Pythagoras was born on the island of Samos, and traveled with his merchant father. He was influenced by the teachings of Thales, and taught by Thales' student Anaximander. He studied in Egypt, and eventually founded his own religious/philosophical school in Croton, on the southern coast of Italy. His followers obeyed strict orders, including secrecy, and lead a communal lifestyle. The Greek philosophers always refer to the Pythagoreans for their learning and mathematical discoveries, as no individual credit is ever given.
Pythagorus was the first person to claim that the earth was a sphere - though it is not clear at all why he thought that. While it may have been based on some form of observation, it may also have been simply because he thought spheres were the most perfect solid.
His view of the universe was probably very simple: the spherical earth at rest in the center of the universe and everything rotating around the earth, each object carried by its own sphere. His school conitnues without him, and in later years,
The Pythagorean view of the cosmos was fairly simple, and did not match the observed motions of the planets. They held that the planets all orbited in giant spheres, and as the spheres rubbed against each other, they created sound. They claimed that this sound created musical harmonies; this music comes to be called the Music of the Spheres. People didn't hear this music because they were so accustomed to it always being present.
The Pythagoreans held that the earth actually orbited a central fire, as did all the stars and planets, and we get night and day due to the motion of the earth. They also added a "counterearth" on the opposite side of the fire. Philosophically, they felt that the center of the universe was the most important and special. Since they also felt that "fire" was more special than "earth," the center of the universe must be fire. (De Caelo, Book II, part 13)
Pythagoras was also the first person to recognize that Venus in the evening and Venus in the morning were in fact the same planet.
Mathematically, the Pythagorus begins a tradition of mathematical proof, and also begin the abstraction of mathemetics. To the Pythagoreans, real numbers were the most important thing, and numbers make up the world. They proved the Pythagorean Theorem. They also discovered that the square root of 2 was an irrational number, (and so not a number as they defined it) and actually tried to supress this knowledge.