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.