The Man of Numbers: Fibonacci's Arithmetic Revolution

By Keith Devlin

In 1202, a 32-year old Italian finished one of the most influential books of all time, which introduced modern arithmetic to Western Europe. Devised in India in the 7th and 8th centuries and brought to North Africa by Muslim traders, the Hindu-Arabic system helped transform the West into the dominant force in science, technology, and commerce, leaving behind Muslim cultures which had long known it but had failed to see its potential.
The young Italian, Leonardo of Pisa (better known today as Fibonacci), had learned the Hindu number system when he traveled to North Africa with his father, a customs agent. The book he created was Liber abbaci, the "Book of Calculation," and the revolution that followed its publication was enormous. Arithmetic made it possible for ordinary people to buy and sell goods, convert currencies, and keep accurate records of possessions more readily than ever before. Liber abbaci's publication led directly to large-scale international commerce and the scientific revolution of the Renaissance.
Yet despite the ubiquity of his discoveries, Leonardo of Pisa remains an enigma. His name is best known today in association with an exercise in Liber abbaci whose solution gives rise to a sequence of numbers--the Fibonacci sequence--used by some to predict the rise and fall of financial markets, and evident in myriad biological structures.
One of the great math popularizers of our time, Keith Devlin recreates the life and enduring legacy of an overlooked genius, and in the process makes clear how central numbers and mathematics are to our daily lives.

• Language: English
• Publisher: Bloomsbury USA
• Release date: Jul 5, 2011
• ISBN: 9780802779076

Keith Devlin

Dr. Keith Devlin is a mathematician at Stanford University in California. He is a co-founder and Executive Director of the university's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He has written 31 books and over 80 published research articles. His books have been awarded the Pythagoras Prize and the Peano Prize, and his writing has earned him the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio. (Archived at http://www.stanford.edu/~kdevlin/MathGuy.html.) He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He writes a monthly column for the Mathematical Association of America, "Devlin's Angle": http://www.maa.org/devlin/devangle.html

Book preview

Author

CHAPTER 0

Your Days Are Numbered

Try to imagine a day without numbers. Never mind a day; try to imagine getting through the first hour without numbers: no alarm clock, no time, no date, no TV or radio, no stock market report or sports results in the newspapers, no bank account to check. It’s not clear exactly where you are waking up either, for without numbers modern housing would not exist.

The fact is, our lives are totally dependent on numbers. You may not have a head for figures, but you certainly have a head full of figures. Most of the things you do each day depend on and are conditioned by numbers. Some of them are obvious, like the ones listed above; others govern our lives behind the scenes. The degree to which our modern society depends on numbers that are hidden from us was made clear by the worldwide financial meltdown in 2008, when overconfident reliance on the advanced mathematics of futures predictions and the credit market led to a total collapse of the global financial system.

How did we—as a species and as a society—become so familiar with and totally reliant on these abstractions our ancestors invented just a few thousand years ago? As a mathematician, I had been puzzled by this question for many years, but for most of my career as a university professor of mathematics, the pressures of discovering new mathematics and teaching mathematics to new generations of students did not leave me enough time to look for the answer. As I grew older, however, and came to terms with the unavoidable fact that my abilities to do original mathematics were starting to wane a bit—a process that for most mathematicians starts around the age of forty (putting mathematics in the same category as many sporting activities)—I started to spend more time looking into the origins of the subject I have loved with such passion since I made the transition from It’s boring to It’s unbelievably beautiful around the age of sixteen.

For the most part, the story of numbers was easy to discover. By the latter part of the first millennium of the Current Era, the system we use today to write numbers and do arithmetic had been worked out—expressing any number using just the ten numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and adding, subtracting, multiplying, and dividing them by the procedures we are all taught in elementary school. (Units column, tens column, hundreds column, carries, etc.) This familiar way to write numbers and do arithmetic is known today as the Hindu-Arabic system, a name that reflects its history.

Prior to the thirteenth century, however, the only Europeans who were aware of the system were, by and large, scholars, who used it solely to do mathematics. Traders recorded their numerical data using Roman numerals and performed calculations either by a fairly elaborate and widely used fingers procedure or with a mechanical abacus. That state of affairs started to change soon after 1202, the year a young Italian man, Leonardo of Pisa—the man whom a historian many centuries later would dub Fibonacci—completed the first general purpose arithmetic book in the West, Liber abbaci, that explained the new methods in terms understandable to ordinary people (tradesmen and businessmen as well as schoolchildren).¹ While other lineages can be traced, Leonardo’s influence, through Liber abbaci, was by far the most significant and shaped the development of modern western Europe.

