So why do you, to your mind, Professor, do you think a lot of people find maths intimidating?

I think when people think about doing maths, they think about being put on the spot.

in class and being asked to do a question in their head.

And that is difficult.

I hate doing that.

If you give me a big sum now, I'll turn around to you and I'll say, no, I'm not doing that, because that's not what maths is actually about.

In maths, you can sit down and you can take your time doing things.

So if you could, for example, help people see one everyday situation differently through the lens of maths, what would you choose one and what might they discover that they had never noticed

It's a bit much for an afternoon's, you know...

Yeah, it's just for a Sunday afternoon diversion to just go and invent a whole new branch of maths.

But this was Euler.

He was, you know, the genius mathematician.

He decided what he would do was abstract each of these four landmasses into points, now called vertices.

And then he connects these vertices with lines, which would be called edges nowadays.

And those lines represent the bridges connecting the different landmasses.

And maybe you can talk a little bit about some of the examples of where graphs show up in everyday life, because they're everywhere, right? Yeah.

Talk, talk about the feedback loops that you mentioned and the, and the self-fulfilling prophecy, what that's all about.

Well, so there's two.

There's this-- there's a, a positive feedback loop can lead to a self-fulfilling prophecy, so that's a, you know, prediction that someone makes, which makes itself come true.

So a, a nice example of that is the placebo effect in medicine.

You know, in, in medicine, um, we have to control for the placebo effect because, uh, what effectively happens is when people get a treatment, even if that treatment has no sort of active chemical in it to actually treat the, the disease that's being treated, people start to feel better simply because they're being treated.

It's often called the lie that makes itself come true.

So we have to make sure in medical trials that we have two arms: one that are given a placebo, so a sugar pill, if you like, and the other that are given the active drug, because just being treated makes people feel better.

But you're saying that coincidences happen-... a lot.