Pythagoras of Samos: (A Brief History)
(569 BC – 475 BC)

It is often said that Pythagoras of Samos was the first “pure” mathematician. Since there exists nothing on Pythagoras’s writings, little is known about his mathematical achievements. However, we know that he contributed greatly to the development of mathematics.

When Pythagoras was in his late teenage years, he visited Thales of Miletus, who by this time was very old. Thales made a strong impression on Pythagoras and contributed to Pythagoras’s interest in mathematics. Thales had a pupil, Anaximander, who also influenced Pythagoras. Pythagoras would attend Anaximander’s lectures.

In southern Italy, Pythagoras was the founder of a philosophical and religious school, where he and his followers were known as mathematikoi. Pythagoras personally taught these people and obeyed strict rules:

(1) that at its deepest level, reality is mathematical in nature,
(2) that philosophy can be used for spiritual purification,
(3) that the soul can rise to union with the divine,
(4) that certain symbols have a mystical significance, and
(5) that all brothers of the order should observe strict loyalty and secrecy.

It is interesting to note that both men and women were allowed in the society.

This group was not interesting in formulating or solving mathematical problems. They were interested in the principles of mathematics, the concept of number, the concept of mathematical figures (such as the triangle), and the idea of proof. Pythagoras studied properties that we know today as even and odd numbers, triangular numbers, and perfect numbers.

Although the famous theorem that we often attribute to Pythagoras was known to the Babylonians before him, he was probably the first to prove it. The Pythagorean Theorem has many different forms of proofs today.

The following is a list of theorems attributed to the Pythagoreans:

(i) The sum of the angles of a triangle is equal to two right angles.
(ii) The Pythagorean Theorem - for a right angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.
(iii) They were able to construct figures of a given area and perform geometrical algebra. (Eg.: solving a(a-x) = x by geometrical means)
(iv) Discovery of irrationals
(v) The five regular solids.

References:

Greenberg, Marvin J. Euclidean and Non-Euclidean Geometries:

Development and History. 3rd ed. New York: W.H. Freeman and Company,
1993. 6-19.

Historical Topics for the Mathematics Classroom. Washington D.C.:

National Council of Teachers of Mathematics, 1969.

http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Thales.html (March 2005)

http://geometryalgorithms.com/history.htm (March 2005)

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