Mr. Stephenson's Compilation of Math History

Ancient Babylon & Egypt (~3500 BC - 2000 BC)

Geometry comes from greek words meaning to measure land. Its basic principles were developed in Babylonia and Egypt to measure farmers' lands after the annual river floods for accurate taxation. It also served well in other pursuits, like building pyramids.

Pythagoras (569 BC - 475 BC)

He probably was the first to prove the "Pythagorean Theorem", but the principle was known 1000 years earlier in Babylonia. His cult-like school discovered irrational numbers like the square root of 2, but they tried to keep the knowledge secret because it didn't fit with their philosophy/religion about numbers.

Theaetetus (417 BC - 369 BC) - [see Euclid below]

Eudoxus (408 BC - 355 BC) - [see Euclid below]

Plato (427 BC - 347 BC)

In Athens about 387 BC Plato founded, on land which had belonged to Academos, a school of learning which, being situated in the grove of Academos, was called the Academy (hence our english word). Over the door of the Academy was written (in ancient greek, but translated here):

Let no one unversed in geometry enter here.

Euclid of Alexandria (325 BC - 265 BC)

Euclid wrote The Elements, a compilation of knowledge that was the primary source for the teaching and learning of mathematics for 2000 years.

The 13 books of The Elements contain:

Books 1-6: plane geometry (based on works of Pythagoras and Eudoxus);

Books 7-9: number theory (incl. greatest common divisors and geometrical progressions);

Book 10: theory of irrational numbers (mainly works of Theaetetus and Eudoxus); and

Books 11-13: three-dimensional geometry (mainly works of Theaetetus and Eudoxus).

Plane geometry is also known as Euclidian geometry.

Al-Khwarizmi of Baghdad (780 AD - 850 AD)

"Al-Khwarizmi and his colleagues the Banu Musa were scholars at the House of Wisdom in Baghdad. Their tasks there involved the translation of Greek scientific manuscripts and they also studied, and wrote on, algebra, geometry and astronomy. Certainly al-Khwarizmi worked under the patronage of Al-Mamun and he dedicated two of his texts to the Caliph. These were his treatise on algebra and his treatise on astronomy. The algebra treatise Hisab al-jabr w'al-muqabala was the most famous and important of all of al-Khwarizmi's works. It is the title of this text that gives us the word "algebra" and, in a sense ..., it is the first book to be written on algebra.

Rosen's translation of al-Khwarizmi's own words describing the purpose of the book tells us that al-Khwarizmi intended to
teach:

... what is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, partition, lawsuits, and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computations, and other objects of various sorts and kinds are concerned.

Now this does not sound like the contents of an algebra text and indeed only the first part of the book is a discussion of what we would today recognise as algebra. However it is important to realise that the book was intended to be highly practical and that algebra was introduced to solve real life problems that were part of everyday life in the Islam empire at that time."