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Hank unravels the fascinating yarn of how the world came to use so-called Arabic numerals -- from the scholarship of ancient Hindu mathematicians, to Muslim scientist Al-Khwarizmi, to the merchants of medieval Italy.

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Sources for this episode:
http://www-history.mcs.st-andrews.ac.uk/HistTopics/Arabic_numerals.html

http://www.ms.uky.edu/~carl/ma330/project2/al-khwa21.html

http://books.google.com/books?id=SpyYKC-pNGoC&pg=PA19&lpg=PA19&dq=1299+florence+law+arabic+numerals&source=bl&ots=eWpWq9worw&sig=IK8Rw1GHypvtQ4Cdi7CNu5b5Io8&hl=en&sa=X&ei=K8rxUb_8NMTIrQHYzYHoAg&ved=0CCwQ6AEwAA#v=onepage&q=1299%20florence%20law%20arabic%20numerals&f=false

http://www.wilbourhall.org/index.html#algebra

 Introduction (00:00)


To much of the world he was known by his Latin nickname Algoritmi, which became the origin of the word 'algorithm'. He pioneered a method for solving problems called 'al-jabr', today known as algebra. Twelve hundred years ago he published the first atlas of the known world, wrote the first math textbook, and was calculating the movements of celestial bodies when Europeans were basically staring up this guy through toilet paper tubes. His name was Abu ʿAbdallāh Muhammad ibn Musa al-Khwarizmi, but you can just call him al-Khwarizmi, the man who made possible the math we use today. Oh, also including all the numbers that we use.

[intro music]

 The House of Wisdom and the first atlas (00:39)


Though his most lasting legacy was introducing so-called 'Arabic' numerals to much of the world, he wasn't an Arab. He was most likely Persian. Born in what is now known as Pakistan around 780, al-Khwarizmi first appears in historical records as an instructor at one of the great ancient Islamic learning institutions: Baghdad's House of Wisdom. Sounding kinda like a theme restaurant owned by celebrity nerds, the House of Wisdom was actually a crossroads of the great civilizations of the ancient world: Babylonian, Greek, Hindu, Arabic, Persian, and al-Khwarizmi liked to wet his beak in the knowledge that each had to offer.

He studied the ambitious math of the Greek scientist Ptolemy, for example, who had tried to measure the world. But al-Khwarizmi discovered that Ptolemy's calculations were wrong, so he corrected and reorganized all the data. With new coordinates and the help of some seventy geographers under his direction, he compiled a book called 'The face of the Earth', a complete explanation of the geography and cartography of the known world, thought to be the first of its kind.

He was also the official astronomer of the court in Baghdad, and as part of his duties he compiled charts to track the moon and five planets. These tables turned out to be so useful and accurate that centuries later they would be translated into Latin and Chinese and circulated around the world.

 Algebra (1:50)


But his real passion was for mathematics, and he eagerly accepted a commission from Muslim leaders to come up with a text for the general public about how to do basic calculations, like for conducting trade and making measurements. The result was a text with the inimitable name 'The Compendious Book On Calculation By Completion And Balancing'. In it, al-Khwarizmi explains how to solve linear equations and quadratic equations with what he called 'al-jabr', or 'completion', by subtracting or dividing an amount from both sides to find the missing figure. You know, 'solving for x'. It's not that he invented algebra, though he certainly refined our understanding of it. Instead, he codified knowledge from a whole bunch of different traditions, especially Greek and Indian, to make life easier for the ninth century equivalents of English majors everywhere.

 'Arabic' numerals (2:35)


In this regard, by far his most lasting achievement came from his study of ancient Indian texts. In 825 he published 'On The Calculation With Hindu Numerals', where he described everything he learned about Hindu mathematics. It was a weird system, with digits from 0, which meant, like, nothing, to 9, and it used decimal places to denote increments of tens, hundreds, and so on. The book didn't exactly fly off shelves of the Baghdad Barnes and Noble, but it would turn out to be one of the most influential books in history.

 Introduction to Europe (3:02)


Because three hundred years later a copy of it was discovered by an English monk who, fascinated with Muslim scholarship, translated the research of al-Khwarizmi, now called 'Algoritmi', into Latin. Soon Europe's scholarly elite was eating it up. The Hindu system was way easier and more intuitive than Roman numerals, which used a base ten for counting and a base twelve for fractions and had no concept of 'zero'.

Men of science began advocating for the use of what became known as 'Arabic' numerals. Chief among them, Italian mathematician Fibonacci, who wrote a whole book about them in 1202. But of course medieval Europe wasn't really all about the new ideas with all the burning people on stakes and the inquisitioning. In 1299 the city of Florence, Italy, actually passed a law forbidding the use of the numerals, not because of some anti-Muslim bias, but because Arabic numerals were just too easy to change. You could make a six into an eight, or throw a couple zeros after something and make a big profit with just a flick of the quill. It wasn't until the 1500s that the numbers began to take hold among merchants as well as scholars, but by that time al-Khwarizmi was forgotten to history, which is why we still call the numbers that the whole world uses today 'Arabic' numerals, despite the fact that the guy we have to thank for them wasn't Arab, and the numbers themselves were Hindu.

 Acknowledgements (4:18)


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