Fibonacci's Rabbits

Excellent easy read of quite complex mathematical ideas

I have previously read and enjoyed Pavlov's Dog by Adam Hart-Davis, but as a self-confessed numbers geek, Fibonacci's Rabbits is right up my street. Usually with books about complex subjects, in this instance mathematics, I would take my time reading it over several weeks but I ended up reading Fibonacci's Rabbits cover to cover in the space of a week. Adam Hart-Davis has a real knack of explaining complex subjects in bite-sized chunks that make it easy for the lay person to understand. With interesting snippets throughout and Monty Pythonesque illustrations, he easily captured and held my attention from start to finish. I even exclaimed a few times when I had my own Eureka moments; discovering things I didn't know and will now never forget. As much as I learned things, it also got me thinking and questioning. For example, there's a section about why there are 60 seconds in a minute and how this is linked to your hands. I wondered if this is why pointers of a clock are called hands. It probably isn't, but I like the idea of this link back to its origin and thinking of it this way means I will never forget this particular fascinating fact. The book is written chronologically over 7 chapters which shows how mathematics has developed over the years from scratches on bones to complex computer code. Each chapter is broken down into between 6 and 9 individual discoveries of around 3 pages long; just enough to scratch the surface of a discovery and explain its origin without getting too bogged down in technicalities. Written in a way that makes mathematics easy to understand for non-mathematicians, Fibonacci's Rabbits is an engrossing and fascinating book. I really wish Adam Hart-Davis had been my maths teacher!

“If I have seen further, it is by standing on the shoulders of giants” Fibonacci’s Rabbits, by Adam Hart-Davis, explains in accessible language fifty significant mathematical discoveries, from ancient times through to the present day. It is divided into seven ages and demonstrates how each featured mathematician built their propositions and then proofs informed by all who had gone before. To enjoy the book fully it may be necessary to have some interest in, if not understanding of, mathematical concepts and principles. “In mathematics, proof is everything, whereas science cannot prove anything. Scientists can disprove ideas, but they can never prove them.” The first section outlines the long history and need for simple tallying and recording. Standardised numerals evolved from primitive marks made when counting. The reasons for and timing of the initial move from such practical applications to more complex and abstract ideas has been lost to time but ancient civilisations throughout the world are known to have used various number systems and calculations to: produce calendars, build pyramids, and study intriguing problems such as squaring the circle. Some of the questions these early mathematicians asked have still to be answered. Others led to proofs that proved useful in practical applications far in their future. “it is easy to get trapped by habitual ways of thinking, and different approaches can lead to new insights” Mathematics is required to be logical and rigorous. Although many of its problems appear theoretical, discoveries are often mirrored in the real world. Key patterns, sequences and shapes turn up in: plants, animals, and their natural habitats. The intrigue of the Fibonacci sequence and associated spiral enabled many new mathematical discoveries yet it is clear that Fibonacci numbers are a reflection of the way things grow – including the reproduction of rabbits. I particularly enjoyed the chapter on zero and the mathematical problem of defining concepts. Having accepted the usefulness of ‘nothing’ whole new fields opened up. Looking at the importance of imaginary numbers it is clear that sometimes all that is needed is a new way of simply notating a complex idea. “In Euclid’s system, the workings of the world are not just the whims of the gods, but follow natural rules. It showed how we can find our way to the truth through logic and deductive reasoning, evidence and proof – not just intuition.” Mathematical problems are only regarded as solved when a verified proof is discovered and written down. “If even a single exception is found, the conjecture fails” “for mathematicians, ‘highly likely’ is not proof” Being unable to find an exception does not constitute a proof, however long the search has taken. There are problems that have finally been solved after hundreds of years, and others that remain outstanding. Chaos theory and how it developed intrigued me – how one tiny event creates ripples that can radically change outcomes. “A very small cause, which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance.” “Really, he argues, the weather is equally as rigidly determined as the eclipse. It is just that the operation of chance with the weather is so major that we just do not have enough knowledge to predict it. Such systems seem to be chaotic, but the normal laws of the universe are still operating entirely regularly.” Today’s intellectually challenging, high level mathematics may have no apparent practical value. And yet, as has been shown time and again over the centuries, it may offer real world insights as future applications are developed. Mathematics is logical but logic can be mind bending. “This statement is false” So many of the chapters were fascinating to read, even those whose concepts I couldn’t fully comprehend. It was fun trying to work out why certain, apparently random objects are included in the many colourful illustrations that accompany the text. This was just one entertaining puzzle in a book that provides insights into works of genius that have laid the foundations of so many discoveries and inventions. Mathematics is an ever evolving discipline and it is exciting to know there is still so much remaining to learn. The congenial structure and explanations provided in this book allow the reader to appreciate how important mathematics is to a wider understanding of our world and the developments we now rely on. Readers will value the tenacity of mathematicians through the ages when they realise the impact their work has had.

