20-year-old math problem SOLVED! The packing colouring problem

[yuCantHandle]

The person that solved this was a GOD at minesweeper

[labibbidabibbadum]

That will be staggeringly bad news to those people who just happen to own an infinite number of square tiles numbered 1 to 14.

[yoweedmofo]

A few decades back, and a few blocks away from CMU (at Pitt), Hales solved another packing problem (the 400 year old Kepler conjecture), also with a computer-assisted proof.

[-MrFozzy-]

I think we’re missing the big story…..the worlds tiniest handheld microphone!

[alexhidell]

I think I figured out Heesch numbers. It's a tessallation BUT it must be finite. That's why the highest number is 6.

[sulanis]

her smile and natural excitement for the topics she talks about makes me want to listen even more.

I never heard of this problem, but its amazing that its been solved. on to the next one.

[nyuh]

oooohhh i would LOVE to learn more about this
such an interesting problem !!

[stapler]

I was under the impression that major graph theory proofs often involve a lot of computer-assisted math, because the scope of such problems can be pretty huge.

[steffahn]

Does it really challenge our idea of what a proof is? As far as I remember, there’s quite a few mathematical proofs that heavily involved computers, e.g. famously the four color theorem; is there something particularly new/different about the way this problem’s proof used computers, compared to how others before it did?

Other than that, great presentation, by the way.

One thing that’s always interesting with such results of “what’s the minimum number of…” is to outline the history of previous results. E.g. what lower-bounds or upper-bounds were known before the final proof that finished the result, nailing it down to 15. In particular, e.g. if previous results may have already shown that 15 is an upper bound (i.e. that packings with numbers only up to 15 are possible), that would be interesting to call out. I always find such results of “this and this upper/lower bound was proven on such and such date” neat, not least to demonstrate how incremental and actively worked on mathematical theory and results can actually be.

[StylosetPapier]

You’re brilliant, entertaining, informative, and lovable.

[maxzet]

it's like they try to solve puzzles no one asks in the first place..

[glenneric]

Beautiful AND those researchers probably.

[caspermadlener]

Belgium people would probably fill up the entire board with ones, since the distance isn't *stricly* bigger than 1.
Love you, Belgium people <3

[Purriah]

If I see ONE MORE pretty, intelligent, soft-spoken, well-articulated math YouTuber, I’m becoming a mathematician.

[jessewilliams]

I like how you say "idear" very satisfying.

[dannygjk]

I had a teacher in grade 8 who had the same accent quirk you have. When saying a word like 'idea' he would do what you do by pronouncing it as if it was spelled 'idear'.

[emex]

It is true. People are the prettiest when they talk about something they really love with passion.

[yuvrajsarathe]

An extremely great example of what a man could do while following NNN🔥🔥🔥🔥

[tomasstana]

Wow, so that's a second unsolved tiling problem solved this year. Could it mean something ??🧐😀

[headlibrarian]

The notion that a computer proof is invalid hasn’t been a thing since 1976, when the map coloring problem was solved.