It’s a story that has been told and re-told over two centuries: A young man steps into the Paris dawn of May 30, 1832, dueling pistol in hand. Long haunted by a premonition of early death, he has spent the night bent over his desk, unburdening his mind of the mathematical insights that teem there, pausing only to scrawl a protest—I have not time—in the margin. On this foggy morning, his premonition comes terribly true: shot in the stomach, the young man dies the next day, cradled in his brother’s arms. Évariste Galois’s mathematical insights, cruelly rebuffed during his short life, will be appreciated only after his death.
The only trouble with this foundational story of modern mathematics is that it’s not true. The posthumous Galois, an innocent whose groundbreaking ideas were neglected by an obstinately ignorant academy during his short lifetime, bears only a passing resemblance to the real Galois, an intemperate revolutionary who had already published his most important discoveries on algebra by the time of his death, and who attracted mentors in the Paris mathematical establishment in spite of his twin gifts for giving offense and for self-destruction. In Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics, Amir Alexander tells the story of how the real Galois became the legendary one-- and how a similar transformation was wrought on mathematicians Niels Henrik Abel and János Bolyai. The transformation, Alexander shows, was a cultural one, and reveals the deep connections between mathematics and its cultural setting.
Alexander spoke with us about how he came to write the book, his findings, and the challenges and rewards of writing about math for a general audience.
Q. When did you first hear the story of Galois? What did you think of it then?
I first heard the story of Galois from a professor when I was a mathematics undergraduate in college. I think that’s how most mathematicians learn the story – it is told by teachers to students, and all mathematicians know it.
Even when I first heard the story it struck me as something more than an amusing anecdote. It seemed to suggest that mathematics is for the young, that only a select few can understand and appreciate its beauty, and that those who pursue it run the risk of being lost to our world. Those are deeply held beliefs among many mathematicians, and so the story of Galois has become something of a founding myth of modern mathematics, passed on from one generation to the next.
Q. How and when did you link his story to the larger narrative you draw out in Duel at Dawn—the idea that mathematics exists as part of the larger culture, and that the stories we tell about (or impose upon!) the lives of mathematicians reveal something about the practice of mathematics?
It’s very hard to say when exactly I noticed the relationship between the story of Galois and the actual practice of mathematics. I’ve been living with mathematics and stories about mathematics for a long time, and the awareness of these interconnections came slowly. But I think I can say something about how I arrived at the idea, the basic thought process that led to it.
First of all, after learning the story of Galois I soon found that it did not stand alone. Only slightly less famous are the legends of Abel, the Norwegian genius who died in poverty at age 26, and Bolyai, the young Hungarian discoverer of non-Euclidean geometry, who was crushed by the indifference of established mathematicians. The basic outline of all these stories is strikingly similar— and even more strikingly, all three lived and work at precisely the same time. Galois, Abel, and Bolyai all produced their mathematics between the mid 1820s and the early 1830s. So it seemed there was a new and dramatic story about mathematicians that appeared at a very specific time. This was the first piece of the puzzle.
The second piece of the puzzle was that the period in question, the early 19th century, was a time of dramatic change in the practice of mathematics. So dramatic, in fact, that some historians have called it the “re-birth” of mathematics, and it is often acknowledged as time in which the modern practice of pure mathematics was born. Whereas the old mathematics was focused on studying the physical world, the new practice was concerned with studying a pure mathematical world, separate from our own and governed solely by mathematical laws.
Overall then, a radical shift in the practice of mathematics and a radical shift in stories about mathematics took place at exactly the same time—in the early 19th century. It seemed to me practically inescapable that these two developments are related.
When I thought about it the connection between the two seemed obvious: The new mathematics required a new kind of heroic practitioner, one who would pursue it wherever it led, even beyond earthly reality. Dramatic heroes like Galois and Abel, who were lost to the world in their pursuit of mathematics, expressed this ideal perfectly. An “otherworldly” mathematics went hand in hand with romantic practitioners, “otherworldly” beings who are strangers in our imperfect world.
Q. Could you say a little about how this work relates to your earlier book, Geometrical Landscapes?
Both books are parts of a larger project of writing a new kind of history of mathematics, one in which even highly technical practices are deeply embedded in their cultural setting. In both cases I show that mathematics is part of broader history by looking at it through the lens of stories told about the mathematics and its practitioners.
Now mathematical stories, like all stories, are the product of their cultural setting: in 17th century we have stories about geographical exploration, in the 18th century stories are told about “natural” men, in the 19th century we have tales of tragic romantic heroes, and so on. At the same time these same stories tell us something about what people thought mathematics is, and who practiced it: the mathematics of a 17th century explorer is very different from the mathematics of a 19th century romantic outcast. Because they are part of both the historical setting and technical mathematical practice, stories are wonderful at connecting higher mathematics to the broad cultural trends of its times. Instead of a separate island of abstraction, mathematics becomes a part of the cultural mainstream.
After Geometrical Landscapes came out, some of the comments I got went something like this: “OK, you showed that in the early 17th century mathematics was anchored in its cultural context. But that is relatively simple mathematics. You couldn’t possibly show cultural connections for modern mathematics, which is far more complex and abstract.” I took that as a challenge: I wanted to show that modern mathematics too has cultural and historical underpinnings. The result was Duel at Dawn.
Q. How do you, as an author and educator, deal with (some) laypeople's aversion to math? Do you think it makes it more difficult to tell stories about math than about other fields, like science? How do you work around and overcome this obstacle?
I am very much aware that many people feel completely alienated from math. Part of my purpose in this book is to try and reverse this, engage people in mathematics, and return it to the mainstream of cultural life. I think stories are a wonderful way of doing that, and from its early beginnings mathematics has always been accompanied by a treasure-trove of stories and anecdotes. They are witty and amusing, and they also carry a moral about the practice and meaning of mathematics. Everyone loves a good tale, and I think people will be willing to follow it to both its historical origins and to its mathematical implications.
It’s interesting that you use the term “laypeople,” suggesting that mathematicians are a select priesthood possessing a secret knowledge. I think many people see things in exactly these terms, and that’s part of the problem: mathematics is perceived as the domain of “geniuses,” and set on such a high pedestal as to be effectively irrelevant to many people.
It was not always this way. In the Enlightenment, for example, mathematical concepts were at the heart of public debates about the nature of knowledge and faith. A wonderful recent book called Naming Infinity by Loren Graham and Jean-Michel Kantor shows that advanced mathematics carried religious and political meaning in early 20th century Russia. I want to make mathematics relevant to most people once again by showing that it is part of the world and part of life. Telling stories is my way to do this.
