HM 23
REVIEWS 89
ring of the integers and its quotient field. . . . I find it equally amazing that all the ingredients of that just now so topical subject of computer algebra are already in the Liber abbaci. Not only do algorithms and their verification appear there but there are at least two topics which may be interpreted as part of complexity theory.... Computation has always been a dynamical subject and so it will always be.
Lu Β¨neburg is fascinated by Leonardo's work, and he succeeds in transmitting this fascination to the reader. He does not like the usual reduction of Fibonacci's importance to the famous rabbit problem; this is equivalent, he says on p. 198, to the stereotyped reduction of Beethoven to the 'da-da-da-daa' of his Fifth Symphony. The author opens up to historians an idea of other ways to investigate and explore such mathematical texts.
The book contains a list of all surviving codices of the Liber abbaci and four coloured tables of selected pages from two of the codices, strikingly illustrating the visual beauty of the old manuscripts. At the end of the book there are some remarkable critical thoughts about the contemporary state of professional mathematics and professional history of mathematics. One example must suffice. In reading a mathematical text, one generally needs no further sources to know whether the proof is true or not. For an historical text, the determination of its truth requires the study of a chain of further sources, a chain that sometimes has no end.