The Bible does not answer all possible questions regarding the role and purpose and reasonable extent and use of mathematics. Mathematical ideas and concepts seem to have existed in the mind of God before mankind elucidated them, but this is more in a Biblical sense that David wrote, “Before a thought is on my lips, you know it completely, O Lord” (Psalm 139:4) rather than the Platonic sense that true mathematical ideas exist in the mind of God before man discovers them and that mathematical discovery is somehow probing the mind of God. To be sure, a created world that gives such evidence of mathematical thinking, combined with God’s assertions of the created order and use of mathematics in Scripture give evidence that the process of creation involved mathematical thinking on the part of the creator.
However, theoretical physics and mathematics are not the best process for knowing God’s thoughts. Einstein wrote, “I want to know God’s thoughts. Everything else is details.” Higher mathematics and theoretical physics may or may not represent some reality in the mind of God in the moments of creation. They more likely represent imperfect attempts to build models that (hopefully) have some usefulness as approximations to the physical creation. The ontology of science suggests that scientific models are gradually approaching some perfect, quantitative “theory of everything” which possesses both mathematical rigor and perfect predictive power.
Knowing God’s thoughts are probably best accomplished by reading God’s word and walking alongside of the creator with eagerness and enthusiasm for the great mandates of Scripture (NT: making disciples of all nations; OT: being fruitful and multiplying, filling the earth and subduing it). We reject any suggestion that people with a given professional gifting or calling (to math or science) are somehow better equipped to know God’s thoughts than other professions (farmers, fishermen, carpenters, etc.) The farmer who has to pray for rain in season, confront the thorns and thistles, and then struggles to harvest his crop before it is destroyed by fungus, insects, or other pestilence is probably walking more closely with the Creator than the mathematicians and scientists who more likely spend time in human, intellectual, and self-dependent frames of reference.
Some consider mathematics to be a science and go about studying the “mathematical sciences.” Most of higher mathematics is not subject to experimental testability as is natural science, so we prefer to categorize math as a scholastic science. Its assertions are testable in the realm of logic and proof. Questions can be answered by careful logic and deduction, by considering the definitions, postulates, and axioms without the need to consider experiments and observations. Potential consequences can be considered true or false based on definitions and premises rather than by experimental measurements. For example, the idea that pi is the ratio of a circle’s circumference to its diameter is not experimentally falsifiable. If an object’s circumference is not pi times the diameter, then a mathematician would conclude the object is not a circle, not that his theory about pi is in error. Likewise, in introductory physics, the kinematic equations depend only on the definitions of velocity and acceleration in terms of position and time. There is no conceivable experiment where these could be falsified. There is no set of physical laws in which the kinematic equations are not true, since they follow directly from mathematical definitions.
Another view of mathematics is that it is a specialized language. Galileo observed that the “Book of Nature” is written in the language of mathematics. Together with other important introductions of mathematics into natural philosophy including Johannes Kepler‘s laws, the analytic geometry of Rene Descartes, the use of mathematics by John Dalton and Robert Boyle in the gas laws of Chemistry, and the introduction of of math into genetics by Gregor Mendel, the stage was set for Newton‘s invention of Calculus to accommodate his masterwork, “The Mathematical Principles of Natural Philosophy.” As a language, the definitions of its quantities, symbols, and operators are much more precise than other human languages. Likewise, the grammar and methods of mathematics leave much less room for ambiguity of interpretation.
If there was ever a ubiquitous language that might empower mankind to build a tower to the heavens, then mathematics is probably it. However, in the same way that God confounded the languages and spread mankind over the face of the earth at the tower of Babel, God seems to have arranged that only a small subset of mankind can master the language of mathematics so fundamental to such engineering tasks. The intellectual jumps from Euclidean Geometry and Algebra 2 (which most of the western world requires for high–school graduation) to Calculus (which is the introductory college math upon which all physics and engineering is built) seems to have effectively limited the participants to a small subset of humanity.
Regardless of whether one classifies mathematics as a scholastic science or as a language, mathematics is a gift from God to empower the divine fiat, “Be fruitful and multiply, fill the earth and subdue it” and to rule over the created world. It matters not whether humans were discovering God‘s real creative thoughts as math was invented or whether we were merely inventing imperfect approximations that were nothing more “than a poor reflection, as in a mirror.” Math has empowered science and engineering.