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In 2000, Keith Devlin set out to research the life and legacy of the medieval mathematician Leonardo of Pisa, popularly known as Fibonacci, whose book Liber abbaci has quite literally affected the lives of everyone alive today. Although he is most famous for the Fibonacci numbers--which, it so happens, he didn't invent--Fibonacci's greatest contribution was as an expositor of mathematical ideas at a level ordinary people could understand. In 1202, Liber abbaci--the "Book of Calculation"--introduced modern arithmetic to the Western world. Yet Fibonacci was long forgotten after his death, and it was not until the 1960s that his true achievements were finally recognized. Finding Fibonacci is Devlin's compelling firsthand account of his ten-year quest to tell Fibonacci's story. Devlin, a math expositor himself, kept a diary of the undertaking, which he draws on here to describe the project's highs and lows, its false starts and disappointments, the tragedies and unexpected turns, some hilarious episodes, and the occasional lucky breaks. You will also meet the unique individuals Devlin encountered along the way, people who, each for their own reasons, became fascinated by Fibonacci, from the Yale professor who traced modern finance back to Fibonacci to the Italian historian who made the crucial archival discovery that brought together all the threads of Fibonacci's astonishing story. Fibonacci helped to revive the West as the cradle of science, technology, and commerce, yet he vanished from the pages of history. This is Devlin's search to find him. -- Back cover.… (more)
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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
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.
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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.
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!
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,
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.
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.
Fibonacci is usually
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.
In Pisa at the time, and
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.
I do not
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.
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.
Take for example the biography of Fibonacci. Because he lived
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.