Chapter 1

The Flood Plain

Tuscany, Italy, September 2002. Like many present-day travelers to Pisa, I took the train from Florence—a small commuter train of four carriages pulled by a noisy diesel locomotive, quite different from the sleek Intercity Express that had whisked me southward from Trento. Even late in the season, the train was crammed with tourists, many of them young people carrying backpacks. Everyone was talking loudly to make themselves heard over the noise from the engine. In my carriage I heard Americans, British, Australians, Germans, French, Scandinavians, and Japanese. A port in the Roman era and a major Mediterranean trading hub in medieval times, Pisa clearly is still an international destination, though these days the main cargo seems to be foreign tourists.

Once the train had left Florence behind, the journey became spectacular, winding its way through the beautiful rolling hills of the Chianti wine region. On both sides of the railroad tracks, the steeply rising slopes were covered with an irregular checkerboard of bright green vineyards, each one laid out with geometric precision. Occasionally, a field would stretch right down to the side of the tracks, giving the passengers a closer view. Now, in late summer, the vines were heavy with the ripening purple grapes that would soon be harvested to make the wines the region is so famous for.

Eventually, the hills gave way to a large flat plain, stretching all the way to Pisa and beyond to the sea. There had been heavy rains just prior to my visit to Italy, and as the train left the vineyards it began to rain once again. As the engine slowed down to arrive at our destination, I saw that the land on both sides of the tracks was still under a foot or more of water. The land here floods regularly, a lasting reminder of why Pisa had become a port in the first place: In Roman times, and earlier, this is where Pisa’s harbor used to be.

By the time the train pulled up in Pisa, the rain had turned into a sustained, heavy downpour. The small, quaint, inexpensive hotel I had booked via the Internet was perfectly located for sightseeing, right in the center of the old medieval city, close to the river. Unfortunately, the railway station was not—it is a “Central Station” in name only. As I had experienced many times in New York City, when it rains in Pisa, everyone travels by taxi. As a result, the station taxi stand before me stood empty. I waited in line for an hour, with only my umbrella to keep me dry, before I was finally able to secure a ride. I soon began to wish I too had my belongings in a backpack, so I could have walked to my destination, as many of my fellow passengers did. It was a damp end to my journey, both literally and figuratively. Still, I was in Pisa at last, about to take the first step in what would turn out to be a seven-year quest to piece together the story of one of the most influential figures in human history, a medieval mathematician who, over the years, had become something of an obsession with me.

My visit had come about quite by chance. I had been invited to Italy to give an address at an international conference in Rome on the newly emerging field of mathematical cognition. I was asked to give lectures at several other universities as well—the industrial powerhouse of Torino in the northwest, the vacation destination Trento in the mountainous wine region in the northeast, the ancient university town of Bologna partway from Trento to Florence, and the spectacular Siena where, more than 20 years earlier, I had been a visiting professor for several weeks.

I had decided to take a two-day detour to Pisa in between my lecturing commitments in Bologna and Siena, in an effort to find out something about Leonardo Fibonacci, a mysterious thirteenth-century mathematician who apparently played a key role in the making of the modern world, and in whose mathematical footsteps I had, in one important respect, been treading for the past 20 years.

Was there enough information to write a book about him? No one else had written one, so I suspected there was not. On the other hand, that yawning gap in the written history of science meant that Fibonacci was the most famous and accomplished scientist never to have been the subject of a biography. I wanted to give it a try.

Figure 1. This Leonardo woodcut provides one of only two images we have of Leonardo. There is no evidence either is more than an artist’s conception.

My interest was certainly not that of the historian, for such I am not. I am a mathematician. What intrigued me about Leonardo was that significant similarity between our mathematical careers. I sensed a kindred spirit.

As I sheltered under my umbrella, waiting for a taxi, I reflected briefly on how different my mathematical career had been from the future I had envisaged back in 1968, when I completed my bachelor’s degree at the University of London and headed off to the University of Bristol to begin work on my doctorate.

Back then, when I was starting out, the only thing I knew about Fibonacci was that he was the mathematician who discovered the famous Fibonacci sequence (he didn’t—I was wrong), which I knew had deep connections to human aesthetics (it doesn’t—I was wrong). It was much later that I discovered he was one of the most influential men of all time. And that his greatness lay not in his mathematical discoveries—though he was without doubt the strongest mathematician of his time—but rather in his expository power. He had the ability to take what were at the time novel and difficult mathematical ideas and make them accessible to a wide range of people. Moreover, he had the instinct to do it in a way that in present-day terminology would be described as a “good marketing strategy.”

As a young graduate student, my role models were not the likes of Leonardo Fibonacci, but the mathematicians who had made major mathematical discoveries—more recent mathematical giants such as Leonard Euler, Karl Friedrich Gauss, Pierre De Fermat, and Kurt Gödel. Like many young people embarking on a mathematical career, I dreamed of joining the ranks of the greatest—of proving a major theorem or solving a difficult problem that had baffled the best minds for decades.

