Interesting, but slow going. For some reason this book was a bit unsatisfying. Something was lacking in the way it was organized. ( )

"The Man of Numbers: Fibonacci's Arithmetic Revolution" enthusiastically summarizes the little that is known about Leonardo of Pisa, later more famously called Fibonacci. Those who read medieval primary texts have become used to the dearth of direct evidence related to such texts, as well as the admirable, if Herculean, labors medievalists are forced to perform to prove the most basic biographical details. In the case of Leonardo of Pisa, the proof for his role in the "arithmetic revolution" has been fairly well-established, and is nicely summarized here. Well-known for his Fibonacci sequence, his greater contribution may have been the role he played in the transmission of arithmetic and algebra from Moslem North Africa to medieval Italy. Interestingly, this transmission appears to have proceeded along two tracks: First, in a formal, Latin primer on algebra--the famous Liber Abaci (1202)--via the educated elite, and second, through transmission to the Tuscan mercantile community in a format more suitable for the problems that would interest them via a lost primer--Di minor guisa--on commercial arithmetic for the "abbacus schools." Thus, Leonardo of Pisa seems to have played a significant role in both the rebirth of classical arithmetic and science, and the economic revolution that was already beginning to pull much of Italy into its cultural renaissance. ( )

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. ( )

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. ( )

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 older
Roman 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, travels
and motivations for his work. Most interestingly, he describes the tremendous
impact the introduction of Arabic numerals had on Western culture, and the way
ordinary 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 not
disappoint on that score. ( )

As a young man Leonardo of Pisa, aka Fibonacci, went into the family trading business, which required knowledge of arithmetic. Between the ages of 10 and 12 his parents sent him to a religious school to learn to read and write, and to learn the Roman system of arithmetic.

In Pisa at the time, and throughout Europe in the late twelfth century, religious schools were the only schools, and only boys were accepted as students. Wax tablets were used for used for writing, and the reading board, a type of abacus, was used in arithmetic using the Roman system, and its Roman numerals.

Many children today struggle to learn to add, subtract, multiply, divide, and take percentages. Think how much harder basic arithmetic was in Leonardo's time, using the Roman system of arithmetic. Leonardo's great contribution to the advancement of knowledge in the West was the introduction of the algorithms for basic arithmetic using the Hindu-Arabic system, with its ten place-valued digits.

Sometime in the 1180's Leonardo's father took a diplomatic post in the Islamic port of Bugia on North Africa's Barbary Coast. Leonardo followed him there a year later, and during his stay learned the Hindu-Arabic system of arithmetic.

In 1202 Leonardo completed the first edition of Liber Abbacci, a book that literally changed the Western World. No copies of this first edition survive, but three copies of the second edition, completed in 1228, still survive. Our current use of the Hindu-Arabic system for arithmetic in the West can be traced back directly to Liber Abbacci, and the multitude of later books more or less based on it.

The mathematical content of this book, as little as there is, is interesting. But the historical content overwhelms the mathematical, and most of the book is about life in the twelfth and thirteenth centuries. I was looking to find more mathematics, but was not disappointed when I did not find it. Highly recommended for anyone interested in mathematics, or history, and especially for those interested in the history of mathematics. ( )

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. ( )

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. ( )

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. ( )

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. ( )

A note about these newly posted non-link reviews.

This book found its way into my hands via the LibraryThing.com “Early Reviewers” program, having been matched with my on-line library by the LTER “almighty algorithm” in the July batch. Unfortunately, the book did not arrive until early October, sort of missing the “early” in “Early Reviewers” for a book that came out the first week of July! Oh, well, I had plenty of other things to read.

Anyway, I was somewhat surprised to have been matched up with Keith Devlin's The Man of Numbers: Fibonacci's Arithmetic Revolution, not having a lot of mathematical books in my collection, although, I suppose, quite a number of biographical books on figures in science and philosophy. This is very much more a look at the man (and a piecing together of his history), rather than the mathematics, per se, so I guess that makes sense.

Leonardo Pisano, filius Bonacci, was from Pisa (of the famed leaning tower), and from the Bonacci family, an attribute which eventually became condensed to “Fibonacci” over time. It appears that his father was a Customs official there, and had, in this role, much contact with the merchant classes, and the business communications of the day. At one point (around 1180-85 CE), Leonardo's father was posted to a North African city, Bugia (presently in Algeria), and, once established there, he sent for his teenage son to join him.

