A Beginner’s Guide to The Argument from Mathematics

by Dr Mark Mccartney
Does mathematics have anything to do with God?

‘Great are the works of the Lord; they are pondered by all who delight in them’ (Psalm 111v2)

These are the words which James Clerk Maxwell (1831-79) had carved into the doors of the Cavendish Laboratory in Cambridge when it was built in the 1870s. Well actually they were carved in Latin, but still you get the point.

Maxwell, now regarded as one of the greatest physicists of all time, was a man who saw ‘pondering’ the workings of God’s creation as a delightful thing to do. And certainly in my own mind, looking around at the shear grandeur, complexity and beauty of the natural world leaves me with the distinct impression that I am looking at one enormous Divine calling card.

The beauty of creation goes all the way down to the equations of physics.

Interestingly when as scientists we drill below the surface to produce mathematical theories to represent the world (chiefly in the area of theoretical physics) it turns out that beauty is also to be found in the equations we write down. More than that, some theoretical physicists see mathematical beauty as a requirement of a good theory.

For those readers who cannot conceive of what mathematical beauty might look like, and still find quadratic equations one of the more stressful parts of their teenage life, I can assure you that mathematical beauty is visible to those versed in the subject. Perhaps it is best described as a combination of concision and breadth of explanatory power.

I have pondered on the beauty of creation at the level of night skies and butterflies, and thought ‘Great are the works of the Lord’. But this particular applied mathematician has found himself thinking the same thing when he looks at the Schrodinger equation (describing things on the atomic scale) or Maxwell’s equations (describing all of electromagnetism).

For me the calling card of creation still has the marks of the divine when it is translated into the language of mathematics.

Whose equations are they anyway?

One of the odd things that many mathematicians experience is the sense of ‘discovery’ they feel when they prove a theorem, or solve an equation. Indeed some mathematicians insist that they are making discoveries. From this perspective mathematics is not a creation of human minds, but rather, as Roger Penrose (a very eminent British mathematical physicist) puts it, ‘mathematical truth is absolute, external and eternal, and not based on manmade criteria and…mathematical objects have a timeless existence of their own’. Now I hasten to add that not all mathematicians take this position (called mathematical Platonism), and furthermore Roger Penrose is an atheist. But, mathematical Platonism is a respectable position, held by  more than a few mathematicians.

Now, if we ask the question whether mathematical Platonism sits more comfortably with atheism or theism, it seems that atheism (which I will equate to materialism – ie there are no things in the universe which are not physical) is in real trouble. Where do these ‘absolute, external and eternal’ mathematical truths exist? In the materialist world there is simply nowhere to put them.

However, for the theist, the answer is quite straightforward. They are thoughts in the mind of God. Thus, if you are inclined towards the idea of mathematics as ‘discovery’ of independently existing truth, then it seems to me it sits more comfortably with theism than atheism.

Of course if you are an atheist you may simply be inclined to say ‘well OK, I wasn’t to fussed on mathematical Platonism anyway’. And that, of course, is absolutely fine. But there remains one other puzzle when it comes to mathematics…

How come the maths in my head describes the universe outside it?

This is not quite as silly as it sounds. The Nobel prize winning physicist Eugene Wigner (1902-95) describes it as the ‘unreasonable effectiveness of mathematics in the natural sciences’.

Let’s say that mathematical Platonism is false. This means that all the mathematics we have is a free creation of the human mind. Well, how come all this mathematical abstraction of complex numbers, partial differential equations, infinite dimensional vector spaces and non-Euclidean geometry turns out to be just the set of things that describe – really well– how the universe ticks?

An atheist response will be that much of the mathematics which humans have created has been done in a ‘co-evolutionary’ way along with our understanding of the natural world. In some cases that is indeed true. However, this is not true in all cases.

A theistic response is to say that we are made in the image of God. Broadly speaking theologians have thought of the image of God as a combination of ‘the three Rs’: Reason, Relationship and Regency. Relationship, in terms of our ability to have deep relationships with others and with God. Regency, in terms of our stewardship of the world we live in. And Reason, in terms of the fact that we can reason deeply about both God, His creation, and our place within it.

Thus, for the theist, the mathematics we create describes the physical world because both our mind and the created order were made by God.

Conclusion

You may have come to the end of this short article positively disappointed with its lack of strong arguments for theism from mathematics. That, in my view, is just how it is. Some perspectives on mathematics (such as mathematical Platonism and mathematics ‘unreasonable effectiveness’) certainly sit more comfortably with theism than atheism, but such perspectives are not universally held, nor are they bound tightly to mathematics.

The beauty and richness of the mathematical description of nature is, however, analogous to the beauty and richness of the nature it describes, and as such to me it a pointer to the existence of a God in the same way that the created order is.

Of course the careful reader will have noted that I have talked generically about ‘God’ and ‘theism’. From the huge grandeur of nature, and the beauty of its laws, we can gather that God is a great and powerful artist. But to find out anything more…well He would have to step into history and reveal Himself, wouldn’t he?


Mark McCartney teaches mathematics at the University of Ulster. His research interests are in the areas of nonlinear systems and the history of mathematics and natural philosophy in the nineteenth century. He is married to a wonderful wife, and has two wonderful children.

 

Further reading:

A good introductory read from an explicitly Christian perspective is:

Bradley & R Howell, Mathematics through the eyes of faith (HarperOne, 2011).

Two slightly more advanced books, which are made up of collections of essays from a range of scholars are:

S Lawrence & M McCartney (eds.), Mathematicians and their gods (OUP,2015).

J Polkinghorne (ed.), Meaning in mathematics (OUP, 2011).

In particular Chapter 1 of Lawrence & McCartney gives an extended form of this article.