Growing up, Leonardo Pisano (“Leonardo the Pisan”, circa 1170 – circa 1250) traveled widely around the Mediterranean, allowing him to study language, absorb the tales of the road and, of course, immerse himself in learning mathematics (motivated at least somewhat by his work, helping out in his father’s business), about how other merchants did arithmetic.
Although he would initially focus on learning and translating foreign-language mathematics writing, he eventually became a legitimate mathematician in his own right and he would go on to create some of the most important mathematics works of the time in Europe, describing positional decimal number notation, the concept of zero and basic long form arithmetic operations that could be done without the use of an abacus. He had a big part in introducing and popularizing the Hindu-Arabic numeral system in Europe.
In his book, Liber Abaci (“Book of Calculation”), he covers a whole lot of ground in well over six hundred pages (in this English translation by Laurence Sigler). Though the title seems like it refers to the abacus, this book is specifically concerned with teaching mathematics and doing arithmetic without the help of the ancient counting device.
This book is his masterpiece, his magnum opus. It is one of the most important books of mathematics of its time.
Leonardo Pisano’s father was Guglielmo Bonacci and his mother (who died when he was still a child) was Alessandra Bonacci. Leonardo became later known by the name of Fibonacci, perhaps as an abbreviation of filius Bonacci (son of Bonacci).
Fibonacci is now considered one of the most important mathematicians of the Middle Ages in Europe.
Liber Abaci contains many problems to work out for the reader. In chapter twelve he describes this fictional rabbit problem:
How Many Pairs of Rabbits Are Created by One Pair in One Year.
A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature of them in a single month to bear another pair, and in the second month those born to bear also.
This gave birth to what Fibonacci is now (rightly or wrongly) most famous for: The Fibonacci numbers forming a sequence (the Fibonacci Sequence) such that its first numbers are 0, then 1, then each subsequent number is equal to the sum of the previous two numbers, i.e. 0, 1, 1, 2, 3, 5, 8, 13, and so forth.
A simple description of a mathematical problem (just one of many, a few paragraphs in a substantial, fascinating book) led to a number sequence that is now, more than eight hundred years after its original publication, routinely covered in computer science curricula to let students study recurrence relations, algorithm design, recursion and dynamic programming.
To be sure, the problem is useful and effective for what it is and I do not mean to take away from that. I will probably explore Fibonacci numbers in future posts. There is much to be said there.
It is intriguing, how so little of a discussion in his book would result in so much work, so much attention hundreds of years later. Then again, when looking broader, there is of course even more to Fibonacci and his work, than just those numbers.
Not only has he done so much more for the field and to make mathematics accessible to the people of Europe, but that number sequence? He was not actually the first to describe it! Strange or not, here we are.
You can guess what people will remember about you, why they will know you. Leonardo Pisano would not have imagined this. How could he?
Think of him on Fibonacci day (November 23).