Leonardo learned about the Hindu-Arabic number system, and other mathematics developed by both Indian and Arabic² mathematicians, when his father brought his young son to join him in the North African port of Bugia (now Bejaïa, in Algeria) around 1185, having moved there from Pisa to act as a trade representative and customs official. Years later, Leonardo’s book not only provided a bridge that allowed modern arithmetic to cross the Mediterranean, but also bridged the mathematical cultures of the Arabic and European worlds, by showing the West the algebraic way of thinking that forms the basis of modern science and engineering (though not our familiar symbolic notation for algebra, which came much later).

What Leonardo did was every bit as revolutionary as the personal computer pioneers who in the 1980s took computing from a small group of computer types and made computers available to, and usable by, anyone. As with those pioneers, most of the credit for inventing and developing the methods Leonardo described in Liber abbaci goes to others, in particular Indian and Arabic scholars over many centuries. Leonardo’s role was to package and sell the new methods to the world.

Not only did the appearance of Leonardo’s book prepare the stage for the development of modern (symbolic) algebra and hence modern mathematics, it also marked the beginning of the modern financial system and the way of doing business that depends on sophisticated banking methods. For instance, Professor William N. Goetzmann of the Yale School of Management, an expert on economics and finance, credits Leonardo as the first to develop an early form of present-value analysis, a method for comparing the relative economic value of differing payment streams, taking into account the time value of money. Mathematically reducing all cash flow streams to a single point in time allows the investor to decide which is the best, and the modern version of the present-value criterion, developed by the economist Irving Fisher in 1930, is now used by virtually all large companies in the capital budgeting process.¹

The only piece of the story of numbers that was missing was an account of Leonardo himself and, apart from a few scholarly articles, of the nature of his book. History has relegated him to an occasional footnote. Indeed, his name is known today primarily in connection with the Fibonacci numbers, a sequence of numbers that arises from the solution to the rabbit problem,³ one of many whimsical challenges he put in Liber abbaci to break the tedium of the hundreds of practical problems that dominate the book.

Part of the reason Leonardo has been overlooked, whereas comparable figures like Copernicus, Galileo, and Kepler were not, may be that to most laypersons science seems to serve a greater purpose than mathematics.

Another reason why generations may have overlooked Leonardo is that the change in society brought about by the teaching of modern arithmetic was so pervasive and all-powerful that within a few generations people simply took it for granted. There was no longer any recognition of the magnitude of the revolution that took the subject from an obscure object of scholarly interest to an everyday mental tool. Compared with Copernicus’s conclusions about the position of Earth in the solar system and Galileo’s discovery of the pendulum as a basis for telling time, Leonardo’s showing people how to multiply 193 by 27 simply lacks drama.

The comparative neglect of Leonardo has no doubt been caused by two other factors. Very little was recorded about his life, discouraging biographies. And Leonardo was more a salesperson of modern arithmetic rather than its inventor. The mathematical advances he described in Liber abbaci were developed by others, and others also wrote books describing those mathematical ideas. In the world of scientific biography, the inventor tends to get the glory. But inventions—an idea, a theory, a process, a technology—need to be made accessible to the world. The personal computer on which I write these words, with its familiar windows, mouse-controlled pointer, and the like, was invented by brilliant teams of researchers at the Stanford Research Institute and the Xerox Palo Alto Research Center in the 1970s, but it was put into everyone’s hands by a few pioneering entrepreneurs. The computer revolution would undoubtedly have happened anyway, just as we would have figured out the motion of the planets had Kepler not lived, and gravity without Newton. But the likes of Apple Computer’s Steve Jobs and Microsoft’s Bill Gates will always be linked to the rise of the personal computer, and in this way Leonardo should be linked to the rise of modern arithmetic.

