What is a biblical worldview in the study of Mathematics? Should a Christian education include study of conceptual Math (that is, math beyond application of formulas) even for a non-math student?
There are some articles and books on the subject of “God in Mathematics.” They all take basically the same approach: Mathematical order in Creation is somehow analogous to order inherent in God, so we study Math to appreciate the inherent mathematical-logical nature of God. Unsurprisingly, these articles and books are written by mathematically-minded people who assume that our being made in the Image of God implies that God is also mathematically-minded, in a superior or transcendent way.
There are two problems with this assumption. First, being in the Image of God means that we are in some analogous sense “like God,” but it does not mean that God is in any sense “like us.” The Bible gives no basis for seeing God as like us — in fact, it portrays God as uniquely unlike anything but Himself. The Creation can reflect God analogously without being ontologically or epistemologically similar to God. The Creation can be fully contingent upon God without God being in any way contingent upon the Creation. God can be fully immanent in the Creation while also being completely transcendent to it, without the Creation possessing any of the essence of God.
Second, while math and logic and order may have fundamental places in the design of Creation, this does not imply that God is inherently “ordered” like the Creation (nor is this the correct meaning of 1 Cor 14:33). The Creation may be ordered by math, but that does not mean that God is inherently ordered in some mathematical way, nor that His “thoughts” are based on formal logic and its mathematical underpinnings. To make the human-logic leap to a notion that “mathematics reflects God’s inherent order” — as logically-oriented people of faith are often inclined to do — is to misunderstand important differences between God and His Creation. Avoiding and overcoming this misunderstanding can teach a truer appreciation of God, while also revealing a truer motivation for the study of conceptual Mathematics.
To understand why we must reject the notion that God is somehow ordered mathematically or logically, we must consider what order actually is. Order implies a sequence or system that allows the finite to be extended beyond its own inherent capacity for understanding, tracking, managing, or predicting something. For example, Amazon uses an ordered system for tracking and managing all of its many products located across the globe. No human could track and manage all the items individually, but a well-designed ordered system allows a finite human to start with one bit of information and work his way to the other information far outside his capacity, and then take effective action to achieve “logical” outcomes.
However, we biblically understand God to be omniscient and omnipotent, and to require no system or ordering to understand, track, or manage anything. Stars, grains of sand, and tornadoes — as well as creation, sin, redemption, and glorification — are all under his sustaining management, without needing any system of ordering, and without any confusion or inefficiency on His part. So we realize that our notions of order and logic are for our benefit inside this Creation, and are not necessarily some revealed inherent property of God Himself. Even if we choose to assume that God must somehow be “ordered” or “orderly” in some way, we have no biblical basis for saying that this order is describable by our logic or is even within our understanding.
If the study of conceptual Math is not some insight into the fundamental systematic nature or “mind” of God, then what is it? First it is important to understand that conceptual Math is created as part of this Creation. God didn’t follow His “mathematical nature” or rely on Math in the Creation process. He created Math when He created Time, Space, Energy and Matter. However, it is also important to understand that Math is something essentially different in the Creation than Matter and Energy, or even Time and Space. In a remarkable and unexpected way, Math turns out to be a “blueprint” for this physical Creation, providing us a humanly comprehensible “language” for understanding and describing how the physical Creation works — and for helping us manage it. Math is a designed element of this Creation, but it serves at a deeper level as a foundational language for describing and even directing (i.e., exercising “dominion,” in biblical terms) our physical world.
Conceptual Math offers us an opportunity to engage some of the Creation’s beauty and functionality that we cannot engage through any other means. But as awesome as it is to encounter some of the beautiful intricacy of what God has designed for us in this Creation, the greater wonder is that this mathematical framework exists at all. Since the 1500’s we have been continually making great discoveries and advances in math-based Science. Each discovery brings wonder of its own, and potential for even greater control over the physical Creation. However, the most amazing thing about the mathematically-based laws of Science is not their opportunity for discovery and application — it is that they exist in the first place! It is a considerations among both secular and theistic scientists that there is no “natural reason” that the universe should be ordered in any way we can understand, since existence does not theoretically require order as we know it. Thus the elegant orderliness of conceptual Math and its connection to the physical Creation reflects a glorious design that doesn’t “have to be” this way, and so is all the more remarkable because it is this way. To truly appreciate why conceptual Math is important, we must realize not that the Creation had to be ordered due to some order inherent in God, but rather that God chose to create conceptual Math, chose to make it the framework for this Creation’s order, and also chose make it a “language” — perhaps even “logos” — that we humans can understand.
Thus the very existence of conceptual Math as the framework or language of the physical Creation is not only an opportunity, but an invitation, from God to study it. He placed it there specifically for us, inviting us to understand, appreciate, and even manage the physical framework of this world He has given us. Studying conceptual Math (and its applications in the Sciences) to the best of our abilities is as important as studying the Humanities and Arts (and their applications in Social Sciences) to the best of our abilities, even for non-math-minded people — just as math-science people should appreciate and study the Humanities, for the same reasons. We are invited to study the whole of the Creation because He made it for us and us for it, not because He is like it in some way. The Creation reflects for us the glory of the infinite God, without limiting Him to some finite logical order, and so our study of each aspect of the Creation to the extent of our individual abilities is part of our worship, our service, and our mission in this Creation.