In their study of mathematical concepts, the Pythagoreans sorted numbers into categories. Numbers like one, four and nine are square because a corresponding number of dots or pebbles can be arranged in a perfect square. One, three, six and 10 are triangular — one, three, six or 10 dots can be arranged into regular triangles. Two, six and 12 are oblong, since the corresponding number of pebbles form rectangles.

Along with describing numbers in terms of math and geometry, the Pythagoreans also described them in terms of non-numerical traits. These traits had more to do with intuition and mysticism than science or mathematics.

For example, odd numbers are masculine and even numbers are feminine. The No. 1 is creative, since the addition of multiple ones can create any other number. Two represents duality and is female, while three is male. As the sum of two and three, five represents marriage, and since it falls exactly in the middle of the numbers one through nine, it also represents justice.

Ten is a sacred number, largely because it is the sum of the first four digits.

After the death of Pythagoras, interest in mathematical mysticism faded. It reappeared in the late 1800s when Mrs. L. Dow Balliett published several books on number vibration, music and colors. According to Balliett, each number has a specific vibration. People, foods, objects and colors also vibrate. In order to live a productive and harmonious life, people should make sure their environment vibrates in harmony with their own vibrations. This concept appears frequently in other new age practices, some of which describe it as an affect of the movement of subatomic particles. However, there has been little scientific study to identify or quantify such a vibration or to analyze its affect on human existence.

Unlike the Pythagoreans, modern numerologists apply numbers to people in addition to applying intangible concepts to numbers. According to most numerologists, the numbers one to nine have unique properties that are the direct result of their inherent vibration. Some of these properties come from Pythagorean writings, and others come from how cultures around the world use and approach numbers.

Some systems designate numbers with repeating digits as master numbers, which include all the attributes of two other numbers:

- 11: 1 and 2
- 22: 2 and 4
- 33: 3 and 6
- 44: 4 and 8

Numerology purports to tell the future, guide human behavior, predict the outcome of relationships and otherwise divine the unknowable by figuring out a person’s numbers. For example, if the No. 9 has a particular vibration, a person whose number is nine has the same vibration. That person can choose what to eat, where to go and how to live based on which choices have a vibration that is compatible with nine.