What Leonardo brought to the mathematics he learned in Bugia and elsewhere in his subsequent travels around North Africa were systematic organization of the material, comprehensive coverage of all the known methods, and great expository skill in presenting the material in a fashion that made it accessible (and attractive) to the commercial people for whom he clearly wrote Liber abbaci. He was, to be sure, a highly competent mathematician—in fact, one of the most distinguished mathematicians of medieval antiquity—but only in his writings subsequent to the first edition of Liber abbaci in 1202 did he clearly demonstrate his own mathematical capacity.

Following the appearance of Liber abbaci, the teaching of arithmetic became hugely popular throughout Italy, with perhaps a thousand or more handwritten arithmetic texts being produced over the following three centuries. Moreover, the book’s publication, and that of a number of his other works, brought Leonardo fame throughout Italy as well as an audience with the Holy Roman Emperor Frederick II. Since the Pisan’s writings were still circulating in Florence throughout the fourteenth century, as were commentaries on his works, we know that his legacy lived on long after his death. But then Leonardo’s name seemed to be suddenly forgotten. The reason was the invention of movable-type printing in the fifteenth century.

Given the Italian business world’s quick adoption of the new arithmetic, not surprisingly the first mathematics text printed in Italy was a fifty-two-page textbook on commercial arithmetic: an untitled, anonymous work known today as the Aritmetica di Treviso (Treviso Arithmetic), after the small town near Venice where it was published on December 10, 1478. Soon afterward, Piero Borghi brought out a longer and more extensive arithmetic text, printed in Venice in 1484, that became a true bestseller, with fifteen reprints, two in the 1400s and the last one in 1564. Filippo Calandri wrote another textbook, Pitagora aritmetice introductor, printed in Florence in 1491, and a manuscript written by Leonardo da Vinci’s teacher Benedetto da Firenze in 1463, Trattato d’abacho, was printed soon afterward. These early printed arithmetic texts were soon followed by many others.

Though Liber abbaci was generally assumed to be the initial source for many, if not all, of the printed arithmetic texts that were published, only one of them included any reference to Leonardo.⁴ Luca Pacioli, whose highly regarded, scholarly abbacus book Summa de arithmetica, geometria, proportioni et proportionalità (All that is known about arithmetic, geometry, proportions, and proportionality) was printed in Venice in 1494, listed Leonardo among his sources, and stated, Since we follow for the most part Leonardo Pisano, I intend to clarify now that any enunciation mentioned without the name of the author is to be attributed to Leonardo.

The general absence of creditation was not unusual; citing sources was a practice that became common much later, and authors frequently lifted entire passages from other writers without any form of acknowledgment. But without that one reference by Pacioli, later historians might never have known of the great Pisan’s pivotal role in the birth of the modern world. Yet Pacioli’s remark was little more than a nod to history, for a reading of the entire text shows that the author drew not from Liber abbaci itself but from sources closer to his own time. There is no indication he had ever set eyes on a copy of Liber abbaci, let alone read it. His citation of Leonardo reflects the fact that, at the time, the Pisan was considered the main authority, whose book was the original source of all the others.

Despite the great demand for mathematics textbooks, Liber abbaci itself remained in manuscript form for centuries, and therefore inaccessible to all but the most dedicated scholars.⁵ Not only was it much more scholarly and difficult to understand than many other texts; it was very long. Over time it became forgotten, as people turned to shorter, simpler, and more derivative texts. That one mention in Pacioli’s Summa was the only clue to Leonardo’s pivotal role in the dramatic growth of arithmetic.⁶ It lay there, unnoticed, until the late eighteenth century, when an Italian mathematician called Pietro Cossali (1748–1815) came across it when he studied Summa in the course of researching his book Origine, transporto in Italia, primi progressi in essa dell-algebra (Origins, transmission to Italy, and early progress of algebra there).² Intrigued by Pacioli’s brief reference to Leonardo Pisano, Cossali began to look for the Pisan’s manuscripts, and in due course learned from them of Leonardo’s important contribution.

In his book, published in two volumes in 1797 and 1799, which many say is the first truly professional mathematics history book written in Italy, Cossali concluded that Leonardo’s Liber abbaci was the principal conduit for the transmission to Italy of modern arithmetic and algebra, and that the new methods spread first from Leonardo’s hometown of Pisa through Tuscany (in particular Florence), then to the rest of Italy (most notably Venice), and eventually throughout Europe.³ As a result, Leonardo Pisano, famous in his lifetime then completely forgotten, became known—and famous—once again. But his legacy had come extremely close to being forever lost.

