# Biography

# Biography

- Science Theory & Philosophy
- Pythagoras (lived c. 530 BC)

- Mathematics
- Pythagoras (lived c. 530 BC)

# Pythagoras (lived c. 530 BC)

Greek mathematician and philosopher, part of whose mystic beliefs entailed an intense study of whole numbers, the effect of which he sought to find in the workings of nature. He founded a famous school that lived as a cultic community governed by what might now be considered eccentric—if not downright primitive—rules, but which during and after his lifetime discovered an astonishing number of facts and theorems, some immortal.

Very little is known about the life of Pythagoras, other than that he was born on the island of Samos and that, possibly obliged to flee the despotism of its ruler, Polycrates, he probably traveled extensively. His work seems to show the influence of contemporary ideas in Asia Minor; nevertheless, Pythagoras is next authoritatively recorded in southern Italy, in the Dorian colony of Crotona, in about 529 BC. There he became the leader of a religious community that had political pretensions to being an association for the moral reform of society. The Pythagorean brotherhood flourished; as a mathematical and philosophical community it was extending science rapidly, and as a political movement it was extending its influence over several western Greek colonies. More distant colonies put up some physical resistance, however, and it was probably one act of suppression in particular—led by one Cylon—that saw Pythagoras exiled (yet again) to Metapontum until he died, possibly around 500 BC. The school continued for something like another 50 or 60 years before being finally and totally suppressed.

Pythagoras was all but obsessed by numbers. He and his community looked for numerical values in all they saw around them, and strove to create relationships in the values they found. In elementary pure mathematics they studied the properties of the numbers themselves, and their practice of representing numbers as lines, triangles or squares of pebbles has given us our word calculate (from calculus, the Greek for “pebble”). It also led directly to a firm basis for geometrical considerations. In this way, they established that the addition of each successive odd number after 1 to the preceding ones results in a square (1 + 3 = 2^{2}; 1 + 3 + 5 = 3^{2}, and so on) and Pythagoras himself is supposed ultimately to have arrived at the theorem to which his name is attached, regarding right triangles. (In fact he is supposed to have proved it from a more general equation he is said also to have formulated:

m^{2} + {1/2(m^{2} − 1)}^{2} = {1/2(m^{2} + 1)}^{2}

and to have noted that if the triangle in question is isosceles, the ratio of the hypotenuse to either side is the irrational number √2.)

Using geometrical principles, the Pythagoreans were able to prove that the sum of the angles of any regular-sided triangle is equal to that of two right angles (using the theory of parallels), and to solve any algebraic quadratic equations having real roots. They formulated the theory of proportion (ratio), which enhanced their knowledge of fractions, and used it in their study of harmonics upon their stringed instruments: the harmonic of the octave was made by touching the string at 1/2 its length, of a fifth at 2/3 its length, and so on. Pythagoras himself is said to have made this the basis of a complete system of musical scales and chords.

He is said also to have taken a keen interest in astronomy, seeking numerical consistency among the celestial movements and objects.

From the *Hutchinson Dictionary of Scientific Biography*, © RM, 2020. All rights reserved. Published under license in AccessScience, © McGraw-Hill Education, 2000–2020. Helicon Publishing is a division of RM.

## Related Articles

Mathematics Mathematics is frequently encountered in…

Chaos System behavior that depends so sensitively on…

Mining The taking of minerals from the earth, including…

Number theory The study of the properties and relationships…