A mathematical phenomenon of the Torah is spiritual ratios (the Torah ratios) of spiritual letter combinations interrelated with unique constants, ratios, and proportions of nature.

Sacred mathematics is essentially the study of the meaning of various spiritual ratios and their connections with physical reality based on connections between spiritual letter combinations and ratios and proportions in nature, daily life, and the universe.

Sacred mathematics begins with the manipulation of sacred numbers that indicate quantitative and logical meanings of diverse aspects of wisdom and ratios of nature, which are constants of unity and harmony in physical reality. The sacred numbers are foundational principles of the Hebrew language and represent numerical meanings of divine and spiritual forces. The sacred numbers and ratios of nature are interconnected.

All things are measurable, commensurable, or proportional in terms of number and have their own numerical properties. The theory of sacred numbers is concerned with properties of the sacred numbers founded by spiritual letter combinations. The key to an explanation of the universe and nature lies in number and form. The general thesis being that everything founded by the sacred numbers, i.e., everything material or spiritual, can be represented by sacred numbers. Thus, for a rational understanding of nature, it is sufficient to analyze the properties of sacred numbers.

Mathematics is based on numbers. Sacred mathematics is based on sacred numbers that reflect bonds between spiritual letter combinations and ratios of the physical world. Modern number theory is a broad subject that is classified into subheadings, such as elementary number theory, algebraic number theory, analytic number theory, geometric number theory, and probabilistic number theory. These categories reflect the methods used to address problems concerning the integers. Sacred number theory deals with gematrical vectors and matrices.

According to Jewish tradition, the world is created by spiritual letter combinations, consisting of 22 Hebrew letters. Gematrical vectors and matrices constitute the unifying concepts necessary for understanding everything from properties of physical matter to musical harmony. From this viewpoint, gematrical vectors and matrices are based on sacred numbers and represent universal and absolute constants and ratios of our world.

Gematria is a system of assigning numerical value to a word or phrase. There are many different methods used to calculate the numerical values of Hebrew letter combinations. Gematria derives added meaning from words or phrases in Hebrew by calculating the numerical equivalence of letters, words, and phrases in a particular text.Therefore, gematria may be used to gain insight into interrelating concepts and for finding correspondences between words and concepts.

The Torah is based on spiritual letter combinations that reflect diverse aspects of wisdom, spiritual knowledge, and spiritual forces. Because spiritual letter combinations have a direct relationship to spiritual forces, the gematria of any spiritual letter combination is the quantitative and logical evaluation of a spiritual force and is a gematrical vector. This vector shows the quantitative and logical meanings of spiritual forces and their directions.

In this connection, a gematrical vector may be used to find correspondences between spiritual letter combinations and properties of elements or objects of nature. Any letter combination can be calculated and represented by a gematrical vector. Thus, we can obtain detailed descriptions of the quantitative and logical meaning of spiritual forces and their directions. By comparative analysis of gematrical vectors and ratios of nature we can find interrelations between spiritual and physical forces and spiritual letter combinations and in this way we can define properties of diverse elements and processes of nature.