The lack of biographical details makes a straight chronicle of Leonardo’s life impossible. Where and when exactly was he born? Where and when did he die? Did he marry and have children? What did he look like? (A drawing of Leonardo you can find in books and a statue of the man in Pisa are most likely artistic fictions, there being no evidence they are based on reality.) What else did he do besides mathematics? These questions all go unanswered. From a legal document, we know that his father was called Guilichmus, which translates as

Reviews for The Man of Numbers

[clmerle · Rating: 4 out of 5 stars]

A slim volume, but well worth reading. Little is known about Leonardo of Pisa's life, but much more is now known of his legacy and the era in which he lived. It also gives a glimpse how mathematical notation changed and became even more symbolic since his time.

[jmccarro · Rating: 4 out of 5 stars]

The Man of Numbers, by Keith Devlin, is an account of Leonardo of Pisa, better known as "Fibonacci". Leonardo is best known for the number sequence, the"Fibonacci Numbers", named after him. (1, 1, 2, 3, 5, 8, 13, 21, 34, ... Can you guess the pattern?)Far more important than this sequence, however, was Leonardo's introduction of the familiar Arabic numerals to Europe. These are the numbers (0, 1, 2, 3, 4, 5, 6,...) that we use now for nearly everything, and they replaced the olderRoman numerals (I, II, III, IV, V, VI,...) that were in use in Europe prior to the thirteenth century.The unfortunate fact is that very little is known about Leonardo, apart from some of his writing. This makes his story rather difficult to tell, so Devlin makes up for the lack of hard data by describing life during Leonardo's time,and speculating intelligently about various aspects of his education, travelsand motivations for his work. Most interestingly, he describes the tremendous impact the introduction of Arabic numerals had on Western culture, and the wayordinary calculation was so profoundly affected.Devlin has a well-earned reputation as a master of telling mathematical stories, and while I would not consider it his best work, this book does notdisappoint on that score.

[hippypaul_1 · Rating: 5 out of 5 stars]

In about the year of 1170 a man named Leonardo was born in Pisa. Opening a book he wrote in 1202 he referred to himself as Leonardo Pisano, Family Bonacci, from this Latin phrase filus Bonacci his present day nickname “Fibonacci” was coined by a historian in 1838. Fibonacci is usually remembered only in connection with the ‘Fibonacci sequence’ however, in this fine book Keith Devlin carefully outlines his role as a towering figure in the movement of Hindu-Arabic numerals and arithmetic from the southern Mediterranean into Italy where it spread into Europe.The system was known in Italy before Fibonacci was born but it had was little used and not seen as being of value. It was the achievement of Fibonacci in his books to describe the system in terms of the problems encountered by merchants. He provided page after page of problems that involved trade, the measurement of land, the division of profits and the exchange of one form of money for another. Each problem was carefully worked out with the problem described in the text and the numbers presented in red in the margin. Fibonacci had written the first practical math textbook and it was copied over and over again by other authors. With real world examples such as “On finding the worth of Florentine Rolls when the worth of those of Genoa is known” he had written the first book on the Hindu-Arabic system that had popular appeal. The type of book that we all use to learn basic arithmetic is the direct descendant of this type of writing. The story of the development of math and math learning is very well told in this most enjoyable book. It in no way requires a math background or skills to read and enjoy. I recommend it to anyone who likes a good story of how our world came to be.A free copy of this book was provided for the purpose of review.

[pw0327 · Rating: 3 out of 5 stars]

