply a collection of facts waiting to be discovered. It was a human endeavor that evolved over centuries, with each generation building upon the achievements of those who came before.[3]
Comte argued that science should not be viewed as a collection of isolated discoveries or biographies of great individuals. Instead, he believed that every science develops according to historical laws and passes through identifiable stages. To truly understand a scientific idea, one must understand how it arose, what problems it sought to solve, and the intellectual environment that produced it.
Although Paul Tannery never explicitly stated that Auguste Comte inspired him to become a historian of science, later historians, notably René Taton, have identified Comte’s influence on Tannery’s historical outlook. They point to his early reading of Comte’s The Course of Positive Philosophy, and to similarities in his belief that science should be understood through its historical development. Tannery ultimately developed his own methodology, emphasizing philology, textual criticism, and careful analysis of primary sources rather than Comte’s broader philosophical system.[4]
He had spent years mastering mathematics as an engineer, but possibly Comte’s philosophy inspired him to ask an entirely different kind of question. Instead of asking, What is mathematics? Tannery began asking, How did mathematics become what it is?
That subtle shift changed the direction of his life.
Mathematics was no longer merely a collection of formulas, theorems, and proofs. It became a story. Every theorem had an origin, every mathematical idea had predecessors, and every great discovery belonged to a larger conversation stretching across generations and civilizations.
Those questions fascinated him and he wasn’t even an academic. He hadn’t spent time within the university’s lecture halls or libraries. His curiosity led him to understand the process of historiography innately. And Tannery’s principles gradually became hallmarks of serious historical scholarship.
As his research deepened, Tannery found himself drawn to one discipline in particular: astronomy. To many modern readers, astronomy and mathematics seem like separate subjects, but the ancient Greeks understood them as deeply connected. Astronomers relied upon geometry to describe the movements of the heavens, while mathematicians often developed new methods to solve astronomical problems. If Tannery hoped to understand Greek mathematics, he realized he also needed to understand Greek astronomy.
That realization culminated in his work titled Researches on the History of Ancient Astronomy, published in 1893. Rather than cataloging ancient observations of the stars, Tannery traced the evolution of astronomical thought from its earliest origins through the Hellenistic period. He examined how successive generations refined mathematical models to explain celestial motions. Furthermore, he demonstrated that astronomy advanced not through isolated flashes of genius but through centuries of careful observation, criticism, and revision. Science, he argued, grows because each generation inherits the questions of the one before it.[5]
The more Tannery studied, the more he recognized another obstacle to understanding the ancient world. Much of what survived from Greece had reached modern scholars only after centuries of hand copying. Every manuscript represented another opportunity for mistakes. Scribes misspelled words. They skipped lines. They added explanatory notes in the margins that later copyists accidentally incorporated into the text itself. Occasionally, entire passages disappeared. If historians wanted to know what Euclid, Archimedes, or Diophantus had actually written, they first had to determine which manuscripts were the most trustworthy. This was particularly effective when he recognized possible tracings of Hypatia’s mathematics in Ptolemy’s Almagest and in the works of Diophantus.
This painstaking work became one of Tannery’s greatest strengths.
He approached manuscripts with the same discipline that an engineer brings to examining a bridge. Every inconsistency demanded an explanation. Every variation between manuscripts became a clue. Rather than accepting the first version he encountered, he compared copies from different libraries, analyzed their relationships, and searched for the reading that most likely reflected the original author. It was slow work, but Tannery understood that every historical conclusion rested upon the reliability of the text itself. Before historians could interpret an ancient mathematician, they first needed confidence that they were reading what that mathematician had actually written.[6]
Perhaps nowhere is this more evident than in his collaboration with the Danish philologist Johan Ludvig Heiberg on Diophanti Alexandrini Opera Omnia, published in two volumes between 1893 and 1895. Diophantus of Alexandria, often called the “father of algebra,” had written the Arithmetica, one of antiquity’s most sophisticated mathematical works. Yet the surviving manuscripts contained numerous variations, omissions, and uncertainties. Tannery and Heiberg painstakingly compared the available evidence to produce the most reliable critical edition of Diophantus’s writings then possible.
For Tannery, this project was about far more than editing an ancient text.
He believed that historians could not accurately describe the development of mathematics unless they first established dependable sources. Every corrected line of Greek text, every restored diagram, and every carefully documented variant helped reveal how ancient mathematicians reasoned. The goal was not simply to preserve old books but to recover ancient thought itself.[7]
As Tannery immersed himself in manuscripts, philosophy, astronomy, and mathematics, he began to notice something remarkable. The same names kept appearing. Euclid. Archimedes. Ptolemy. Diophantus. These figures were familiar to historians, but they did not stand alone. Their work belonged to a much larger intellectual tradition that included professors, commentators, editors, and philosophers whose contributions were often overlooked.
