Vivas and Prime Numbers

“Anything could happen!”

I’ve heard academics and PhD candidates say that about the viva, and while there’s a sort of truth to it, the statement also misses a lot. Anything could happen, but it rarely does. The vast majority of vivas are completed within three hours, most vivas have two examiners and there are common opening questions. While there’s no way you could expect a particular script of questions they might ask you, you can reasonably expect certain areas to come up.

Going back to my pure maths days, the topic of viva expectations reminds of prime numbers. There are infinite prime numbers – 2, 3, 5, 7, 11 and so on – numbers which can only be divided by themselves and 1 without leaving a remainder. There is no end to them. And yet there are many, many ways we can categorise them.

There’s one even prime, and infinitely many odd ones. There are primes that form little pairs, twin primes, which are separated by adding 2, for example, 3 and 5, 5 and 7, 11 and 13. There are primes like 23 and 37 that aren’t twin and don’t form little couples. After the number 2 we could group together all primes according to whether or not they are 1 modulo 4 or 3 modulo 4 – but really we’re getting away from the topic here!

There are infinitely many primes, they go on for ever – and yet there are many useful ways we can group them, categorise them and learn from them.

There are countless different vivas, anything could happen, but also patterns and structures that we can see and even expect.

Again: anything could happen in the viva, but “anything” very rarely does. It’s far more useful for you to find out about common expectations and learn from them than to try and prepare for infinite possibilities.