Recently, I was interviewed on a BBC religious affairs programme, “All Things Considered.” The programme asked the question, “Does God Do Maths?” and they spoke to some Christian mathematicians about the relationship between their faith and mathematics^{[1]}. Toward the end, the producer asked me about the relationship between mathematics and music. I suggested mathematics might be the music of heaven! They liked that, and it was featured at the programme’s start. But what did I mean?

I have loved music for as long as I can remember, before I was interested in maths. By music, I mean blues, rock and roll and the like. I admire classical musicians, but their music does nothing for me. Sorry to all classical music lovers. I learned to play electric guitar and, for many years, played in church worship bands. However, I don’t generally think of music and mathematics at the same time. So, what is their connection?

### Logic

Firstly, both mathematics and music have a logical structure. Mathematics is about examining structural patterns and drawing conclusions. Likewise, in music, whether it is scales, harmonies, or the verse-chorus structure of a song. Each has its rules to be followed, yet the rules are capable of never-ending variations. Both mathematicians and musicians are explorers working their way through the logical landscape of their matter, bringing new insights and creation.

### Beauty

Secondly, both mathematics and music possess beauty. To mathematicians, there are beautiful equations. Take, for example, Euler’s formula^{[2]}. It contains all the most important numbers in mathematics: 0, 1, e, pi, and the imaginary number I:

As someone who started their life in Astrophysics, I regard Einstein’s gravitational field equations as one of the most beautiful^{[3]}:

Its beauty lies in its simplicity and the profundity of the physical principles contained within it. The equation is not just a set of symbols but is embedded in the vast logical structure of differential geometry and properties of the real universe. There is so much implied by such a short equation.

Likewise, music has beauty. It could be the moving lead guitar lines of BB King in “The Thrill is Gone” or the sheer energy of Elvis’ version of “Hound Dog”. Perhaps it is the often tortured lyrics of a Hank Williams song or the feeling of Thea Gilmore delivering her own personal story in song. Music’s beauty is its ability to *move* people and elicit an emotional response. Is that not what mathematics does to those who search its depths?

### Creator

Through their logic and beauty, both music and mathematics reveal the minds of their creators. We know how Hank Williams feels from his lyrics and singing. We know how BB King feels from the notes that are played. Such music must have a creator and the form of that music says much about the person who created it.

Likewise, the mathematical “universe” must have a creator. The mind of God is revealed in mathematics. We know how God feels by the way mathematics is structured. Its logic gives insight into the logic of God. Its beauty speaks volumes of God’s beauty.

### Mathematical Universe

Notice I said the *mathematical* “universe”^{[4]}. This is much bigger than the physical universe that we normally think of as creation. Of course, the physical universe is included. But there is so much more when mathematics is considered. As a research student, I was often struck by the fact that I could prove certain things were true even though they had no manifestation in the physical universe. If that physical universe was taken away, such things would still be true. To me, the mere existence of mathematics shows there is a creator. God does maths!

If heaven is God’s domain outside of this physical universe, and God does maths – a system that reveals his mind, then I think I could be convinced that mathematics is the music of heaven!

### References

- All Things Considered, Radio Wales. Programmes are only kept for a month.
- For an intro to Euler’s Formula for complex numbers see Maths is Fun.
- Einstein’s gravitational field equations are a bit tough. You could try watching Einsten’s Field Equations for Beginners!
- People speculate about the mathematical universe. See WikiPedia and the paper by Max Tegmark.

**Tags:** Einstein, Euler, Music, Radio Wales