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The geometry of genius

December 01, 2016
To a pure mathematics genius, the unsolved problem looms like an unconquered peak to a mountain climber. “The driving interest for us was that we couldn’t solve it ... so we had to solve it,” says Brisbane maths mountaineer Ivan Zelich, “It was something that no one had found before, so it was much more encouraging to try and solve it.”
In the final episode of Decoding Genius, host Lily Serna tries to get inside the head of Zelich, who was a 17-year-old schoolboy when he co-published a mathematical theorem with an American teenager in 2015.

To put it in context, Serna asks Zelich if creating a new theorem is perhaps 10,000 times more exciting than solving a difficult Sudoku puzzle, and Zelich politely points out that, “you could consider it in the same realm, but … Sudoku is solved by someone, it’s proposed, so when you’re doing it, you know there must be a solution, but when you create your own theorem, you don’t even know if it’s possible…”


"Maths is the language of the universe and I love to see how it’s related to things in real life,” says teenaged mathematics genius Ivan Zelich.

The great leap forward for geniuses such as Zelich is that no longer do they have to tackle the mountains alone: the internet means that even teenagers a world apart can find each other and collaborate, something that wasn’t possible just a couple of decades ago.

Zelich and Xuming Liang, a fellow teenager in San Diego, USA, met in an online maths chat forum and discovered they were working on the same geometry problem. They compared their approaches and combined their brilliance. “Together we managed to finish a problem that we couldn’t finish,” Zelich explains in Decoding Genius. The result is the Liang-Zelich Theorem, a fundamental result in geometry.

Zelich Liang Theorem by GE Australia on Scribd

“Having a research paper published represents knowledge that’s new to humanity,” says Zelich’s university professor, Peter Adams, who says their youth makes their achievement completely astounding. Serna explains that the very fact that technology has made it possible for such geniuses to find each other and work together has supercharged collaboration, and augers well for humanity.

The episode wraps up Serna’s journey through genius, exploring the Mensa society, the way that giftedness is set alight, how the IQ of the global population is changing, the neuroscience of the subconscious brain and a mysterious sixth sense to which geniuses seem to have access.

Her interview with the thoughtful Zelich is truly inspiring. The teenager, now 18 and studying a Bachelor of Advanced Sciences at the University of Queensland, said at the time his theorem was published that he wants to use his genius to “contribute to humanity in the best way I can … either through neuroscience or understanding the universe through string theory and quantum mechanics”.

As much as he loves pure mathematics, Zelich knows that brilliance only makes an impact when it steps beyond theory. The ability to think creatively and differently is a critical partner to genius, says Zelich, “because if you don’t have creativity, you’re not going to create innovations.”

New to Decoding Genius? If you’ve missed other episodes in this mind-boggling series, check them out and fill your ears with synapse-igniting brilliance. We can’t all be geniuses, but we can all be inspired!