# Finding Fibonacci

The name of Fibonacci is connected with the Fibonacci sequence, which hooks up with rabbits and the golden ratio. Most of this knowledge is only partially correct. The man was born around 1175 in Pisa, and died somewhere around the middle of the 13th century. His name was Leonardo of Pisa (Leonardo Pisano), and Fibonacci is a nickname invented by historian Guillaume Libri in 1838 because Fibonacci in his most famous work *Liber abbaci* (1202) he announced himself as *filius Bonaci* although his father's name was Guilielmo Bonacci. So instead of "son" he may have meant to say "of the Bonacci family". The rabbit story is only one of the hundreds of examples he uses to illustrate the strength of calculating with the Hindu-Arabic number system as we know it today worldwide. This *Liber abbaci*, written in Latin, is a true work of mathematics following the Euclidean approach of logic derivation. It also explains many techniques to solve problems like the rule of three, the rule of false position, and so many algebraic recipes we are quite familiar with today. And, most importantly, it contains also many illustrative examples and whole chapters with practical applications from commerce and finance. The rabbit example is only one of them. It was known for centuries by Indians in connection with Sanskrit poetry long before Fibonacci. The name Fibonacci sequence was coined by Édouard Lucas in the 19th century. And Fibonacci never connected the sequence with the golden section φ. Luca Pacioli in 1509 called φ the divine ratio and the news was spread that this number appearing in nature so often should represent perfection and beauty. Devlin debunks also this myth.

What Devlin admires most in Fibonacci is that he is the initiator and the instigator of spreading the revolutionary system of Hindu-Arabic numerals, after which the world could never be the same. The *Liber abbaci* is a marvelous piece of didactics, but it is written in Latin, not the language used by bankers and merchants. There is no original copy of the book left, only later transcripts. There are however hundreds of shorter versions written in local Italian dialects, and these are the ones that were used to actually spread the new numeral system and the algebraic methods. Fibonacci referred at several places to a shorter version of his book, his *Liber minoris guise* or *Libro di merchaanti* which probably is the primal source of all these vernacular *libri abbaco*. It had however never been found until in 2003 Rafaella Franci identified a manuscript in a Florence library that directly referred to Fibonacci. This is the missing link between Fibonacci's *Liber abbaci* and popularization of the method via the *libri abbaco* and it identifies Fibonacci as the man who was also behind the mechanism for spreading the method. This popularization of mathematics is also dear to the heart of Devlin who wrote several books with that intention. He is also an intensive blogger and columnist, gives expository public lectures, and appears often in the media. This is what Fibonacci probably would have done if he had lived today.

The main point that Devlin wants to make is that Fibonacci should be glorified not for modeling the reproduction capacity of rabbits but for his insight in the possibilities offered by this new numeral system and the ingenious way in which he helped to spread it in the Western world. In 2011 Keith Devlin published a book on Fibonacci: *The Man of Numbers. Fibonacci's Arithmetic Revolution* (Walker Publishing Company) which is intended to be a biography of the man, but since so little is actually known, it also is an extensive discussion of his *Liber abbaci* and the man's legacy and influence. Devlin uses abbaci with double 'b' as Fibonacci did, although a single 'b' is more common as Sigler did in his English translation of the *Liber abbaci* in 2002.

The present book *Finding Fibonacci* describes Devlin's quest to collect the sources and information needed to write Fibonacci's biography. The title that may be inspired by Aczel's *Finding zero*, an account about his quest for the first appearance of 0 to represent zero in a number. In the present book Devlin summarizes what is already in *The Man of Numbers*. It is a "the-making-of" version with a lot of background information and told as a first-person narrative. If he is more objective in *The Man of Numbers*, he lets his admiration for the man who caused this revolution in the Western world run more freely in this book.

In fact gathering all the information went with a lot of lucky coincidences and unfortunate setbacks. Sometimes the situations are really funny when English-Italian communication was not optimal or when he had to deal with the Mediterranean laid-back attitude. But we also learn of his emotions when he is finally paging through these very old manuscripts. The buildings in which the manuscripts are kept, the people that he interviewed, his search for the statue of Fibonacci, his pictures of street signs referring to Fibonacci, and much more are described. You might as well be interested in seeing some pictures available on the website of the MAA related to his visits of the cities and the libraries and copies of some pages in the old manuscripts.

It is also an amazing story how Sigler's English translation of the *Liber abaci* finally appeared in 2002 just 800 years after Fibonacci finished the original. In fact the translation was finished in 1997 with only some editorial details left when Laurence Sigler died of cancer. His wife Judith decided to handle the last details, but then the project was abandoned from the publisher's side. The computer of Sigler had to be hacked to recover most of the text, but the typesetting was lost. Springer then got interested in publishing the book but it required to do the typesetting all over in LaTeX. It took Judith about five years to finalize the work.

There are also a few chapters referring to what happened after the publication of *The Man of Numbers*. For example his consultation of the manuscript in Florence that was discovered by Rafaella Franci and identified as "the missing link". He also includes a short chapter in which he draws a parallel between the arithmetic revolution caused by Fibonacci and the computer revolution initiated by Steve Jobs. He has some vimeo links about that: Leo & Steve (part 1) and Leo & Steve (part 2). And finally, he learned from William Goetzmann that much of the mathematical analysis that governs the international financial markets has its origin in the *Liber abbaci*. In particular the computation of the present-value, which means that with this method one may compare the relative economic value of differing payment streams, taking into account the changing value of money over time. The present value of a euro is less than its future value because of its investment and interest potential.

All in all a book to be recommended. If you already read *The Man of Numbers* it is most informative to read this "behind the scenes" version and know how it came about (and what happened after its publication). If you didn't know *The Man of Numbers*, you at least get a summary of what is in there too. Only it is told in a much more personal and lively version. It is working to some kind of climax with the consultation of the "missing link" book in Florence. Nevertheless, it made me go back and read *The Man of Numbers* too, which has much more information about the contents of the *Liber abbaci*, and that made me look up Sigler's translation in the library. It illustrates well how Devlin can motivate his readers.

**Note:** After I finished this review, I learned from Davide Castelvecchi's blog Fibonacci’s real mathematical legacy that there is some doubt about the "missing link" indeed being the missing link.

**Submitted by Adhemar Bultheel |

**10 / Apr / 2017