The person that solved this was a GOD at minesweeper

Me putting 0 in every cell

PLEASE make a longer video on this.

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

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.

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

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.

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

Spinal chills, your eyebrow gives...

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

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

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.

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'.

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

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

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.

They’re making a problem for themselves at this point

Beautiful AND smart..... those researchers probably.

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

As a student majoring physics, my disappointment is immeasurable and my day is ruined.

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

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

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

Your passion is infectious! Thanks! 🐞

it feels like everyday we hear about a new proof in graph theory that "challenges the definition of mathematical proof" because it was computer assisted i mean, the proof for the 4 color theorem is almost 50 years old

I like how you say "idear" very satisfying.

I guess filling the grid with 0's or negative numbers works but that's not what we're looking for. ^^ A long video on this would be super interesting! :)

I absolutely ADORE you!

the way mathematicians keep solving arcane problems I have troubles even thinking of lmao

I can't cope with the eye brow wiggle

i like the way you hold the mic like an British royalty drinking tea :D

Oh no! You missed an opportunity to say “Manhattan distance metric”! 🙁

Ah! Similar to the 4 color theorem.

Does it actually challenge the way we think of math proofs though? On face value, it doesn't seem dissimilar to the proof for the four colour theorem (as in, regarding the use of computational methods for proof)

The moment she started explaining I got confused and realized why answering this took 20 years

I love your videos!!

Cool! I'd like to know how/why it's 15 though!

I think if he is 20 years old he could solve himself, he really needs to grow up

Appel and Haken provided a computer assisted proof of the Four Colour Theorem in 1976. I think think this was the first computer assisted proof.

This must be heaven for people who love sudoku

Omg I love your wall decor! I recognized the Einstein Field Equations, but can’t say I’m familiar with the other two though. This is like exactly what I need for my house, thanks for the inspiration

Now include the rule measuring in diagonals as well. How many numbers would you need?

NO WAY I JUST THOUGHT TO MYSELF THAT 15 SOUNDED RIGHT, RIGHT BEFORE YOU SAID IT

Your vids are great. Would be more awesome if you could mention the potential applications of these mathematical discoveries as well.

So, it is extensible? If we change how we measure distance, or define a way to use fractions, can we find those magic numbers?

I’m sad to say I don’t understand the full implications of this but I know it’s yet another amazing discovery

Appel/Haken’s Four Color Problem was the first book I picked up at the institute library when I started studying math.

I can’t find references to this problem or its name. Does someone have the official name of this maths problem?

i love how high level math is just asking the most obscure, random question known to man, and then someone is just like, "i can figure this out" and writes like a 20 page proof on what the answer is

Ahhhh! You sank my battleship!

"They solved it in an interesting way-" i expected you to say guessing after that lmaoo

Forget the solution, I wanna know who are the people that come up with such math problems!!

"This discovery challenges our idea of what a mathematical poof is" That last sentence hits *hard*

It's interesting how so many of these unsolved/unsolvable math problems are just some sort of plane made up of shapes or numbers with a rule that limits the number of possible arrangements of said shapes/numbers, and then the goal is to try and achieve a specific arrangement despite the rule. What is it about that setup that is so compelling? I guess it's like a puzzle, but instead of having precut pieces and a picture on the box you have numbers/shapes and rules as to how you can lay them out.

can't help thinking "minesweeper" when I see that grid.

Yes, tell us how the idea of mathematical proof was challenged and what it the new or deeper view that is being suggested to replace the old limited idea. Please and thank you.

Please tell me from where can i get those really cool looking maths artwork that you have in the background

Could they generalize to n dimensions?

hey jade , how about making a video on the history of mathematics . How everything started - numbers , counting , etc .. and how those evolved ..

It makes me want to start by adding 1/2 + 1/3 etc. The ones take up half the space and I think the twos would take a third. But that quickly adds up to more than one. I'd really like a long video explaining this revolutionary proof

Here's a thought... unless you're trapped on an uninhabited island with only graph paper to play with... WHYYYYYYYYYYYY!?

Don’t forget the four color theorem, my personal fav also solved with a computer and solved in around 1980, don’t quote me on this. I love how this super simple problem has such a almost paradoxical solution

All thanks to the Indian Numerals system that made all calculations possible.

I doing research in packing coloring on graphs, trees.

Lol. You make everything sound fun. Hahah

I know you want my brain 💪 🧠 LMAO 😂. hope the math I left on the blackboard helps plus the other files I handed off to other people through conversations I've had

Computers have been used in a great number of proofs, both in finding proofs, testing hypotheses, data visualization and brute force exhaustive search. This has been going on for decades.

Did she say “how many numbers are needed to fill an infinite grid?” Infinite grid needs infinite numbers

Hexagonal version of this is also mathematiclly interesting.

Sudoku players: Now, this is a challenge

I am mathematician and even I don’t know why this was needed, first we were fascinated by cyclic geometry/ groups now we are fascinated by non random - sudo random patterns 😮, we are just a weird species !

Even the four color theorem of topology had been solved in the "untraditional way" in the 1970s. If a computer is used for proving a mathematical proof there should be no doubts raised so long the language used is Turing complete.

The first computational proof was the 4 colour theorem, and people kicked off about it then. It started off with clever maths and then turned into proof by exhaustion of over 1200 cases, which people dodnt like as a proof

On the square grid, it had to be one order of complexity greater then the complexity of any homotopy of unrestricted association. In the sphere, it's likely 23, being one more then compactness while limiting one to completeness, and still leaving room for soundness and a singularity.

Dangit, now I've got to come up with another totally random "problem" to stump mathematicians!

Thanks so much.

Do mathematicians just spend their time coming up with hypothetical problems then solving them? Like what is the real word application for this.

But what are the useful applications of this if any?

In short..they asked an AI

"Infinite [...] _fill_ "

This is actually a pretty good idea for a coding challenge.

How did they do it?

So the question was how many numbers can we fit in an infinite scale until it starts forming a pattern. Because when it does form a pattern you can stick that pattern up till Infinity

They solved sudoku!

The proof is basically "so we tried every possibility and this pattern is the smallest that repeats."

Would you be able to get away with just 2 numbers: 0 and 1? The problem probably is defined as "using natural numbers excluding zero", but this wasn't said in the short.

Could you please share a video explaining the idea and how it challenges our understanding on mathematical proof

mathematicians have run out of things to do and are doing side quests now, apparently

To that the letter "O" in the alphabet is also in numbarical or if the number 15. The letter "O" is symbolic of the circle 😊

I say that there's numbers are exclusively next to each other when they are diagonal

I’m curious about the potential practical applications for this.

Does this mean the answer was not 42?

So what was the process of this answer??

Well now I want to know what the magic number is for other regular tiles, like triangles and hexagons.

what use does that equation have?

What practical use is that?

From where those topics read

I want to see their reaction to solving the problem

Can we extend to complex numbers?

can you provide the documentation or the proof?\