I don’t know how best to describe this; the only time I have ever shed tears in school (and this is not a metaphor or a fanciful example or hyperbole; I mean real tears running down my face and dripping on my copybook) was when I was aged eight, in Second Class, and trying to understand the maths problem we had just been given – and failing miserably.

The teacher was sympathetic but baffled; no matter how she tried to explain it, it Just. Did. Not. Click. With. Me.

Other subjects, I could feel my mind “wrapping around” them (think of an enzyme binding to a substrate) – it was like my brain ‘reached out’ and took hold of the concept.

Maths – no. It was like trying to jam a key into a lock where you couldn’t even get it in the hole, never mind force it to turn.

It still functions like that – I get so far and then – jammed up. No shape. No way this will fit. You may as well tell me “Just flip your left hand over and you’ll have two right hands!” when it comes to getting my head round maths.

Now, of course, I have to believe that Deiseach is telling the truth about her experience - that she just gets permanently stuck after a while and can't wrap her mind around something.

But if I were teaching a math class, and I had a student cry because she didn't understand the material - not because she couldn't get the right answer on the test, or because she couldn't perform the calculations, or memorize something, but because she didn't understand - then I would identify that student as special, and worth cultivating, and possibly unusually talented at math - because she knows the difference between getting the right answer and understanding the math!

Math is big and it has lots of parts. There are lots of different ways to get stuck. You can be stuck because you're just not familiar enough with some common identities or ways of solving equations, in which case the solution seems to be slogging through a bunch of problem sets or flashcards until you get it. But then there is another type of stuck, where even if you can follow each step, the whole thing makes no sense to you. Some people never even know that it's supposed to make sense. Others are bad at telling the difference between a proof they can recite, and one they really grasp intuitively. But knowing the difference - that's gold.

When you're stuck on a concept, you can't just slog through the way you can when you're stuck on vocabulary. You have to take a break. Sometimes your brain is tired. Sometimes you need to see something used in a few different ways. And sometimes you've gotten stuck because you're trying to understand it one way, and that doesn't work, and your mind needs time to reset before trying another approach.

And then, of course, if there's something basic you've missed, it can be really hard to notice that too. Unfortunately there don't seem to be good, readily available checklists to go through to see whether you've missed some simple identity or definition that a proof relies on. I've had a weird mathematical education, so it's happened many times that I've been stuck on a problem forever, only to find out that there's a well-known, easy to prove mathematical identity that makes the problem trivial, that I would have recognized the application of immediately, if only I had ever heard of it.