I will have to admit, this is not what I expected. Kevin Devlin has gained popularity as a proselytizer of mathematics, and this book on Fibonacci seems to be the perfect vehicle for someone as erudite and learned in the mathematical arts as Devlin. But this book was a disappointment.I do not attribute it all to Devlin however. He chose a very difficult and hardly simple task. As Devlin himself admitted, there is scant history on Fibonacci the man, let alone his mathematics. Devlin must have had a devil of a time gaining proper perspective on the man's life and his ability as a mathematician. He has had to depend on mostly tertiary sources and a very active imagination to tell the story.In addition, the main contributions of which Devlin is writing about: the importance of the Arabic number system on the evolution of western commerce and science is something that we take for granted. the idea of how to represent numbers is such a large part of our DNA that the discussions, very well crafted discussions, seem to be obvious and rather a waste of breath. It is of course anything but a waste of breath, but it just seems that way. The other major issue is that Fibonacci was not the originator of the number system, he was the popularizer through his writings. And popularizers rarely get the respect that originators get.Lastly, Devlin is a mathematician, his attempt at history writing is admirable but not entirely rigorous nor is his writing of the history riveting. The mathematics was quite well written, but the history part was less than satisfying, partly due to the lack of original material on which to base the story on, and partly because the historical writing seem to be pedestrian and somewhat rushed. I have to hand it to Prof. Devlin for giving it the old college try, and there seems to be quite a bit of hard work and scholarship involved, it just wasn't a mathematical nor a history page turner.

[lmhtwb · Rating: 4 out of 5 stars]

The Man of Numbers is advertised as a biography of Leonard of Pisa (aka Fibonacci) and his importance in the development of algebra and/or arithmetic. While the book does talk about both, both topics are dealt with on a superficial level.Take for example the biography of Fibonacci. Because he lived in the 13th century and because there is almost nothing actually known of his life, Devlin explains some about what Fibonacci's education and upbringing might have been. While interesting in some areas, his discussion totally avoids the question of why did Fibonacci study Arabic mathematics and see it's importance. Others surely had the opportunity, but failed to grasp it.This brings up the second flaw in the book -- while Devlin says Fibonacci brought to Europe algebra, the Arabic numerals, and the use of zero, he never quite explains fully why it is important or what the math was at the time in Europe.While I enjoyed the book on one level, I was frustrated by the lack of details. Admittedly, the details for much of the book simply do not exist (such as the biography), which then begs the question, "Why write a bio of someone of whom little is known?" It did spark my interest in medieval mathematics, so for that I'm happy.If you have little background in math history and/or medieval history, this book would be interesting.

[woakden · Rating: 4 out of 5 stars]

I clearly remember puzzling out the relationship between the numbers in the Fibonacci sequence back in grade school, so I was vaguely expecting a bunch of interesting number puzzles from this book. Instead, what I got was a fantastic historical and mathematical tour of Italy in and around the 13th century, and an appreciation for the revolution caused by the introduction of the numerals 0-9 and the new way of doing arithmetic.While I had a vague idea that doing arithmetic with roman numerals was annoying, I hadn't really thought about how much easier it is to use 0-9. The introduction of the new math was totally revolutionary, affecting the complexity of trade in the newly emerging banking, and insurance industries. Like most brilliant new ideas, it was resisted (in some cases legislated against), and then eventually simply replaced the previous system to the degree that we don't even think about it anymore. Fibonacci is famous for publishing the first practical guides to using the new mathematical tools, and appears to be the direct ancestor of day's math textbooks. Devlin puts some translations of Fibonacci's solutions to example problems alongside the solutions that people today would be familiar with from a high-school math class, and it is shocking to see just how far we have come. If you're someone who doesn't like looking at equations, these are easy to skip past as they're simply for illustration...and I suspect that Fibonacci's approach to arithmetic might give you a whole new appreciation for them!This was a great book. Nice and short. Devlin's style is easy to read and entertaining, and I learned a lot. I'm definitely planning to investigate some of his other books.

[elenchus_1 · Rating: 3 out of 5 stars]

