Mathematical artist: why hyperbolic space is awesome

Dried apples, ghostly skirts, beads and twisted balloons are just some of the tools Vi Hart uses to explore hyperbolic space, a Pringle-like geometry where angles in a triangle add up to less than 180 degrees and the parallel postulate of Euclidean geometry – that that there is only one straight line running through a given point that is parallel to another line – breaks down.

(Image: Kendrick Brinson)

With no formal training, the 22-year-old has been breathing life into mathematics conferences for years. In 2009, she started posting videos to YouTube, including the poignant tale of a triangular creature called Wind who lives on a Moebius strip. Her videos went viral and have garnered more than 3 million views.

She tells New Scientist why mathematics classes should focus more on “what’s awesome” and how art can inform the subject.

See more: “Weird geometry: Art enters the hyperbolic realm”
What motivates your various mathematical creations?
Curiosity. If I put together things in a certain way, what will happen? Sometimes I don’t really know. That’s really exciting.

How did you get into recreational mathematics and mathematical art?
Basically through my father [the mathematician, computer scientist and mathematical sculptor George Hart], following him and tagging along to conferences when I was younger. Conferences are wonderful places to meet many people who are doing what they are passionate about. They are very inspiring. I basically live and breathe math conferences.

You majored in music in college. To what level did you study mathematics formally?
The idea of a “level” really makes no sense. There are so many parts of mathematics. I didn’t take any math classes in college but I learned so much at these conferences. When I was younger, I would go to talks and not really understand anything; maybe pick up on a few key concepts,

or look at pretty pictures. The more I went, the more I learned.

The things I was learning were often things that you don’t learn until grad school. And by then I was missing the stuff that any math major knows very well. So I know a very different set of things than your average math person.

Was it hard to learn about these concepts without formal training?
You don’t actually need to know a lot of the groundwork and the basics to appreciate the exciting bits of mathematics. The more technical things are still awesome as tools and are necessary in some places. But luckily I am usually with other people who do know that stuff.

How did you resist studying mathematics?
They don’t teach a lot of the stuff that I am trying to show at college. Every school should replace calculus with recreational math. There’s all this fun beautiful stuff that people would enjoy. While some of the other math is more useful for some jobs in the real world, it isn’t actually necessary for the average high-school student to know calculus. We should be focusing more on how beautiful or awesome things are.

Every day I get an email from somebody saying, “Thank you for showing me that math is awesome – I had no idea that it would be that cool”. That is very gratifying to me. I have to show high-school students that what they are learning is not what math is.

A lot of your creations centre on hyperbolic space – why do you like it so much?
It’s basically a different set of assumptions about how geometry might act in space.

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Mathematical artist: why hyperbolic space is awesome