Pythagoras

Pythagoras is credited with proving the Pythagorean Theorem (a² + b² = c²). He explained the origin of the universe in terms of mathematics. Pythagoras may have discovered the irrational square root of two.
"Pythagoras" The Oxford Dictionary of Philosophy. Simon Blackburn. Oxford University Press, 1996. Oxford Reference Online. Oxford University Press.

• Foundations of Greek Geometry
  Student paper by Michael Tirabassi. Section on Pythagoras discusses five discoveries of the school:
  1. Sum of the angles in a triangle.
  2. The Pythagorean theorem
  3. irrational numbers
  4. five regular solids (polyhedrons)
  5. geometrical algebra
• Geometry Then And Now
  Another student paper, by Jordana Wiener. If anyone in your family is studying geometry, you'll quickly see what Wiener is driving at. This interesting page enforces the value of geometry and the universality of student recalcitrance.
• Prime numbers
  Pythagoras comes first in this history of mathematics page with his theory of amicable and perfect numbers. Perfect numbers have divisors that added together equal the number and amicable numbers are two numbers whose divisors added together equal each other.
  Source: www%2Dgroups.dcs.st%2Dand.ac.uk/%7Ehistory/HistTopics/Prime%5Fnumbers.html
• The Golden Section
  Timothy Reluga writes, "The first mathematical occurrence of the golden section and it's associated figures is found in the school of thinkers founded by Pythagoras."