Independently from Saint Augustine, Saint Ambrosius (340–397), Archbishop of Milan, authored the Hexahemeron. Hexahemeron was first presented in Lenten lectures by Saint Basil (329–330 to 379), the bishop of Caesarea Mazaca in Cappadocia (modern-day Turkey). Saint Ambrosius was exchanging letters with Basil and must have been influenced by Basil, and he was notable for his influence on Augustine of Hippo. The hexahemeron must have been an issue in the beginning of the 5th century.
There was no place to talk about Epicureanism after 429. And, Epicureanism was forgotten together with the Lucretius poem De Rerum Natura.
Scientifically, the Latin numerals are not helpful in developing science by estimating the magnitude of some number. In a sense, the Dark Ages helped in importing the so-called Arabic numerals into Europe in the Islamic era, which began in 622 when Islamic armies started to conquer Arabia, Egypt, and Mesopotamia. In a century, Islam had reached the area of present-day Portugal in the west and Central Asia in the east. The spread of Islam across Western Asia and North Africa encouraged an unprecedented growth in trade and travel by land and sea as far away as Southeast Asia and China. Its Golden Age was roughly between 786 and 1258 (the year Baghdad fell to the Mongols) with stable political structures and flourishing trade. In this Golden age, of course astronomy was useful for determining the Qibla, the direction that should be faced towards Mecca in which to pray. Arabian merchants traded merchandise all over the world to India, to Indonesia, and even to the Far East. During this period, Catholic Europeans got the Oriental spices and also the Indian numerals through Arabian merchants.
Richard Bulliet, Pamela Crossley, Daniel Headrick, Steven Hirsch, and Lyman Johnson state, “Indian mathematicians invented the concept of zero and developed the ‘Arabic’ numerals and system of place-value notation used in most parts of the world today”.6 The development to the currently used numerals was gradual, and the Arabian merchants used it for trading during the third Islamic caliphate, the Abbasid Caliphate (Capital Bagdad, 750–1258), and most Europeans must have thus learned the Arabic numerals.
According to the ancient Indian mathematical text found in 1881 in the village of Bakhshali, Mardan (near Peshawar in present-day Pakistan), the Indian numerals was used around 385 and 465, the estimate given by the carbon dating of Maan Singh.7 The Bakhshali manuscript, Fig. 1(a), contains the “placing symbol” (a bullet) in the second line from the bottom. In Fig. 1(b), the “placing symbol” is written as 0. Here, two aspects are of concern in mathematics. First of all the beautiful Arabic numeral itself is not important. The important thing is that it is just one connected letter. As shown in Fig. 1(b), some original Indian numeral forms survive until now but the important aspect of it is just one unit. It is not so in Chinese and in Latin. The second is the placing mark, the bullet in Fig. 1. The placing mark is very useful in the present-day decimal system. It is also useful in binary numbering or in any other numbering system. If we used the duodecimal numbering system, we must have used two more one-unit characters for 10 and 11. The placing can still be the bullet. Today, the decimal-system numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 are used more often than the Roman alphabets. The book On the Calculation with Hindu Numerals by al-Khwarizmi (c. 780–850) written about 820 and the book On the Use of the Indian Numerals by al-Kindi (801–873) were principally responsible for spreading the Hindu–Arabic numeral system throughout the Middle East and Europe.
Figure 1: The Bakhshali manuscript marked on birch bark (a), and the Indian numerals (b).
In particular, al-Kindi was an Arab Muslim philosopher, deeply affected by the Greek Neoplatonist, and one of his lifelong efforts was to make the Greek thought acceptable to a Muslim audience, which was carried out at the House of Wisdom in Baghdad, an institute of translation and learning patronised by the Abbasid Caliphs. Like Simplicius, he was a prodigious writer, writing at least 260 books on geometry (32 books), medicine and philosophy (22 books each), logic (nine books), and physics (12 books).
While Christians in Europe were blocked from the knowledge of the ancient Greeks, al-Kindi spread the Greek view of the solar system from Ptolemy, who placed the Earth at the centre of a series of concentric spheres, in which the known heavenly bodies (the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and the stars) are embedded, which would be changed by Copernicus after the Dark Ages of the Europe. Al-Kindi must have been influenced by Saint Augustine (354–430) in attempting to demonstrate the compatibility between philosophy and natural theology, and had successfully incorporated Aristotelian and (especially) Neoplatonist thought into an Islamic philosophical framework as the first philosopher writing in the Arabic language. Most medieval Islamic mathematicians wrote in Arabic with some others writing in Persian.
In al-Kindi’s view, the knowledge of God is the goal of meta-physics, but later the most influential Islamic philosopher al-Farabi (c. 872 to 950–951) strongly disagreed with him on this issue, saying that metaphysics is actually concerned with the first principle, and as such, the nature of God is purely incidental. A first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. In philosophy, first principles are from First Cause attitudes taught by Aristotelians. In mathematics, first principles are referred to as axioms or postulates. In physics, theoretical work is said to be from first principles or ab initio, if it does not make assumptions such as an empirical model and a parameter fitting. In the West, several centuries after al-Farabi, René Descartes (1596–1650) described the concept of a first principle in the preface to the “Principles of Philosophy: Now these principles must possess two conditions: in the first place, they must be so clear and evident that the human mind, when it attentively considers them, cannot doubt of their truth; in the second place, the knowledge of other things must be so dependent on them as that though the principles themselves may indeed be known apart from what depends on them, the latter cannot nevertheless be known apart from the former.” Central to al-Kindi’s understanding of metaphysics is God’s absolute oneness, which he considered an attribute uniquely associated with God. In addition to absolute oneness, al-Kindi also described God as the Creator or an active agent. Of God as the agent, all other intermediary agencies are contingent upon Him. The key idea here is that God ‘acts’ through created intermediaries, which in turn ‘act’ on one another — through a chain of cause and effect — to produce the desired result. In reality, these intermediary agents do not ‘act’ at all; they are merely a conduit for God’s own action.
In contrast to al-Kindi, who considered the subject of meta-physics to be God, al-Farabi believed that it is related to God only to the extent that God is a principle of absolute being. Al-Kindi’s view was, however, a common misconception regarding Greek philosophy among Muslim intellectuals at his time in Baghdad, and it was for this reason that Avicenna (c. 980–1037) remarked that he did not understand Aristotle’s metaphysics properly until he had read a prolegomenon written by al-Farabi. Neoplatonism was started in the Platonic tradition by Plotinus (c.