Tomorrow, that is Saturday 8 June 2024 at the time of publication, I’ll be heading off to Big Finish Day.

Every year since 2016, Big Finish has run the Paul Spragg Memorial Competition. It’s a competition that invites writers (who are not already published by Big Finish) to submit a short story idea, accompanied by a 500-word extract. One lucky person will then be commissioned to write their story, have it performed by an actor and see it published (for free!) before the end of the year. I’ve thought about entering it myself a few times now, but haven’t managed it so far. Turns out that thinking of a great story idea and then turning it into good prose is actually quite hard.

I have managed to jot down a few story ideas though. One of them was about the French mathematician Evariste Galois (1811 – 1832). He is best known for his work in number theory and group theory; he even has an entire branch of mathematics named after him called Galois Theory. He was also quite politically active and was repeatedly arrested during his short life for his political activities, spending several nights in a prison cell. I’d already written a pretty neat blog about how Galois sort of features in Matt Smith’s debut episode here!

Galois wound up being fatally shot in a ‘duel of honour’ on 30 May 1832. We’re not really sure who shot him, or who he was shot over (presumably a mutual love interest with the other duelist) or why he felt compelled to write down all the maths he knew the night before the duel. I thought these question marks over the final days of his life would make an excellent Doctor Who story. It taps into a similar vein to other historically-based Doctor Who stories such as why Charles Dickens was inspired to write his final (unfinished) ghost story, or why Agatha Christie mysteriously went missing for nine days.

But now, I cannot submit this idea as a Big Finish Short Trip. Somebody has got there first.

The Galois Group is an Eleventh Doctor and Valarie story, written by Felicia Barker and read by Safiyya Ingar. For those not keeping up with Big Finish’s extensive output, Valerie Lockwood is an audio-original companion played by Safiyya Ingar. She’s a human with cybernetic augmentations from the 54^th Century and first meets the Eleventh Doctor, played by Jacob Dudman, in the third volume of The Eleventh Doctor Chronicles, beginning with The Inheritance, a riveting story about a virus spreading through the digital money system. Here’s the synopsis for The Galois Group:

There are rules to travelling in time, rules that Valarie Lockwood thought she understood. But, when she has an opportunity to break those rules, she seizes the chance. Valarie’s going to have to learn the hard way that the laws of time are there for a reason.

Rather than focus on the mystery surrounding Galois’s death, like I had previously suggested, Barker has come up with an even cleverer idea that instead takes us into the realms of mathematical horror. Doctor Who has done this sort of thing before on both TV and audio. The Twelfth Doctor episode Extremis written by Steven Moffat sees the Doctor and his companions discovering they are living within a computer simulation and must confront their artificial nature of their existence. Meanwhile there’s a Fifth Doctor audio drama called Iterations of I, written by John Dorney, which is a ghost story about people being turned into imaginary numbers by an iterative computer program.

The Doctor and Valerie find themselves trapped within a space-time paradox as the Web of Time gets fractured by meeting of multiple versions of Galois. This is, thematically, quite neat when you know that Galois is best known for his work in group theory, an area of mathematics all about using abstract algebra to describe the symmetry and structure of objects. Galois essentially becomes the victim of his own mathematical ideas through sheer bad luck. Almost as bad as the luck he had on 30 May 1832. As the Doctor quips at one point, “It’s paradoxes all the way down!”

The solution to their predicament lies in solving the maths problem at hand. The Doctor says that he must “Draw a diagram!”, a phrase I heard so many times throughout all the lectures I attended during my mathematics degree. Barker has even taken on this advice herself to ensure that the maths does indeed check out. I love how I managed to predict there would be no less than four versions of Galois in the story given that four is the minimal size of a finite (or Galois) field. I’ll let you Google what that is for once. Just trust me when I say it’s clever.

There’s also several bits of mathematical geekery and wordplay going on: the versions of Galois trade looks of “mutual non-plussedness”; the first version of Galois is denoted as Galois prime (G’); the solution is declared using QED (quod erat demonstradum); and there’s even “an asterisk hanging over the answer” (asterisks are commonly used in group notation).

One of Galois’s other great contributions to mathematics was that he was the first mathematical to come up with an ingenious proof that there is no general solution by radicals (a fancy word for algebraic roots) for solving quintic polynomials, which are algebraic equations where the highest power is five. You might just about recall learning the quadratic formula in GCSE maths, which solves algebraic equations where the highest power is just two. So it’s basically that on steroids. Once you know all that, and that Galois was a politically active mathematician, the moment when the Doctor declares that “There simply exist no radical solutions” suddenly becomes a lot funnier. Or maybe it’s just me?

So if you fancy learning a bit about one of the cleverest and most tragic figures in the history of mathematics, or just want to hear a great story, then I highly recommend you pick up this boxset of Short Trips as soon as possible. And if you fancy learning another connection I’ve spotted with Galois and Doctor Who, you can read all about it here.

Oh, and a very Happy Big Finish Day to all of you at home!