Mathematics is the abstract study of topics encompassing quantity, structure, space, change, and other properties. Mathematicians identify patterns in such properties and formulate conjectures. They resolve the truth or falsity of these conjectures by mathematical proof.
Like scientific methodology, mathematics is a human invention, a tool of sorts. Unlike science, mathematics is not based primarily on the observation of physical phenomena, but views on the relationship between mathematics and reality have changed over time. The ancient philosopher Plato supposedly believed that pure geometric forms are more real than anything humans can perceive. At the time of the scientific revolution in the 1600s, it was still common among a tiny elite of natural philosophers, such as Galileo, to view the universe as basically mathematical, having been put in order by the Abrahamic god. This view collapsed long ago.
Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Thus by Lovecraft's time, the idea that mathematics relates to a higher truth was largely abandoned. Albert Einstein (1879–1955) stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."
Because of the cultural legacy of idealism and because patterns naturally attract superstition, writers often use higher mathematics as phlebotinum (external link), explaining any aspect of a plot in a way that is interchangeable with magic. Lovecraft himself did this in "The Dreams in the Witch House", inspired by the lecturer Willem de Sitter (1872–1934). Mathematics is amplified in Lovecraft's portrayal, readily penetrating the mysteries of the universe, and thereby unveiling the Mythos.
Horror is often deeply conservative. So it is with mathematics. In a common type of plot, the universe is revealed as being essentially mathematical, usually through the trope of efficacious apophenia. This is where patterns that would be insignificant in reality turn out to have meaning. For example, in the movie The Number 23 (2007), the plot relies on multiple characters growing obsessed with the number, which is unnaturally prevalent and sinister. For a number to have that kind of importance, it would be necessary for human inventions like mathematics or numerology to be central to the universe. This implies anthropocentrism, the opposite of Lovecraft's "cosmicist" foundation for the Cthulhu Mythos.
