How a Hobbyist Solved a 50-Year-Old Math Problem (Einstein Tile)

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As Dave got his fair share of praise in the comments and the real world, I like to thank and praise the "trained" scientists for supporting Daves' finding and setting his name even first in the publication. I like it!

That is not the guy I was expecting to see singlehandedly solve a 50 year-old math problem. What a legend

The way he casually proceeds to discover more versions makes it apparent this discovery was not a fluke but a stroke of genius! So weird that a cut-up multi-hexagon didn’t prop up in an exhaustive search of some graduate’s geometric sim or something.

Can you imagine those mathmaticians while working on the first proof? “Alright guys, this is big. We’ve possibly got an Ein Stein tile, we need to spend all our time with this. This is a mathematic breakthrou-“ phone rings “Dave? What is it? We’re working on proving your tile!” “I’ve found another one.” … … … “What?” “I’ve found another one.” Dave is a goddamn legend!

Genuine props to Dave for discovering a full hat trick of advancements in aperiodic tilings.

Dave's achievements make me think of Escher, another person who approached quite mathematical geometric concepts from an artistic standpoint.

I love how Dave didn't just strike gold once, but three times and counting. It points to a way of thinking that isn't available to most mathematicians - and it seems to come relatively easily to Dave.

As a math enthusiasts in the middle of a home remodel, I think my tile guy is going to be extremely upset that I learned about this

it's amazing that Dave got credit, so many academics would have stolen/undermined his contribution. Bravo!

One thing I love is that Dave is credited as lead author on the paper, even though the way the story played out he discovers the shape versus created the mathematical proof (eg inspiration was the lead over perspiration)

I love stories of people with weird abilities. Without any formal training, this guy seems to have brain that’s somehow wired to find aperiodic tiles. It just goes to show how amazing the human race is!

Damn the production work of this video was insane. I really enjoyed the visualisations a lot. Thank you for all that effort.

Dave is a case of someone reaching an abstract solution after a life of empirical work, actually pretty common for craftsmen, but he knew to contact the people who could distill it into formal knowledge A great example of reaching out to people with similar goals but different methods

Dave seems like the epitome of the humble genius. A great video as always!

Dave has an amazing visual way of thinking. It is a gift and it is a gift that is very useful in many fields not just in mathematics and bathroom floor tiling.

This is easily the best exposition of the hierarchy argument. I've seen several videos on the aperiodic monotile but you're the first one to really help me grasp that part. Thank you!

This is so fascinating. I would never have thought that new mathematical discoveries could be made by mere mortals at this point. I was certain that would be a “a computer calculated the aperiodic monotile” video. Go Dave!

The amazing thing is that David Smith was not the first amateur mathematician to make a series of breakthroughs in tiling theory. In the 1970s, amateur mathematician Marjorie Rice discovered four different, previously unknown pentagonal tilings on the plane (among many other findings involving tilings). In 1999, one of those pentagonal tilings was made into actual floor tiles and used to tile the foyer of the headquarters of the Mathematics Association of America, in Washington DC.

There are some areas of STEM where you can contribute even without a formal background; where curiosity, lots of experimentation, an encyclopedic knowledge of the subject and a keen eye can carry you pretty far. My warm congratulations to Dave for spotting not one, not two, but three solutions to a half-century-old problem. Not that the three other collaborators don't also deserve credit for the rigourous proof, an essential part of the full solution. But this is the type of problem where coming up with a good conjecture is the most difficult part, not proving it. It was mainly Dave's insight and observation (and hard work, presumably) that cracked this one. So yeah... congrats to all, but Dave's the man! :P