The Most Amazing Math Discovery of 2023: Einstein’s Hat

The Einstein or the Einstein Tile was discovered this year. It is an asymmetrical shape that can cover any flat area in a non-repeating pattern.

Its mathematical name is ‘an aperiodic monotile’. 

From Scientific American

David Smith, a maths hobbyist, discovered it this year, and named it ‘the Hat’. The Red tile above shows why he called it ‘the hat’.

Mathematicians know a lot about periodic monotiles and the patterns produced by tessellating shapes such as squares on a chessboard or hexagons in a patchwork quilt (below).

But an ‘aperiodic monotile’ producing a non-repeating pattern is rare. This could be the simplest example ever discovered. The monotile is called ‘the hat’ or ‘the Einstein’. Obviously, it should be called Einstein’s Hat. (Below)

Eintsein 1920

Meanwhile, the National Museum of Mathematics (MoMath) in New York and the United Kingdom Mathematics Trust (UKMT) in London became so excited about this discovery, they ran a competition asking members of the public to submit creations using Einstein’s Hat. A panel of judges assessed 245 submissions from 32 countries.

Here are some of the submissions highlighted in an article by Siobhan Roberts in the New York Times ( What Can You Do With an Einstein?,10 DEC 2023):

Evan Brock,  31, Product Designer from Toronto took out one prize with his Einstein’s Hat Ravioli.

Garnet Frost, 70, of London made a 24-foot frieze with 1,500 ceramic tiles.

Nancy Clark, 11, of London, made an Einstein’s Hat hat.

What could you make?