In the matter of your short discussion in your page in the matter of the "invention" or "attribution" of mathematics, "algebra," in this instance, but also geometry and trigonometry, you are absolutely right; the Arabs did not "invent," numerology and numeric computation.
The Greeks indeed, c.380 BC (your date) or thereabouts had certainly thought up and thought out the bases of the mathematics which is taught with greater, but usually lesser, competence in our colleges, universities and "public" schools today.
The name "algebra" is certainly "arab," or "arab-persian," "arab-farsi," etc. But the matter of this form of mathematics was formed and codified in the peninsulas and archipelagos of the Peloponnese and "Hellas," long, long before the first "Arab" appeared on what was then the edge of the known world.
What happened? Why does there exist this gross misconception with regard to the real and racial origins of today's advanced mathematics? Why do so many people, especially, for some reason, public school teachers in the primary grades, attribute to the Arabs the "palm" for "inventing" mathematical computation? The answer to the first question is simple: historical ignorance. As well as a nearly innate desire to attribute to anyone whose skin is not White and whose race is not European the "prize" for inventing so much of what makes our world go round. If this trend continues, by mid-century, the negroes of (what is left) of Detroit shall celebrate Martin Luther King as the "inventor" of the motor car, and not Henry Ford. But, perhaps they do so already.
The answer to the second question may be found in the explication of a "seismic" historical event which occurred in the "Middle East" early in the 5th century, c.620. On this date, the Prophet Mohammed, whose unbalanced "prose," ("Hadith," etc.), was, per the great English historian (and FreeMason) Edward characterized as being "at times lost in the clouds," and " ...at other times crawls in the dust, ..." undertook the "great going forth" from Medina to Mecca, and then, beyond, thereby initiating the phenomenal expansion of the strange new "faith" or heresy of Islam which today may claim more adherents than Christianity.
The "armies" of Islam, actually small bands of fighters, mercenaries, and fanatics, Christian renegades, overran most of what had been, till then, some of the most populous and prosperous provinces of the Eastern and Western Roman Empire. Which by then was very much on the decline. Starting from Mecca in 620 AD ("Anno Hegira"), the Muslims reached Tangier in present day Morocco by c.640 AD. By 699 AD they had taken Roman Carthage. And the entire North African Shore, the home of St. Augustine, "father" of Latin Catholicism, is in the hands of Islam to this day. As well as almost all of what today is termed the "Middle East."
This momentous development "ruptured" the organic unity of the Mediterranean. And the contacts, especially between the more industrious, urban, populous and wealthy Eastern provinces, and the more backward, latently barbarian Western provinces (modern France, Spain, Portugal, England, etc.), were lost. The "seats" of learning in Antiquity, the universities, the schools of philosophy -- and mathematics, were all in the East: Antioch, Ephesus, and, especially, Alexandria, ("al-Iskandrya"); even Carthage had a not inconsiderable reputation for general learning, and especially rhetoric and the law. Now, all were in the hands of a new, aggressive, and militant culture and society. The culture and society of "Arab" Islam.
It was due to this unforeseen "irruption" of Islam that Western Culture and learning lost contact with and access to the major intellectual and academic "artifacts" of it's culture: philosophy, rhetoric, the law, even prose and poetry -- and mathematics.
But, the Arabs did not, "invent" these things; they captured them, they fell, oh so fortuitously into their hands. The Arabs played no role in their development and elaboration. The Arabs, I must repeat did not, "invent" mathematics; it is entirely a product of Western genius.
And, not only did they capture them, they aggressively and violently denied those whose inheritance they were, from access to their intellectual, cultural and "racial" "property." In the 1920s, a French historian, the late Henri Pirenne, articulated a theory per which he argued that the advent of Islam broke the organic unity of the Mediterranean world; and, made of the Mediterranean an "Islamic Lake." The Arabs, by patrolling this "inland sea" in their galleons, (built on a Roman-Byzantine template), -- and worked and crewed by Christian slaves, cut Western Europe off from the economic "entrepôt" of the southern and eastern "Med." As a consequence, in Western Europe, commerce stagnated; and the complex socio-economic structures of Late Antiquity were replaced by a series of rudimentary, austere, impoverished "institutions" we today refer to as the "feudal system." Economic and social atrophy were "complimented" by a similar (and catastrophic) decline in learning. Europe lost her access to her traditional centers of culture and learning (which had survived the "fall" of Rome), but not the Arab conquest. As a consequence, cultivated society, the "life of the mind," and advanced learning, in the arts and sciences, the practical (or "useful" arts), -- and advanced and practical mathematics, died out in Europe.
