Poythress, Vern. Redeeming Mathematics: A God-Centered Approach.
Several years ago I was introduced to what is known as presuppositional apologetics. That’s a mouthful of a phrase, but the basic gist is this: the reason that anything at all exists is because of God. Or, as apologist Cornelius van Til put it, “there are no brute facts.” Probably the most famous articulation is the Great Debate between Bahnsen and Stein, in which Bahnsen danced circles around the ill-prepared Stein with the concepts of presuppositionalism.
I find this brand of apologetics compelling, because it very directly attributes maximum glory to God for all things. Further, it encompasses all the other brands of apologetics. Evidential apologetics (a la Josh McDowell) and classical apologetics (a la Sproul) are various expressions and valid tools to be used, but all based upon the truth of Scripture and its immediate application to the real world.
In that vein, Vern Poythress has written a series of books that propose to demonstrate the reality that all that we know and all that is has God as the foundation. He has written on science, sociology, chance, logic, philosophy, and this volume on mathematics. (I’ve read the first part of Redeeming Science but none of the other volumes in the series.)
I had high hopes for this book, but I was largely underwhelmed. Dr. Poythress has a long-standing and well-known friendship with Dr. John Frame, and their work overlaps often. (This is a good thing.) Poythress employs Frame’s three perspectives to explain why math necessarily comes from God alone.
The three perspectives are the normative, the situational, and the existential. The normative perspective deals with what God declares to be so (hence “norms” or “normative”). The situational perspective deals with an actual scenario to which the truth applies. The existential perspective deals with an individual’s perception of the truth. The only way mathematics can properly balance all three perspectives is if the source and foundation is the Triune God Himself.
That last paragraph pretty much sums up the last dozen or so chapters of the book. Laws and principles of math (numbers, operations, etc.) are true because they conform to the thoughts and mind of God (normative perspective); the laws and principles of math apply in actual circumstances (situational perspective); we as image-bearers of God are able to think about and reason via the mathematical laws and principles (existential perspective). Every chapter basically asserts these three sentences, just with a different topic.
This doesn’t mean in any way that I disagree with Poythress at all. I think he’s absolutely right. I just found the repetition tedious fairly quickly. I think this book would be better served as an appendix or an additional couple of chapters in Redeeming Science than as its own work.
Redeeming Mathematics is an important book as a starting point of sorts. I’d definitely use it as a springboard into more robust descriptions of presuppositional apologetics (e.g., John Frame’s Apologetics to the Glory of God is a great resource).
If you’re interested in seeing math nerds geek out about math, I’d highly recommend the Numberphile YouTube channel. I don’t always understand exactly what’s going on, but it is fun to see people who are genuinely passionate about math show how it is beautiful and amazing and strange. Whether they intend it or not, it almost always leads me to worship and wonder at the God who is the root (pun intended) of all mathematics.