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New shape discovered by University of Waterloo scientist makes TIME's Best Inventions of 2023 list


A University of Waterloo scientist has made a discovery which has found its way onto TIME’s Best Inventions of 2023 list.

Craig Kaplan, an associate professor in computer science, helped discover an “einstein” – a longstanding mathematical problem deemed impossible for more than 60 years.

An einstein is a formation of shapes that perfectly interlocks with one another, without gaps or overlaps, like the bricks that assemble a house. In an einstein, the pattern of shapes never repeats.

Until recently, scientists had yet to discover a shape that could create such a pattern.

“The first stirrings of this problem in mathematics were in the early 1960s,” said Kaplan.

Craig Kaplan holds "the hat." (Spencer Turcotte/CTV Kitchener)

In the math community, the concept is referred to as an aperiodic monotile. Mathematician Hao Wang put forward the belief in 1961 that such a shape did not exist. That notion remained until Kaplan and his international colleagues cracked the code.

“I chose the best possible route to achieve that, which is sit around and wait for someone to email you,” he joked.

That email came from David Smith, a retired printing technician in England. In it, Smith alerted Kaplan to the existence of “the hat,” called that because of its resemblance to a fedora.

Craig Kaplan, at the University of Waterloo, helped discover an “einsten” – a formation of shapes that perfectly interlocks with one another. (Spencer Turcotte/CTV Kitchener)

The hat has made noise around the world and it seems there could be practical applications of the shape on the horizon too.

“There’s been an incredible response from all kinds of hobbyists and artists and designers and craftspeople turning these into real world objects,” said Kaplan. “One example that I love is right here – this is a soccer ball,” he said, holding up the ball covered in the mysterious 13-sided shape.

A brewing company in Dublin created these cans inspired by Kaplan’s discovery. (Spencer Turcotte/CTV Kitchener)

While Kaplan insists there is nothing magical about the discovery, he hopes it helps shape people’s mindset when approaching future problems that may seem impossible.

-- With files from CTV Toronto Top Stories

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