The Arab practice of privateering and terrorizing their way around the Western and European shores of "their" sea left a Western European of Southern France and Spain, cut off by hundreds of miles from the arithmetical library at Alexandria. Thus, he had precious little opportunity to become even modestly well-versed in mathematics if a troop of pathological mass murderers, swinging crescent shaped scimitars, continually made land fall near his village to carry his family and neighbours off to the slave marts of Algiers or Tunis.
Further from this, we must resist the (erroneous) temptation to "congratulate" the Arabs for "keeping safe" this priceless legacy of Western thought during those long centuries when the Western World was too backward and barbarous to appreciate properly this legacy. In fact, when the Arabs did take Alexandria, apparently with the help of treasonous elements amongst the resident jewish population, the first thing they did with the fabled "library at Alexandria" was to burn it down!! Several centuries later, c.1120 AD, a Western traveller, perhaps Genoese or Veronese, in Alexandria "on business," visited the ruin of the old library and saw there the niches in the walls, where the "priceless" scrolls were kept; the walls were still scorched with the marks of the fire which had burnt these "priceless" scrolls to a crisp.
One must also bear in mind something very important about the Arabs -- the Arabs are not, emphatically not, inventors. They are imitators -- like the Asians in our own day. But they are not inventors, they are not innovators. In fact, the "derivative" nature of every facet of Arab/Muslim "civilization" may be noted in the fact that, of all the vast territory which the Arabs (and their surrogates), "conquered," from the Pillars of Hercules to the West to the sun-baked plains of Central India to the East, the Arabs, across the whole of that vast territory only founded one new city. Of all the cities we currently equate with a preponderant "Muslim" "identity" : Tunis, Algiers, Tangier, Istanbul, Damascus, Baghdad, etc., none are "Arab" cities. Before the advent of Islam these cities, were Roman, Greek, Persian, Indian, but not "Arab."
The same is true of language, education and religion. The Islamic "religion" is simply, at it's essence, an extremely simplified form of Christianity. Mohammed, a trader and a rover by profession, had only ever experienced two streams of religious thought: the myths and terrors of his people's animist beliefs in the Arabian "boot," and the "high religion" of cultivated westerners whom he met in the bazaars of Damascus, Jerusalem and Constantinople. The same is true of language. One might say, truthfully, that there is "no such thing" as "Arabic." Each distinct region of the Arab world speaks it's own version of "Arabic." In North Africa, much of the population speaks Algerian "jihaba," a dialectical "patois," incorporating a mixture of "arabic," with a substrate of Berber and some "lost" Latin and Greek words. Look at a map of North Africa, and the Middle East, note place names which incorporate the word "Ksur," or "Qsur," in the full title. Those places are, or were, before the disaster of 620 AD and after, "Roman" fortresses or fortified cities; "Ksur" is a corruption of the Latin "castro," meaning "camp," (not castle), or "strong place."
And the same is true of mathematics. Mathematics is not an Arab invention. The Arabs took over the centers of learning of the Eastern Mediterranean. Western Europeans were denied access to and exercise of their patrimony. In fact, there are historians who state that the Arabs played almost no role in the preservation of this unique intellectual legacy of Western thought. The Arab economy was then (it still is today to a degree), founded upon chattel slavery. And some historians thoughtfully, and forcefully, declare that it was the thousands of well educated, intelligent Greek slaves and indentured servants in Arab territory captured from the West who were really responsible for preserving and "handing down" the Western heritage of mathematical computation during those dark centuries when the arms of Islam controlled the Mediterranean; and Western Europeans remained "buttoned up" in dark and damp castle keeps, surviving on the threadbare socio-economic "protocols" of the feudal system, waiting for St. Benedict to waken them from their barbaric slumber and send them off on Crusade. Which effort wrested the holy places of Western Christendom from their Arab interlopers, and bore home, amongst the silks and fabrics, Egyptian tangerines and "Damascened" silver, the priceless works of literature, poetry, rhetoric, law, and -- the mathematical sciences. It was only with the advent of the Crusades that our heritage and patrimony, the priceless legacy of Western Man, saw its redemption and was brought home, after a lapse of many centuries to its rightful heirs. Now, written in a foreign language, the original Greek and Latin copies long gone, were consigned to oblivion. These works were probably labouriously copied out by a Greek slave of Antioch or Edessa, in Arabic calligraphic, to assist the instruction of his master's sons. And for the illumination of his own posterity.
The Arabs did not "invent" mathematics or algebra or trigonometry. Anyone who says that they did is a fool and a liar.
Sincerely Yours,
J.L F. 28 May 2001