The Hat: an aperiodic monotile

This lecture and panel discussion celebrates the discovery, by 'amateur' mathematician David Smith, of a single shape that completely covers an infinitely large flat surface without repeating: the Hat (and its companion, the Spectre).

Chaim Goodman-Strauss, one of the authors of the paper describing the new work, will give an overview. This will be followed by a panel discussion with Chaim, fellow author Craig Kaplan, mathematician Marjorie Senechal and Nobel Laureate Roger Penrose. The discussion is chaired by Henna Koivusalo.

@OxfordMathematics

[JellyMonster]

I had two amazing days at the Hatfest. Great to see and hear the talks and discussions again.

Just to recap, the hat (8-kite) and turtle (10-kite) are polyforms, whereas the Spectre is not (it cannot be placed on an underlying periodic grid) and so is pretty unique.

A big thank you to the organisers and others that had come from far away places (some gave me gifts!).

Oh, and I should say that I'm not an amateur mathematician either.

[alienalajna]

Back in high school, I loved math. When we got to calculus, I found it no less than beautiful. My classmates who struggled with it found my enthusiasm weird. I went in another direction (art), and so now much of what you say is way over my head. But I have also intuitively always loved patterns as a sort of manifestation of natural law. (Big fan of Escher.) But the term "amateur" came up. I agree that it shouldn't be a disparing term. In the late 1970s I worked as an assistant to the noted photographer Irving Penn, involved partly with his commercial photography (fashion, products, portraits, etc.) and partly with his personal work. A brilliant but very modest man, he once referred to his personal pursuits in photography as his "amateur" work (pronouncing the hard "t"), in the original French sense of one who does it for love, not as a mere dilettante. So let's hear it for amateur mathematicians! (When I first saw the hat, it seemed to me a t-shirt.)

[quasi-crystal]

30:58 As a professional toilet fixer, I can say I have had the absolute pleasure of fixing this man's toilet

[zehlenmath]

Can someone tell me where can I access the software that I can generate the pattern of Einstein tiles

[alienalajna]

Agggh! Sorry again! "Home, home on the range...deer...antelope etc.... - where never is heard - a discouraging word - and the skies are not cloudy all day". NOT "disparaging", which is a bit short of a synonym. You can tell I'm not from Texas - I don't have the proper aperiodic hat.

[chrisholding]

Its the job of the tyler to ensure the building is tiled? 😂🎉