Devlin's The Man of Numbers effectively establishes two points:1 - Little biographical detail can be confirmed about Leonardo of Pisa (Pisano), but consensus finds him a capable mathematician who greatly influenced the practical aspects of arithmetic through workbooks aimed at teaching merchants a better way to do business. The primary text, Liber abbaci was published in 1202 and revised 1224, was widely popular, and recognised by mathematicians as well as royalty. (His nickname Fibonacci might be a derivation of a patronymic linked to a grandfather rather than his father.)2 - Prior to Liber abbaci, European / Western mathematics lacked the zero symbol for calculations (though the counting board did use a placeholder), a numeric system predicated on place value (a numeral's position indicating one, tens, hundreds, thousands), and single characters representing a given number (contra Roman numerals using multiple characters for a single number, e.g. VIII as 8). Fibonacci advocated the adoption of an Indo-Arabic numeric system, using the characters 0 - 9 in specified positions.Fibonacci followed up on the implications of his preferred system, bringing to light its many advantages beyond that of simply commerce. Logical and mathematical thinking both were aided by this system.//Devlin's story makes clear that mathematics depends upon a remarkable coincidence: manipulation of mathematical symbols (a kind of game) is mirrored in patterns evident in values and quantities "out there in the world" (natural reality). Using earlier systems, these useful manipulations simply were cumbersome or often impossible, and so we could not avail ourselves of the advantages. Fibonacci grasped this quickly, contributing to the advance of algebra while using the Indo-Arabic number system he adapted from merchants. He was not a one-trick pony.European merchants used counting boards not the abacus, the latter being Chinese and not much used in Europe. Counting boards were trays with depressions used for holding counters; depressions arrayed in columns, and counters could be marked or coloured to indicate orders of magnitude. An empty depression could hold the place of a zero, but there was no counter (symbol) for zero. Similarly, arithmetic usually relied upon finger / hand systems, with each digit standing in for a quantity and multiplication relying upon complex interactions of digits (fingers!). Finger reckoning worked quite well, but was constraining in comparison with the Indo-Arabic number system, took more training/skill, and left no documentation of the computations.Base 10 offers few advantages and some disadvantages over other options such as Base 12: 12 has more factors than 10. Of course, we have 10 fingers, 10 toes, and yet some few cultures used Base 12 or 60 despite having the familiar anatomical constraints.Paired with Tobias Dantzig's Number, Devlin offers a nice illustration of the number system we use, and suggests the important aspects of what seems commonplace. Look for other books to serve in a similar role as Devlin: an entertaining vignette within Dantzig's survey of mathematics and number.

[janeslist · Rating: 4 out of 5 stars]

This book is a biography of Fibonacci, although actually not that much is known about him. It reviews what is known, and then spends much time on the history of how he made the first major introduction of the Hindu-Arabic number system to the western world. It is a quick but rather bland read but it was interesting to see what numbers, arithmetic, and math in general, were like in the past. The best aspect of the book, I think, is that it shows us a time before symbolic algebra was invented, before our quick pencil and paper methods of calculation were well known, when even figuring out linear equations was a challenge. And the fact that we know these methods of calculation owes a lot to Fibonnaci, who did much more than describe a sequence about rabbits.As a math tutor, with this book I can now even more strongly share that idea that the basic math we practice is the winner-so-far in a long line of human trial-and-error about notation and algorithms.

[claude_lambert_10 · Rating: 5 out of 5 stars]

I read books on the history of math because I am interested in how people think, not specially in math. This is a very touching book on how arithmetic was introduced to Europe in 1202 by Fibonacci, an Italian we know almost nothing about. At the eve of what was to become "global trade", arithmetic came just on time. What made it possible was the introduction of the numerals 0 to 9 and place value. This, Fibonacci inherited from India via the Arab world: he made popular what we now consider basic knowledge all over the world. It could be a dry book, it is not: under the bright, intelligent, incisive style of Keith Devlin, there is a lot of love and emotion, the ambition to correct a wrongdoing of history: if you know Fibonacci's name, it is probably for the wrong reason. The book tells you a lot on how people thought: how do you solve problems when you do not have mathematical symbols? Devlin guides us through some problem solving examples from the Fibonacci's book of calculation, I found this entertaining. I live in Savannah GA where no kid knows how to divide by ten, because teachers have forgotten the importance of place value: this is the kind of book that would remind them what arithmetic is about: it is the first step to democracy.

[dekesolomon · Rating: 4 out of 5 stars]

