Khwarizmi

Muhammad ibn Musa Khwarizmi (محمد بن موسى ابو جعفر الخوارزمي‎)

He was a Persian mathematician, astronomer and geographer. He was born around 780, most probably in Khwārizm, in Uzbekistan, which was then part of the native Iranian-Khwarizmian Afrigid dynasty, and died around 850. He worked most of his life as a scholar in the House of Wisdom in Baghdad.

His Algebra, written around 820, was the first book on the systematic solution of linear and quadratic equations. Consequently he is considered by many to be the father of algebra, a title some scholars assign to Diophantus. In the twelfth century, Latin translations of his Arithmetic, which explained Arabic numerals, introduced decimal positional number system to the Western world. He was among the first to use zero as a place holder in positional base notation. The word algorithm derives from his name. He revised and updated Ptolemy's Geography as well as writing several works on astronomy and astrology.

His contributions not only made a great impact on mathematics, but on language as well. The word algebra is derived from al-jabr, one of the two operations used to solve quadratic equations, as described in his book.

Page from a Latin translation, beginning with "Dixit algorizmi"

A page from al-Khwārizmī's Algebra

Corpus Christi College MS 283

Plato (Platon)

Plato (427 BC – 347 BC)

Plato was a Classical Greek philosopher, mathematician, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the foundations of Western philosophy. Plato was originally a student of Socrates, and was as much influenced by his thinking as by what he saw as his teacher's unjust death.

Plato's The Republic, Latin edition cover, 1713

Plato's sophistication as a writer is evident in his Socratic dialogues; thirty-five dialogues and thirteen letters have traditionally been ascribed to him, although modern scholarship doubts the authenticity of at least some of these. Plato's writings have been published in several fashions; this has led to several conventions regarding the naming and referencing of Plato's texts.

Although there is little question that Plato lectured at the Academy that he founded, the pedagogical function of his dialogues, if any, is not known with certainty. The dialogues since Plato's time have been used to teach a range of subjects, mostly including philosophy, logic, rhetoric, mathematics, and other subjects about which he wrote.

Early modern latin incunabulum of Plato's Timaeus, 1491

Education

Apuleius informs us that Speusippus praised Plato's quickness of mind and modesty as a boy, and the "first fruits of his youth infused with hard work and love of study". Plato must have been instructed in grammar, music, and gymnastics by the most distinguished teachers of his time. Dicaearchus went so far as to say that Plato wrestled at the Isthmian games. Plato had also attended courses of philosophy; before meeting Socrates, he first became acquainted with Cratylus (a disciple of Heraclitus, a prominent pre-Socratic Greek philosopher) and the Heraclitean doctrines.

Papirus Oxyrhynchus, with fragment of Plato's Republic

Plato and Socrates

The precise relationship between Plato and Socrates is an area of contention among scholars. Plato makes it clear, especially in his Apology of Socrates, that he was one of Socrates' devoted young followers. In that dialogue, Socrates is presented as mentioning Plato by name as one of those youths close enough to him to have been corrupted, if he were in fact guilty of corrupting the youth, and questioning why their fathers and brothers did not step forward to testify against him if he was indeed guilty of such a crime. Later, Plato is mentioned along with Crito, Critobolus, and Apollodorus as offering to pay a fine of 30 minas on Socrates' behalf, in lieu of the death penalty proposed by Meletus. In the Phaedo, the title character lists those who were in attendance at the prison on Socrates' last day, explaining Plato's absence by saying, "Plato was ill".

The relationship between Plato and Socrates is problematic, however. Aristotle, for example, attributes a different doctrine with respect to the ideas to Plato and Socrates, but Plato never speaks in his own voice in his dialogues. In the Second Letter, it says, "no writing of Plato exists or ever will exist, but those now said to be his are those of a Socrates become beautiful and new"; if the Letter is Plato's, the final qualification seems to call into question the dialogues' historical fidelity. In any case, Xenophon and Aristophanes seem to present a somewhat different portrait of Socrates than Plato paints. Some have called attention to the problem of taking Plato's Socrates to be his mouthpiece, given Socrates' reputation for irony.

Aristotle (384 BC to 322 BC)

Aristotle 

Introduction

Full name Aristotle
Born 384 BC
Place of birth Stageira, Chalcidice
Died 322 BC
Place of Death Euboea
School/tradition Peripatetic school Aristotelianism
Main interests Physics, Metaphysics, Poetry, Theatre, Music, Rhetoric, Politics, Government, Ethics, Biology, Zoology
Notable ideas Golden mean, Reason, Logic, Passion

The Temple of Hephaestus in the central district of Thission.

Aristotle was born in Stargirus in northern Greece. His father was the personal physician of the King of Macedonia. Because his father died when Aristotle was young, Aristotle could not follow the custom of following his father's profession. Aristotle became an orphan at a young age when his mother also died. His guardian who raised him taught him poetry, rhetoric, and Greek. At the age of 17, his guardian sent him to Athens to further his education. Aristotle joined Plato's Academy where for 20 years he attended Plato's lectures, later presenting his own lectures on rhetoric. When Plato died in 347 BCE, Aristotle was not chosen to succeed him because his views differed to much from those of Plato. Instead, Aristotle joined the court of King Hermeas where he remained for three years, and married the niece of the King. When the Persians defeated Hermeas, Aristotle moved to Mytilene and, at the invitation of King Philip of Macedonia, he tutored Alexander, Philip's son, who later became Alexander the Great. Aristotle tutored Alexander for five years and after the death of King Philip, he returned to Athens and set up his own school, called Lyceum.

Aristotle's followers where called the peripatetic, which means "to walk about," because Aristotle often walked around as he discussed philosophical questions. Aristotle taught at the Lyceum for 13 years where he lectured to his advanced students in the morning and gave popular lectures to a broad audience in the evening. When Alexander the Great died in 323 BCE, a backlash against anything related to Alexander led to trumped-up charges of impiety against Aristotle, Aristotle fled to Chalcis to avoid prosecution. He only lived one year in Chalcis, dying of a stomach ailment in 322 BCE.

Aristotle wrote three types of works: those written for popular audience, compilations of scientific facts and systematic treatise, the systematic treatises included work for logic, philosophy, psychology, physics, and natural history. Aristotle's writings were preserved by a student and were hidden in a vault where a wealthy book collector discovered them about 2000 years later. They were taken to Rome, where they were studied by scholars and issued in new editions, preserving them for posterity