The questions that had guided Paul Tannery for years were about to lead him toward one of antiquity’s most misunderstood scholars.
Asking Different Questions
By the end of the nineteenth century, Paul Tannery had accomplished something remarkable. He had published critical studies on Greek philosophy, astronomy, and mathematics, edited ancient texts, and demonstrated that understanding science required far more than simply cataloging discoveries. Yet his greatest contribution was not any single book or edition. His greatest contribution was teaching historians to ask different questions.
Before Tannery, many histories of mathematics followed a familiar pattern. Math history celebrated great mathematicians, listed their discoveries, and arranged them chronologically, almost as though mathematics advanced through a series of isolated flashes of genius. Although these histories were valuable, they often left unexplored the broader intellectual world in which mathematics developed. Historians rarely asked why certain mathematical ideas emerged when they did. There was no evaluation of how they were transmitted from one generation to the next, or of how philosophy, astronomy, politics, and education shaped the development of scientific thought.[8]
Tannery believed that those questions mattered just as much as the mathematics itself. As a result, he helped establish a way of thinking about the history of math and science that emphasized evidence over assumption. He recognized that every historical claim required support from reliable sources. He knew that every manuscript had to be examined critically. And he understood that every conclusion had to fit within the broader intellectual environment of its time.
He argued that mathematical ideas did not appear in isolation. Every theorem had a history. Every scientific breakthrough rested upon earlier discoveries, teachers, debates, and traditions. To understand Euclid, one had to understand the mathematical culture of Alexandria. To appreciate Diophantus, we need to examine the manuscripts that preserve his work. To study Greek astronomy, one also had to understand Greek geometry and philosophy because those disciplines developed together. In Tannery’s view, the history of mathematics was not simply the history of numbers or proofs. It was the history of people trying to understand their world through reason. That perspective gradually transformed the discipline.
And tannery truly transformed the discipline of math and science history. Among those who appreciated and referred to his work are highly acclaimed historians, mathematicians and scientists. I’ve done podcasts on a few of them and they are, to name a few, British scholar Sir Thomas Heath, Adolphe Rome, Professors Wilbur Knorr, Maria Dzielska, Raviel Netz and Professor Edward Watts at UC San Diego.
For Sir Thomas Heath, he recognized that Tannery had established a higher standard for historical scholarship. Rather than merely translating ancient mathematics into modern notation, Heath sought, as Tannery had done, to understand what the Greek mathematicians themselves were attempting to accomplish.[9]
Nearly a century later, Professor Wilbur Knorr of Stanford University approached Greek geometry with many of these same assumptions. Knorr was interested in mathematical results and in how those results developed over time. His studies explored the evolution of geometric ideas, the educational traditions that preserved them, and the textual history of ancient mathematical works. Like Tannery, Knorr recognized that mathematics cannot be separated from the historical communities that produced it. Although Knorr occasionally challenged conclusions reached by earlier historians, including Tannery himself, he continued the same scholarly tradition of returning to the original sources, questioning inherited assumptions, and reconstructing mathematical history from the evidence rather than from legend.[10]
Maria Dzielska’s influential biography Hypatia of Alexandria demonstrated this approach beautifully. She treated the surviving sources not as unquestionable authorities but as historical documents that must be evaluated critically, compared carefully, and interpreted within their cultural context.[11]
Although these historians employ methods and evidence unavailable to Tannery, they continue to pursue the same fundamental goal: understanding ancient science within the historical world that produced it.[12]
This is Paul Tannery’s greatest legacy.
He demonstrated that the history of mathematics deserves the same rigor that mathematicians bring to their own discipline. A mathematical proof requires evidence, logical consistency, and careful reasoning. Tannery believed that history demanded exactly the same qualities. He taught historians to question unsupported assumptions, to examine manuscripts critically, to understand ideas within their historical context, and to allow the evidence to guide their conclusions.
These principles may seem obvious today precisely because scholars like Paul Tannery worked so diligently to establish them. His books did more than preserve knowledge of ancient mathematics. They helped define what it means to study the history of science as a serious academic discipline. By asking better questions, Tannery encouraged generations of historians to move beyond simple chronology and to explore the rich intellectual traditions that shaped mathematics, astronomy, philosophy, and science throughout the ancient world.
