Pythagoras and his followers were important for their contributions to both religion and science. His religious teachings were based on the doctrine (teaching) of metempsychosis, which teaches that the soul never dies and is destined to a cycle of rebirths until it is able to free itself from the cycle through the purity of its life.

Pythagoreanism differed from the other philosophical systems of its time in being not merely an intellectual search for truth but a whole way of life which would lead to salvation, or to be delivered from sin. An important part of Pythagoreanism was the relationship of all life.​​The historian Eusebius compares Pythagoras to Moses, while Augustine of Hippo (354–430 AD), the early Christian theologian and philosopher, dismissed Pythagoras’ theory of metempsychosis without actually naming him, yet generally communicated profound respect for him. In On the Trinity, Augustine discusses Pythagoras’ modesty in referring to himself as an “admirer of insight” rather than a “sage.”

The Pythagoreans, as a result of their religious beliefs and careful study of mathematics, developed a cosmology (dealing with the structures of the universe) which differed in some important respects from the world views at the time, the most important of which was their view of the Earth as a sphere which circled the center of the universe. It is not known how much of this theory was credited to Pythagoras himself.

The mathematical knowledge carried out by Pythagoras and his followers would have been enough to make him an important figure in the history of Western thought. However, his religious sect and the self-discipline and dedication which he taught, embracing as it did a vast number of ancient beliefs, make him one of the great teachers of religion in the ancient Greek world.

The Pythagoreans believed the world was a sphere and that the sphere was the most perfect shape. They then took that idea a step further, theorizing that the Earth was the center of the universe because all objects are pulled to the center of something, which creates a sphere (in this case the Earth).

As a mathematician, he is known as the "father of numbers" or as the first pure mathematician, and is best known for his Pythagorean Theorem on the relation between the sides of a right triangle, the concept of square numbers and square roots, and the discovery of the golden ratio.

Pythagoras' beliefs that made an impact in Mathematics:

• All things are numbers. Mathematics is the basis for everything, and geometry is the highest form of mathematical studies. The physical world can understood through mathematics.

• The soul resides in the brain, and is immortal. It moves from one being to another, sometimes from a human into an animal, through a series of reincarnations called transmigration until it becomes pure. Pythagoras believed that both mathematics and music could purify.

• Numbers have personalities, characteristics, strengths and weaknesses.

• The world depends upon the interaction of opposites, such as male and female, lightness and darkness, warm and cold, dry and moist, light and heavy, fast and slow.

• Certain symbols have a mystical significance.

• All members of the society should observe strict loyalty and secrecy.

The belief that at death the soul transmigrates into another body, is described by Dicaearchus as the best known of Pythagoras' teachings. Even though the details of Pythagoras’ lessons remain unknown, it is possible to get a general idea from other sources such as Aristotle, who writes about the lessons of the Pythagoreans without referencing Pythagoras directly.

One of Pythagoras’ fundamental principles seems to have been metempsychosis, which is the belief that all spirits are godlike and that after death a spirit moves into another body. He is believed to have been reincarnated into the scholar Hermotimus, who beheld the shield of Euphorbus in the sanctuary of Apollo. His last manifestation was as Pyrrhus, a fisherman from Delos.

Pythagoras established the mysterious society of the Pythagoreans in southern Italy. The Pythagoreans put forward a hypothesis that stated that everything known to humankind could be clarified with numbers, explicitly entire numbers. This rationale made perfect sense to them, and it is easy to see why. Even today, we use numbers for everything from working out wind speeds in a storm to calculating the speed of a vehicle.