When the Roman Empire collapsed in 476 C.E., Germanic tribes took over the Western portion of Roman Empire. (The eastern portion, headquartered in Constantinople persisted until 1453). Despite being “barbarians” the Germanic peoples absorbed at least some respect for Roman civilization and a desire to maintain it. However, despite their best intentions, they still had a poor understanding of the Roman heritage they had taken over. Their loosely knit states had local nobles ruling their lands and sometimes following their kings in war. The few trained Roman bureaucrats that were left became scarcer with each generation. Bit by bit, orderly Roman rule gave way to a more casual kind of order, veering more and more toward anarchy. Taxes went uncollected; roads, bridges, and aqueducts went unrepaired; and public order broke down, sending towns and trade into decline.
Unlike the Romans, the “barbarians” had no concept of an abstract state to inspire their loyalty. Instead they based their political order on their loyalty to a local chieftain or king. Since the kingdom was the personal property of the king, it was divided amongst his heirs upon his death. Western Europe disintegrated into anarchy as local nobles rebelled against their kings and fought each other in their own private wars. This in turn would encourage raids and invasions by such peoples as Vikings from the north, Arabs from the south, and nomadic Magyars from the east. Such raids and invasions would only encourage more turmoil, which would bring in more invasions and so on. To aggravate matters even further, this cycle of anarchy and invasions would also feed back into the original cycle involving land as a source of wealth. And so it would go, as these mutually reinforcing cycles of decline, anarchy, and invasions would continue to feed into one another, dragging Western Europe down into further chaos. Not until money came back into circulation could the nobles’ stranglehold be broken. This was because money did not regenerate itself, thus keeping nobles and officials constantly dependent on the king.
While European civilization descended into backward rural feudalism, the territory governed by Muslims entered what many historians call “The Islamic Golden Age” which lasted from roughly 800 A.D. through 1200 A.D. It was there that the savant Al-Khwārizmī (from whose name we get the word “algorithm”) essentially invented applied mathematics. It was there that astronomer al-Biruni began to invent modern experimental physics and anticipated the work of Copernicus and Kepler. It was there that Ibn Sina (Avicenna) wrote the most important books of medicine up to that time, and kept alive the tradition of ancient Greek philosophy — which would later have a huge influence on Europe. The region was a hotbed of technological innovation and intellectual boundary-breaking.
Then it all went wrong. After about the year 1200, the region declined, and Islamic science and medicine and philosophy declined with it. Why did this happen? The conquests of the Mongol Empire, which destroyed many of the region’s huge, well-irrigated cities, were part of it. The decline had begun centuries before the Mongols showed up, which was an increasingly anti-science attitude on the part of the Muslim rulers of the region.
One of the most prominent anti-science leaders was Nizam al-Mulk, the unofficial leader of the Turkish Seljuq Empire. In the late 1000s A.D., he established a number of religious institutes, part of whose purpose to combat the rationalism that had emerged in Central Asia. Perhaps the most important figure in this anti-rationalist movement was al-Ghazali, an accomplished philosopher who had written a book attacking his contemporaries. Al-Ghazali used the tools of logic and reason themselves to argue that only faith, not rationalism and science, can offer insight into the truths of the world. Al-Ghazali led the charge for Islamic world’s transition from center of global science to fundamentalist backwater.
Considering how unsuited Roman numerals are for mathematical calculation, it is puzzling how long the decimal place-value system took to be widely used In Europe. Mathematics in Europe entered a Dark Age. Consider something as basic as zero. From the time it was invented as a mere placeholder, the way to tell 1 from 10 and 100, between 500 and 400 B.C. in Babylon. In India they developed a positional number system (according to the Bakhshali manuscript) as early as the 1st century CE. as part of a place value system with zero denoted by a dot, which is called shunya-sthAna, “empty-place”, and the same symbol is also used in algebraic expressions for the unknown (as in the canonical x in modern algebra). The oldest known text to use zero is the Jain text from India entitled the Lokavibhaga, dated 458 AD. For mathematics to advance in Europe, centuries had to pass for the zero innovation to pass from Babylon, then India, followed by Al-Khwārizmī, entering Spain around 900 C.E., and appearing in the Codex Vigilanus in 976 C.E.
- 976. The first Arabic numerals in Europe appeared in the Codex Vigilanus in the year 976.
- 1202. Fibonacci, an Italian mathematician who had studied in Béjaïa (Bougie), Algeria, promoted the Arabic numeral system in Europewith his book Liber Abaci, which was published in 1202.
- 1482. The system did not come into wide use in Europe, however, until the invention of printing. (See, for example, the 1482 Ptolemaeus map of the world printed by Lienhart Holle in Ulm, and other examples in the Gutenberg Museum in Mainz, Germany.)
- 1549. These are correct format and sequence of the “modern numbers” in titlepage of the Libro Intitulado Arithmetica Practica by Juan de Yciar, the Basque calligrapher and mathematician, Zaragoza 1549.
Al-Khwārizmī, in full Muḥammad ibn Mūsā al-Khwārizmī (born, c. 780, Baghdad, Iraq—died c. 850), Muslim mathematician and astronomer whose major works introduced Hindu-Arabic numerals and the concepts of algebra into European mathematics. Latinized versions of his name and of his most famous book title live on in the terms algorithm and algebra.