Some of my contemporaries succeeded. In 1963, only a few years ahead of me, the young American mathematician Paul Cohen solved Cantor’s Continuum Problem, a puzzle that had resisted all attempts at resolution for more than 60 years. But as is true for the vast majority of mathematicians, eventually I had to settle for far less.

During the course of my career, like most of the world’s 25,000 professional mathematicians listed in the International Directory of Mathematicians, I solved a number of minor problems and proved several respectable but largely unremarkable theorems. I taught at various universities, in Scotland, Norway, Germany, Canada, and the United States (where I moved permanently in 1987), and I wrote a number of textbooks for mathematicians and students. Again, these are all fairly typical career moves for many academic mathematicians, though perhaps I moved around more than many and ended up writing more books than most.

But along the way, almost by accident, I discovered another talent, perhaps my true calling: an ability to explain often obscure, advanced mathematical ideas to a general audience. I found that, through my words, I could make mathematics come alive for others not versed in the subject.

An unplanned sequence of events resulted in my discovering this ability and thereby embarking on a second career path as a public expositor of mathematics. In the early 1980s, having returned to the UK after four years in Norway and Germany, I grew increasingly frustrated by the fact that magazines and newspapers often carried articles on science—biology, physics, chemistry, and so on—but hardly ever on mathematics. On the few occasions when they did cover mathematics, they did so badly, often getting the main idea entirely wrong. In March 1983, I decided to do something about the situation, so I wrote a short piece and sent it in to the British national newspaper the Guardian.

It was an April Fools joke, to be published on April 1. I described some mathematics that, while true, was so counterintuitive, most readers would note the date and assume it was a spoof—and in so doing they would fall victim to the real joke: The article was true.

A few days later, the science editor, Anthony Tucker, phoned and informed me that they could not publish it. “But,” he said, “I like your style. You seem to have a real knack for explaining difficult ideas in a way ordinary people can understand.”

Tucker encouraged me to try again, and my second attempt was published in the Guardian on May 12, 1983. Several more pieces also made it into print, eliciting some appreciative letters to the editor. As a result, when the Guardian launched a weekly, personal computing page later that year, it included my new, twice-monthly column Micromaths. The column ran without interruption until 1989, when my two-year visit to Stanford University in California turned into a permanent move to the United States.

I soon discovered that I liked my new role of “expositor.” I have always been passionately interested in all aspects of mathematics, and never liked the fact that so many people have a completely false impression of this wonderful subject. Most people think that mathematics is just about numbers, but that’s not true at all. Yes, numbers play an important role in the subject, but mathematics is not about counting. It’s about pattern and structure. It’s about the hidden beauty that lies just beneath the surface of the everyday world. I relished the challenge of constantly trying to find ways to explain new developments in advanced mathematics to the lay readers of my column. The frequent appreciative—and occasionally baffled—letters I received from readers further fueled my commitment.

Encouraged by the success of my column, I began writing books and articles for a general readership, including some for the business world. I also gave lectures to lay audiences and started to make occasional appearances on radio and television. From 1991 to 1997, after moving to the United States in 1987, I edited FOCUS, the monthly magazine of the Mathematical Association of America, and since January 1996 I have written a monthly column, “Devlin’s Angle,” for the MAA’s Web magazine, MAA Online. (The column is now in blog format.)

Early in 1995, I got a break that led to my becoming a regular contributor to primetime national radio in the United States, with the media identity “the Math Guy.” I got a telephone call one day from National Public Radio’s Saturday morning news magazine show Weekend Edition. The host, Scott Simon, wanted to interview me about the solution to the 350-year-old problem known as Fermat’s Last Theorem, which became a major news story after the Princeton mathematician Andrew Wiles had solved it a few months earlier.

Although Scott and I would not meet for many months—then as now, we record most of our interviews with me in a studio in California and Scott at the NPR studios in Washington, DC—we hit it off immediately over the air. Listeners loved our intimate, humorous banter—which from the start has been completely unrehearsed and spontaneous. Many wrote in to the program to say so. Again, without any planning, I found I had another new role, this time a “radio personality,” appearing on the show every few weeks. Eventually, I acquired my “stage name.” The receptionist at the studio I used soon started to greet my arrival with “It’s the math guy.” I mentioned this to the Weekend Edition producer one day, and he replied, “Oh, that’s what we put you down as on our scheduling board.” And so the NPR Math Guy was born.

Each new step brought me further pleasure, as more and more people came up to me after a talk, or wrote or emailed me after reading an article I had written or hearing me on the radio. They would tell me they found my words inspiring, challenging, thought-provoking, or enjoyable. Parents, teachers, stay-at-home moms, business people, and retired people would thank me for awakening in them an interest and a new appreciation of a subject they had long ago abandoned for being either dull and boring or beyond their understanding. I came to realize that I was touching people’s lives, opening their eyes to the marvelous world of mathematics.

None of this was planned. I had become a “mathematics expositor” by accident. Only after I realized I had been born with a talent that others appreciated—and that by all accounts is fairly rare—did I begin to work on developing and improving my “gift.”

In taking mathematical ideas developed by others and explaining them in a way that the layperson can understand, I was following in the footsteps of others who had also made efforts to organize and communicate mathematical ide...