Blurbs on the dust jacket inform me that Dr. Keith Devlin is "the math guy" at National Public Radio. Devlin's intellectual and professional credentials are impressive. Among other achievements he is an author of considerable experience having written some 30 books. Now Devlin offers us a new title: The Man of Numbers: Fibonacci's Arithmetic Revolution (New York: Walker & Company; 183 pp; 2011; $25.00).I should first say that Man of Numbers is knowledge presented correctly. Of the book's 183 numbered pages, 158 are text followed by 8 pages of Notes, a 6-page Bibliography and a useful, 10-page Index. Regarding format, even Kate Turabian could not fault Man of Numbers.To the laity (That's folks like you and me.) the Bibliography is positively terrifying -- which is to say that Dr. Devlin did a stellar job on his homework. Sources cited include 13th- and 14th-century mathematics texts in the form of illuminated manuscripts that were hand-copied by medieval monks in Latin.So it is that while I know not what course others may take, nobody will catch this writer checking the verity of Dr. Devlin's assertions. I'm pleased to take his word for every fact published in Man of Numbers, and I hereby award him an A+ for research. Devlin also writes a fine hand; so it may therefore seem odd that, as someone who reads for pleasure, I cannot recommend this book to most readers.My primary beef is that Man of Numbers is a book for those who are deeply interested in math trivia and the history of math but not for those who enjoy biography or history in general. "Man of Numbers" and "Fibonacci" get star billing in the title but, fact is, the whole book contains just enough hard facts about Fibonacci the man to make a decent-sized caption under a picture of Fibonacci in Who's Who. The overwhelming majority of what's in this book is concerned with algebra, with the evolution of algebra, and with those (mostly anonymous men) whose work helped speed the evolution of algebra.I should add, too, that Fibonacci's alleged role in speeding the advancement of algebra is not proven in this book but is rather inferred from internal evidence which appears in this, that, or the other medieval manuscript. And while the bits of internal evidence may be numerous and identified by serious scholars (they are), inferences drawn from internal evidence are not hard facts. There is room yet for some ambitious, unknown Gradgrind to come roaring in from the bullpen and pitch Fibonacci out of the box in which some of today's historians place him.While I personally understand the importance of math and enjoyed some juicy bits of trivia I found in the book (The insurance business is the child of pirates and extortionists.) I don't give a snap for the study of math. I bought this book because I took it for a biography of Fibonacci, which it is not. Long, dreary pages of antique math problems made this a tedious read for me.Solomon sez: Man of Numbers is not for general readers but could be a hit with math lovers. Four stars for a good job that I didn't much care for.

[billpilgrim_1 · Rating: 4 out of 5 stars]

This is a biography of Fibonacci, who is deemed responsible for the introduction of the Indo-Arabic number system into regular use by Europeans. It is somewhat hard to tell his life story, however, because there is so little that is really known about him. There is a lot of supposition in this book. But, the author makes the best case for concluding that it was his efforts that led to the use of our ten digit, base ten, numeric system, throughout Europe.Parts of the book are less interesting. I did not pay that close attention to the discussion of the Arabic pre-cursors to Fibonacci, and questions about what their real names were. But, I was sort of a math nerd in high school, so I found most of the math in the book to be interesting.

[drneutron_1 · Rating: 4 out of 5 stars]

Back in the 70s and early 80s, computers were these mysterious machines tended by a select few specialists. Then along came engineers who invented a much more efficient way to use computers through keyboards and mice and graphical user interfaces. But until people like Bill Gates and Steve Jobs came along to introduce this better way of computing to the masses, all these great improvements didn't make much difference.So what does this have to do with Leonardo of Pisa, a mathematician also known as Fibonacci who lived at the beginning of the 13th century? Well, at the time, pretty much everybody in Europe used Roman numerals, crude techniques for calculation, and counting tables for business, engineering, navigation, and everyday life. The Arabs used an adaptation of an Indian system using ten numerals and arithmetic essentially that of modern day. It was a much more efficient system, but only those European scholars who knew Arabic or had access to a Latin translation of Arabic works knew anything about it. Leonardo, though, spent time in his youth with his father as representatives of the Pisano business community in north Africa, and while there learned about the Arabic system. He was quite a talented mathematician, and wrote a text codifying and explaining this new system that became a widely regarded work and led to the eventual growth of mathematical education in Europe.A Man of Numbers is a small book, but one packed nicely with the delightful story of Leonardo and his time. Devlin spends time discussing the fascinating ramifications of the adoption of the Arabic system on commerce and education, nearly every aspect of life. He also takes on the question of Leonardo's influence on later writers of arithmetical and algebraic works. Of course, Devlin discusses the Fibonacci sequence as well, the one thing Leonardo is remembered for today, in spite of his wide ranging influence in the 13th and 14th centuries.Highly recommended, even for non-mathematical people. There's a bit of math here, but it's all very well explained!