@Sam_on_YouTube
They also got really lucky that the number WAS 30. They may have just ended up proving that it was greater than 30. And then we would have to try to prove it's 31.
@furbyfubar
Minor nitpick: Writing "Image from Flickr" is not giving credit to the maker of the image. In the case of the DNA Sequencing image it was by Darryl Leja, NHGRI. The image is in the public domain (at least as per how it's listed on Flickr) so legally you don't have to credit anyone for it. But crediting Flickr and not the person who made it rubs me the wrong way. It would be like if someone wrote an article about the contents of this video and credited the research and ideas in it to "YouTube". Also, for an image licensed under CC-BY it wouldn't count as properly giving credit to only write where you found it.
@cube_cup
That part of the 'if the triangle is empty, there must be an empty hexagon' is gorgeous! And that was Marijn's big breakthrough. The way you faded him out felt like you slighted him a bit. I really wanted him to explain it
@SellymeYT
36:24 "So if no human can read it, how can we know for sure it's valid? The short answer is that instead of making a human do it, we used grad students"
@kylewood4001
Someone HAS to formalize a constant for “atoms in the observable universe”, it’s referred to WAY too much for it not to be
@rocky_wang
Like the “Four Color Theorem”, the proof is a tedious phone book rather than an elegant argument 😂😂😂
@MoiraLachesis
Much simpler proof for quadrilateral: connect all pairs of points. If any two intersect, they form the diagonals of a convex quadrilateral. If none intersect, they you have a complete planar graph. Complete graphs with 5 or more nodes are never planar.
@davidblauyoutube
37:30 Whoa, I didn't know that the initial Four-Color Theorem proof was faulty. And I did know that the classification of finite simple groups was insanely lengthy, but I didn't know that portions were proved using computer searches. Good stuff!
@IsaacDickinson-tf8sf
I like that they divided by 0 through the transformation
@paulpinecone2464
Here is an interesting result based on things like Moore's law: If a computation takes more than three years don't do it. You will get the result faster by waiting. Obviously this applies to the length of mental work you might have to do as well. If the cost of a result is within the range of a few more than three years, although you might hasten it's discovery by researching efficiency techniques, it is unlikely to be worth it. Put it in the queue and go work on something that is not dependent on CPU time.
@awesomeleozejia8098
10:20 The issue is self-intersection. Consider a 5-point star, the five points will each have the same direction of turning but it also intersects itself.
@ManicShot
Beautifully presented and I can see the many hours of love that went into it. The interviews were insightful and helped it feel grounded. Can I make a suggestion? When you've finished a soundbite from an interviewee and you resume narrating, perhaps try cutting to something else, rather than staying on the subject and fading their sound out, because it appears as if you're talking over them. It's a minor gripe really, but thought you'd appreciate the comment that something there didn't quite feel right. Please don't let that detract from this being an excellent and truly well-crafted video. Looking forward to the next one!
@raedev
Did not expect to hear Mark Overmars be involved in this in any way. My gamemaker heart feels proud
@ytbvdshrtnr
At 16:01 I "knew" the answer couldn't be 30 because in Law and Order if they catch the bad guy 20 minutes in, they've got the wrong guy because there's so much episode left. And there was still a lot left to this vid.
@khoda81
OMG, sat solvers are my favorite thing. Please make a video about how the proof verification works!
@jimsmindonline
I love how so many problems in mathematics start with a simple question, and often balloon into so many ideas it becomes almost overwhelming! But there's often a simple pattern in there somewhere, which we as humans love so much.
@pineapplewhatever5906
3:35 I can't help but notice that the four known cases are powers of two plus one.
@rocketlover-v8g
26:16 Wow, the middle triangle proof is very elegant! This is math-gasm worthy!
@puernatura8998
Not only did George and Esther Szekeres remain married for the rest of their lives, they both died on the same day within an hour of each other. 28 August 2005.
@PurpleMindCS