I'm not a great fan of '50 things' type books, though they seem eternally popular, but as was the case with Adam Hart-Davis's psychology title in the same series (Pavlov's Dog), I was pleasantly surprised, in part because the topic was well-suited to the format, and in part because the Hart-Davis has three pages of text to play with rather than just an illustrated spread. After giving us some foundational and historical aspects of mathematics, from the origins of base 10 and base 60 to pi and zero, Hart Davis gets onto more meaty material, ranging through everything from chaos theory to game theory, plus some lighter weight but enjoyable mathematical deviations such as the Fibonacci sequence rabbits in the book's title, or the strange 3D shapes known as scutoids. It's all easy reading - no mathematical experience required - and a good way to get a feel for the way that maths is so much more than arithmetic, geometry and algebra. One minor irritation is the way that every item is titled as a question, some of which aren't actually answered in the text. So, for example, we get 'How big is infinity?', which gives us a quick tour of ancient Greeks, Galileo and Cantor, but (perhaps thankfully) doesn't actually attempt to address the question. This entry also demonstrated why this format has its limits on a big topic (no pun intended) like infinity. Hart-Davis mentions, for example, Hilbert's Hotel - but doesn't take the reader through what's involved, so we just get a vague statement that Hilbert used a series of ingenious proofs to show that despite the infinite set of rooms being full, an infinite set of extra guests can be accommodated. There's no point saying this unless it's opened up in a bit more detail. Despite a few issues with generalisation like this, though, it's a readable and enjoyable exploration for the key aspects of mathematics, plus some of the fun bits.

Excellent book but fell down on ARE TAXICAB NUMBERS DULL. Read and re-read the section over and over. The maths didn't add up. 1729 = 13 + 123 = 93 + 103. I'd read about the significance of the number 1729 but this didn't make sense. Then l realised it should have read 1^3 + 12^3 and 9^3 + 10^3. Publishers website no longer exists. Spoils what otherwise is an excellent book!

If you have little to no understanding of math then this is a good book for you as it goes over many complex concepts without using any equations and focusing mainly on the history of maths and the people who made the discoveries. However if you want more details then look elsewhere. There is even a blatantly wrong graph on page 82. The exponential graph does not give you 2.7 at x=1 after talking for so long about that number!

REALLY GOOD BOOK

This is a lovely book, a real history of maths and why it’s important to us as human beings. As a teacher of maths I come across so many pupils who are very reluctant to engage as they don’t see the point. It’s great therefore to have interesting stories that appeal to the less logical. It’s a book that doesn’t need reading from start to finish, you can dip in and out of it finding the subjects that interest you the most. I have read various chapters as bedtime stories with my son, who gets to chose the chapter. The only problem being it often creates more questions than it answers and sends us down an investigative rabbit hole at bedtime! The book isn’t a “how to” manual, it won’t help improve your maths but will help enthuse the reader. Nicely written; it’s an easy read without dumbing down. Overall I’d highly recommend for older children, teenagers and adults. Thank you to the publishers, who provided me with a copy in return for a fair and honest review.