Paul Michael Kielstra

OK, everybody and their dog is writing about this, so here’s my effort.

The first three words of the Bible, in Hebrew, translate to “In the beginning, God created.” Before we know that God is loving, or just, or merciful, or even that he understands any of these things, we know that he is creative, in the sense that he creates. The very next thing that God does is to speak, saying “Let there be light.” A two-word interlude establishes that there was light, and then we get more action from God, who determines that the light is good. This pattern repeats for the first five days of the Genesis 1 creation story: God speaks, he creates, and he assesses.

It is in this context that, on the sixth day, God creates humanity “in his own image,” giving them some sort of dignity not afforded to other created things (or, we commonly understand, to humanity’s creations). It’s not completely clear what this means from this passage alone, but, given what God has just been getting up to, I would argue that, at least in part, it indicates that humanity has been endowed with special ability to speak, create, and assess. This doesn’t necessarily define us – I’m not advocating for an Aristotelian “Man is the rational animal” claim – but, whatever it does mean to be human, some amount of dignity in speech, creativity, and rationality comes with it for free.

Mathematics, as a field, as a culture, and as an industry, is built entirely on these three skills. To be a successful mathematician, you have to have new and useful mathematical ideas. You have to demonstrate that they work. You have to tell everyone about them. If you can reliably do all three of these, you will, modulo office politics, luck, privilege, and so on, succeed as a mathematician. Once again, I’m not trying to say that “Man is the mathematical animal,” but I do make the weaker claim that mathematics relies on tools with which God has given humans special ability.

If this is the case, it might at first glance seem strange that the Bible makes next to no mention of mathematics, and that when numbers do show up it’s clear that exact calculations to high precision aren’t something that the book is really interested in. 1 Kings 7:23 gives measurements that, if read as exact numbers and not rounded approximations, imply that pi is three. The numbers in the book of Numbers can be difficult to translate. In fact, this strengthens my reading. One of the Bible’s first priorities is to establish that God is far bigger and more powerful than humans could ever imagine. If we don’t understand this, we cannot worship properly, and we completely miss the point of the incarnation. It makes sense that the Bible usually focuses on God doing things that humans can’t, or won’t, do. In the Old Testament, God speaks a universe into being, brings about dramatic miracles, predicts the future, manipulates geopolitics at will, and so on. The incarnate Christ performs even more miracles, has the perfect response to every question posed to him, and dies on the cross not as an overpowered man but as someone giving up his life of his own free will. Before he began his formal ministry, he was a builder, and presumably a conscientious one, but we never see anything he built. The Bible’s lack of interest in mathematics implies not that humans can’t do it, but that they can, and they can do it well enough that it’s not so interesting to someone who wants to think about things that God can do that humans couldn’t begin to try.

All of this leaves Christian mathematicians in a unique position with respect to LLMs. The various AI companies are all selling some variation on the claim that their models are capable of speaking, creating, and reasoning in a way somewhat comparable to humans. They’ve made inroads in a lot of places, but they’ve arguably got the furthest in math and computer science. LLMs can solve undergraduate math problems easily, and the more advanced ones, given enough computing power, can sometimes complete research-level proofs if someone feeds them the main ideas. In the short term, this is really quite scary, and, in the medium term, it will almost certainly lead to a major change in how mathematics is done.

In the long term, though, I am confident that mathematics will remain a human endeavor, because humans, being made in the image of a creative, rational, communicative God, are uniquely good at being creative, rational, and communicative. LLMs might throw their digital hats in the ring, and they might well be useful tools, but humans have a God-given advantage at everything that their creators are trying to make them do. Nor is this advantage restricted to just the most highly-skilled humans. We “do math” not only when we prove grand new theorems, but also when we help a friend with a calculation or even listen to a political speech and check in the backs of our minds that the percentages being cited actually do add up. No matter what part you have to play in the world of math, you were created in God’s image, and that lets you play that specific part better than any other creation ever could.

That said, we are still left with one major problem: articulating how, exactly, humans beat LLMs. I’ll admit to not wanting to commit too hard here. I’ve found LLMs to be unimaginative and wooden compared to humans. They have a genius for writing hundreds of lines of code to do something that a two-minute search would have found a standard library for. I could go on, but I don’t know which of these problems will be fixed in the months and years of development to come, and, more importantly, I don’t know if they’re even the biggest problems with LLM-generated work or if they’re just the problems that I, personally, notice most. At this time, especially given the pace of development, I do not know.

Much as it may look like it, this is not bad news! Rather, I would argue that this is actually a huge opportunity for both mathematicians and theologians. Mathematicians, famously, can’t agree on a definition of “mathematics,” and theologians have similar trouble pinning down the idea of the soul. If we accept the tautology that whatever is unique about humans must be something that LLMs can’t duplicate, and the stronger premise that whatever mathematics is it must be something that humans are uniquely good at, then looking carefully at what LLMs can do will allow us to correct many of our own misconceptions in these areas. For example, clearly the ability to string together words into complex texts is not part of what the Bible is referring to when it says that humans were made in God’s image. Before now, we would have had to argue about that, and there might not have been a satisfactory answer. Today, I can just get an LLM to demonstrate the behavior.

So, then, as Christians, we know that there is something special about being human, and that this extends in some way to the ability to do math. As mathematicians, we are in a perfect place to evaluate what LLMs do and don’t bring to the mathematical table. Let us therefore move forward, experimenting with LLMs as we personally see fit, bringing them into our research where they are helpful and ignoring them where they aren’t, secure in the knowledge that we have a tangible advantage over them, and looking forward to the day when we can confidently say what that advantage is. As we do so, we won’t just discover new math. We’ll be able to refine our understanding of who we are, who God is, and what our place is in the universe he created. This is the fundamental task of all science, and right now we have a chance to contribute to it in a way that very few other disciplines can.

Plus, we’ve already got a counterexample to the Jacobian conjecture out of it, which is also pretty cool.