In the world of Harry Potter, Hermione Granger's favorite subject is arithmancy. The novels don't offer much detail, but they make it clear that arithmancy involves the magical properties of numbers. Hermione learns to use complex charts to perform numerical divination, or tell the future using numbers.

In the real world, arithmancy is known as numerology. According to numerologists, everything in the world is dependent upon the mystical properties of numbers. These properties come from the numbers' inherent vibration. Other new-age practitioners use the term vibration to describe beliefs in the power of items like crystals, gemstones, colors and essential oils.

As the theory goes, each number has a unique vibration, giving it certain properties. These properties can shed light onto a person's behavior or predict whether romantic partners are compatible. Numerological analysis can determine a person's lucky number or lucky day. Recurring numbers can offer clues into how the world works or the significance of people and events. According to many numerologists, nothing happens by accident -- everything happens because of numbers.

Public domain image Pythagoras

Most numerologists credit Pythagoras with founding the field of numerology. Pythagoras was a philosopher who was born in Greece around 569 B.C. Historians don't know much about Pythagoras, since little of his original work survives and most of the people who wrote about him did so hundreds of years after his death. In fact, some historians believe that the discoveries usually attributed to Pythagoras really came from several of his followers. In addition, some historians argue that the personality traits ascribed to him -- like that he would not allow his followers to eat or even touch beans -- are apocryphal.

Pythagoras and his followers, known as Pythagoreans, studied mathematics, music and philosophy. Many textbooks credit the Pythagorean school with several important discoveries, including:

• The Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²)
• The mathematical proportions in musical harmonies, likely discovered through the use of stringed instruments
• The first irrational number, the square root of two, or Pythagoras' constant

In addition, Pythagoras and his followers believed in mystical properties of numbers. According to Underwood Dudley, author of "Numerology: Or What Pythagoras Wrought", the Pythagoreans became interested in number mysticism after discovering a particularly fascinating fact about numbers. If you add up a series of odd numbers beginning with the number one, the result is always a square number.

The sum of sequential odd integers, beginning with one, is a square number.

Discoveries like this led the Pythagoreans to the conclusion that "all is number." According to one interpretation, this means that people can measure everything in the world and describe it in terms of numbers and proportions. This is a reasonable idea, and it has had a big influence on science and mathematics. But according to another interpretation, "all is number" means that everything in the world is made of numbers and can be reduced to a numerical value.

The latter interpretation is the foundation of numerology. We'll look at what else numerology involves in the next section.