One of the points the author makes early on is how numbers and counting are so intrinsically intertwined with our modern existence that it hard to imagine a world where dealing with numbers was something of a specialty, the tools of certain trades. In the world that Leonardo Pisano grew up in, every major trade center was likely to have its own sets of weights, measures, and currency, and the calculations were done with either complex finger computations (leading to the term “digit” surviving as a number notation) or worked out on a abacus … neither of which lent themselves to preserving the details of the math. Also, in the European world, any written numbers were expressed in Roman numerals, which, due to their structure, were not very useful for anything other than addition and subtraction.

In Bugia, young Leonardo was exposed to the Islamic system of numbers, which had absorbed influences from India, including the concept of the place-keeping “0”, and the three-place separations that we still use today (ie. 1,000,000). While this was not unknown in Europe (having come across with the Islamic invaders into Spain, etc. some centuries before), Leonardo saw the utility of this in the context of trade.

Frankly, he almost was forgotten to history, but his name survived in later math books that referred back to his publications. A great deal of The Man of Numbers is tracking down the historical threads which lead back to Fibonacci and what survives of his books, and looking at the nature of these books from what remains. His main product, Liber Abbaci or “Book of Calculation” was a book of how to do calculations, and examples of these, and problems to be solved, a familiar format for math books ever since. However, the problems in his book were all “word problems”, as modern “symbolic” notation hadn't been developed, so what we'd write as x²=40x-4x² would be a whole paragraph of descriptive text.

The book tries to piece together the fragmented bits of Leonardo's biography and work, and fit these into the cultural milieu of his time, and the years following. It is fascinating that a figure like Leonardo, who is so well known for the mathematical entities that have come down from “Fibonacci”, has been so little known in terms of his biography and bibliography. This reads something like a mystery, trying to prise this information out of surviving material (much of which sits untranslated in late medieval sources in various Italian cities) to get a clear look of the man and his work.

Obviously, this being out only a few months, The Man of Numbers should be available in the more comprehensive brick-and-mortar book vendors. Of course, the on-line guys have it, with both of the big boys currently offering it at a 43% discount (with used copies coming in at right about the same price point so far). This was certainly an fascinating read, and anyone interested in math, the medieval world, or a story about researching obscure topics, should find this quite enjoyable.

A link to my "real" review:
BTRIPP's review of Keith Devlin's "The Man of Numbers: Fibonacci's Arithmetic Revolution" (737 words)

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. ( )

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. ( )

How do you write a book on a man about whom almost nothing is known? Leonardo Pisano (Fibonacci) is such a man. Keith Devlin's answer is to write about the effect that this man's masterpiece Liber Abaci had on the history of Europe. Unable to see the man directly, we can gain some notion of his importance by the way that his work changed Italy, Europe and the world.

An Italian mathematician of the late 12th and early 13th centuries, Leonardo of Pisa (hence Pisano) was an early pioneer in the education of Europeans in the Hindu-Arabic number system and its uses in arithmetic and algebraic calculations. Leonardo did not bring our modern number system to Europe. It was already known. He does not appear to have added appreciably to the body of knowledge concerning mathematics. Most of the techniques and problems illustrated in his works were due to earlier Arabic scholars. What makes Leonardo an important man is his practical educational work among the merchants of Italy. He trained a generation (or more) of Italian business men and educators , writing books which served to spread efficient computation beyond the borders of Italy and into northern Europe.

'The Man of Numbers' outlines the transformation of Italian business due to Fibonacci's efforts. He illustrates the practical importance of the work with examples of problems and their solutions from Liber Abaci, an effort which will make you thankful for the centuries of pedagogical progress made since Leonardo's time. Unfortunately, I felt that the book left me with more questions than answers. Devlin's book is not meant to be a history of commerce and the influences of mathematics on business, but one is left with the feeling that this is where the real story lies. Having been shown a glimpse of this history, I found myself wanting more.

Throughout the book, I kept remembering the old James Burke documentary series, Connections. I kept wanting Devlin to make that connection on to something beyond his limited subject. I can't really fault him for this, as that was not his goal. However, I think that this could be a great starting point for someone more ambitious. Someone who would take us from the earliest records of counting and business record keeping of, let's say, the Egyptians or Sumerians up to the stock market collapse of 2008. ( )

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. ( )

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. ( )

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! ( )

Nora's book, July 2014