Sharing the beauty of networks

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Dr Mason Porter discusses the beauty of network maths, and how he and his colleagues have pioneered a programme to teach others about this vital area of mathematical understanding.

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Mason Porter – Mathematical Institute, University of Oxford [MP]

I got into science based on what I find visually appealing. I saw lots of really nice pictures of lots of fancy patterns created, by mathematical objects called fractals and in trying to figure out how those pictures were created, I became interested more in the notion of mathematics and mathematical modelling itself and then I just kept asking why; never particularly stopped, don’t particularly want to stop.

The importance of studying networks lies in two facts; for one thing it’s fun (which is ultimately what I care about), for another it’s ubiquitous. It’s a language that shows up in many places and there’s a lot of mathematics underneath it and that also adds to the excitement of trying to learn about it.

We set out to teach students about the mathematics of networks. We’ve done this through workshops in Summerville where some students have come to visit and also through visiting them at their schools.

In many other areas of mathematics, in order to even explain the problem in the first place, you have to go through a lot of preparation and for networks you can say okay, well how do you think that Facebook recommends friends to you? and a lot of people who are young will already say, yeah, I wonder how that happens?.

We wanted to pick students who had not yet chosen what they wanted to study at university, so we focused on year 9; so 13 and 14 year olds.

Our own ability to communicate has gotten better. Sometimes we tried analogies that we thought might work but didn’t work, or we were using too much jargon.

I think the team has gotten better as things have gone on. I mean, that’s an obvious statement but it’s still nice to observe it.

I think the biggest surprise in the workshops was that the most successful module was a theoretical mathematics module about graph theory. I really like that stuff but I wasn’t expecting students to be necessarily as engaged in that one. We show the students, every planar map can be coloured by four or fewer colours but there was one student who just kept trying to get five colours and he was not deterred by the fact that we told him it was mathematically impossible and that’s the type of persistence that you want to see. So it really shows the power of mathematics because you just need the abstract mathematics presented in an exciting way.

Mostly the kids have reacted very well to this; we’ve gotten a lot of really nice, positive feedback. They seem to be excited.

Children from one of the Summerville workshops

I didn’t know about networks and I had never thought, really, about the four colours and the different colours in the maps.

It was kind of like a new perspective with maths. We kind of learnt that it’s not just about numbers and stuff, it’s just in day to day life as well.

[MP]

I am hoping that more of them will go into mathematics. The ones that don’t go into mathematics, I am hoping more of them will go into science. And even someone who just does the same thing that they would have done before, I hope that they go look at the world and they go outside after the talk, and throughout their lives, and say I see a network there.