In doing so, he left behind something more enduring than any single publication. He left behind a method, a way of thinking, that continues to guide historical scholarship today.
Some of history’s most enduring contributions have come from people who refused to stop asking questions. So many people imagine scholarship as something reserved for universities, funded research, or prestigious academic appointments. Paul Tannery’s life reminds us that intellectual curiosity belongs to everyone.
He asked questions that many others overlooked. How did Greek mathematics actually develop? Who influenced whom? Which ancient texts could be trusted? Which stories reflected historical evidence, and which had grown through centuries of retelling? Most importantly, what should we do when history gets it wrong?
Those questions became the foundation of a lifetime of study.
Tannery’s revelations changed the questions that future historians began asking. Rather than viewing mathematics as a collection of disconnected discoveries, scholars increasingly examined it as part of a larger human story shaped by culture, philosophy, education, and the exchange and presentation of ideas. Tannery established that perspective, and historians of mathematics and science continue to build upon it today.
Perhaps that is the greatest lesson of Paul Tannery’s life.
He did not spend his career in a university lecture hall. He spent his days working as an engineer in the French tobacco administration. Yet when the workday ended, he returned home and pursued the questions that fascinated him. Night after night, year after year, he quietly built a body of scholarship that would influence generations of historians.
That is incredibly encouraging.
It reminds me that curiosity does not require permission. It does not require a faculty appointment, a research grant, or a prestigious title. It begins with a question and the willingness to keep following it, even when no one else understands why it matters.
Perhaps you have a question like that.
Maybe it is history. Maybe it is music, astronomy, biology, genealogy, languages, or some other subject that captures your imagination. Whatever it is, don’t dismiss it simply because it isn’t your profession.
The next great contribution to human understanding may not begin in a university office. It may begin at a kitchen table after dinner, in a garage workshop on a Saturday afternoon, or with someone opening a book simply because they want to know more. That someone could be you!
[1] Ivor Grattan-Guinness, Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (London: Routledge, 1994), 1465–67; June Barrow-Green, “Paul Tannery,” in Biographical Encyclopedia of Mathematicians, ed. Stephen J. Farthing (New York: Routledge, 2019).
[2] Thomas Hockey et al., eds., The Biographical Encyclopedia of Astronomers, 2nd ed. (New York: Springer, 2014), 2207–8; “Paul Tannery,” MacTutor History of Mathematics Archive.
[3] Auguste Comte, The Positive Philosophy of Auguste Comte, trans. Harriet Martineau (London: George Bell & Sons, 1896), 25–43; Ivor Grattan-Guinness, Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, 1465–67.
[4] Taton, René. Paul Tannery (1843–1904). 1954. https://doi.org/10.3406/rhs.1954.3462.
[5] Paul Tannery, Recherches sur l’histoire de l’astronomie ancienne (Paris: Gauthier-Villars, 1893), v–xii.
[6] Paul Tannery, Mémoires scientifiques, vol. 1 (Toulouse: Édouard Privat, 1912), vii–xv; Anthony Grafton, Defenders of the Text: The Traditions of Scholarship in an Age of Science, 1450–1800 (Cambridge, MA: Harvard University Press, 1991), 1–23.
[7] Diophantus of Alexandria, Diophanti Alexandrini Opera Omnia, ed. Paul Tannery and Johan Ludvig Heiberg, 2 vols. (Leipzig: B. G. Teubner, 1893–1895), Preface.
[8] Paul Tannery, Pour l’histoire de la science hellène (Paris: Félix Alcan, 1887), i–xv; Ivor Grattan-Guinness, Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (London: Routledge, 1994), 1465–67.
[9] Thomas L. Heath, A History of Greek Mathematics, 2 vols. (Oxford: Clarendon Press, 1921), passim, especially the Preface and numerous citations to Tannery throughout both volumes.
[10] Wilbur R. Knorr, The Evolution of the Euclidean Elements (Dordrecht: D. Reidel, 1975), ix–xiv; Wilbur R. Knorr, Textual Studies in Ancient and Medieval Geometry (Boston: Birkhäuser, 1989), 1–12.
[11] Maria Dzielska, Hypatia of Alexandria, trans. F. Lyra (Cambridge, MA: Harvard University Press, 1995), 1–18.
[12] Reviel Netz, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History (Cambridge: Cambridge University Press, 1999), 1–20; Edward J. Watts, Hypatia: The Life and Legend of an Ancient Philosopher (New York: Oxford University Press, 2017), xv–xxiii.