Very busy so I had to do this one over dinner, think of it like a math dinner date! Join Wrath of Math to get exclusive videos, lecture notes, and more: kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin More math chats: kzbin.info/aero/PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO
@ethos8863Ай бұрын
The 317 joke is severely underrated. I've been giggling a while after that one
@kyay10Ай бұрын
Any hints on what it is? Obviously it'd reach 325, but i don't see the joke there
@ethos8863Ай бұрын
@@kyay10 the joke is that the way he was going made it seem likhe was about to prove the lower bound was 325 and then he casually says the lower bound is actually just nine, one number higher. it's funny as in "if the number is 9, why did you say 325?"
@WrathofMathАй бұрын
The joke is 1) that one would be dumb enough to suggest such a large sequence when we know a much smaller one is sufficient and 2) it's amusing foreshadowing for the actual upper bound of 325 that we prove later in the video
@JacksonBockusАй бұрын
To me the pigeonhole principle has the best combination of “incredibly obvious fact” and “incredibly unintuitive implications”. So many weird facts can be proven by creatively transforming them into applications of the pigeonhole principle.
@poorman-trendingАй бұрын
That’s got to be the nastiest looking piece of pizza I’ve seen in awhile.
@billiboi122Ай бұрын
My gluttonous ass would still eat it
@SamuelBrown-g7dАй бұрын
@@billiboi122same
@davidroddini1512Ай бұрын
I don’t know. It doesn’t look nasty to me 😜
@headpenguin8758Ай бұрын
looks like raw meat
@friendfrequent3330Ай бұрын
call this a mario bros speedrun cause why he eating a pizza?
@WrathofMathАй бұрын
very hungry, I ate an entire Shaq-a-roni pizza
@acmhfmggruАй бұрын
Yes, absolutely you should make video(s) on Ramsey's theory. There is intetest!
@WrathofMathАй бұрын
Good to know! I have to make some lecture videos on the subject still for my graph theory playlist, but they are a great candidate for these more casual video as well.
@omegahaxors9-11Ай бұрын
This is like a mathematical version of "you need at least 3 colors to make a map of countries without overlap"
@landsgevaerАй бұрын
You need 4, on a plane. Which in itself already is mathematical problem.
@der.SchtefanАй бұрын
The only colour you need is Farrow&Ball. Their magnificent colours remain unmatched!
@CY3O923Ай бұрын
0:00 Dam, that pizza looks good and 1:18 Can i have some?
@WrathofMathАй бұрын
all gone :(
@ethos8863Ай бұрын
I think the van der waerden problem has a very simple reason it must be true. It's hard to verbalize succinctly but essentially, of any given length, the number of unique ordered colorings is finite. After that length, you must either pick a new coloring or reuse an old one. If you reuse an old one, you now have the restriction that going forward, the distance between this coloring and its earlier use being d, in d turns, you cannot reuse this coloring, so you have to use a different coloring(which also must be a reuse if an old coloring). What happens is you essentially create a bunch of "mines" which limit the colorings you can pick over some interval. The outcome is that you run out of colorings and must pick a coloring which hits landmine, so to speak
@WrathofMathАй бұрын
Well said!
@landsgevaerАй бұрын
Now turn that into a proof... 😉 Like, if every next layer of mines add a probability 3^(-n) of being hit, the total probability of hitting a mine still only amounts to 50%. Or, more to the point perhaps, prove that it is impossible to smartly lay the mines such that a narrow path always remains. There is a reason why proofs are required to be rigorous. And why theorems that have already been proven often seem obviously true in hindsight. Otherwise you would be able to prove the twin prime conjecture and what not with this reasoning as well...
@isobarkley23 күн бұрын
holy shit those sharpies are CLEAN
@WrathofMath22 күн бұрын
only use the best!
@Happy_AbeАй бұрын
The proof seemed to only work because you assumed the third entry in Bi and Bi+j was a red. Otherwise we wouldn’t get a sequence from the first in Bi to the third in Bi+j and so on. It will still work but i think the case where the 1st and third entry in Bi have different colors should be addressed too.
@henryptungАй бұрын
Yeah, the proof rushed a little. Could have gone through the cases in sequence, assuming WLOG that the first entry is red: 1. Second entry red: If third is red, then internal progression. If third is blue, then use proof argument (1-2-3 instead of 1-3-5). 2. Second entry blue: If third is red, use proof argument, If third is blue, use proof argument but in decreasing order (3-2-1 instead of 1-3-5). Would better illustrate the general idea of using multiple sequences targeting the same element (in the i+2j segment) and constraining it so all color choices result in a color-matching progression. Would also demonstrate why the choice of length 5 is important (you're guaranteeing the presence of an AAB or ABB color progression).
@Happy_AbeАй бұрын
@ fully agreed, that’s great!
@WrathofMathАй бұрын
Yeah for brevity I covered that one specific case, as the others are similar. Glad to have them addressed here!
@danielrhouckАй бұрын
This feels similar to the monocolor rectangle problem from 2 weeks ago. Interesting applications of the Pigeonhole Principle for coloring points
@WrathofMathАй бұрын
Pigeonhole principle is constantly useful!
@GestersmekАй бұрын
I'm assuming the answer is yes, but is it a coincidence that the Van Der Waerden numbers of W(2,3) and W(3,3) happen to be equal to 3² and 3³ respectively?
@TyroRNGАй бұрын
Given that W(4,3)=76 and not 81 I think it can be assumed to be a coincidence.
@DoogeАй бұрын
This is the law of small numbers, there's just so few integers at the start of the number line that patterns will arise where there aren't any / there might be a more complex predictor that we haven't found
@andrewkarsten526818 күн бұрын
@@TyroRNGdo we have w(r,3)≤3^r by chance? That would be a relatively nice result for an upper bound
@hello_hi1Ай бұрын
Both of the cases look like where k is 3 look just like k^r
@txikitofandangoАй бұрын
Swank
@phyphorАй бұрын
"gargantuan" ... Graham's number laughs
@ciCCapROSTiАй бұрын
I love tinkering like this, does it actually have any real world use?
@empathogen75Ай бұрын
It gets used in computer science in a variety of ways, as are most of the interesting results in number theory, eventually.
@charlesmarshall7045Ай бұрын
Are you secretly sponsored by fluorescent marker makers? :)
@WrathofMathАй бұрын
Nope, just Papa Johns!
@bigjazbo9217Ай бұрын
If you like this sort of thing, you must buy "Three Pearls of Number Theory" by Khinchin. The proof of Van der Waerden's Theorem is the first of the three "pearls" in this short and very inexpensive book. Khinchin was one of the great mathematicians of his time. He presents the proof clearly and methodically. (The other "pearls" are equally compelling.)
@WrathofMathАй бұрын
I think I have heard of that book, but I don't have it - I'll definitely check it out!
@frogstudАй бұрын
Reminds me of the sock drawer
@WrathofMathАй бұрын
True
@cotlimАй бұрын
3:16 Thats why 7 ate 9
@WrathofMathАй бұрын
Agreed
@meoutpeaceАй бұрын
well i'll just color from 1-9 and color 0 blue so then i don't have that sequen... well, i'll have a +1 progression and, uhh OKAY YOU GOT ME!
@wilTfrieАй бұрын
you said: 1red 2red 3blue 4blue 5red HOLD ON 5 -2 --- 3
@andrewkarsten526818 күн бұрын
That’s not an arithmetic progression though, 1,2,5 doesn’t fit
@SonniXDАй бұрын
My thoughts while watching 💭 Super Mario and Pizza 🍕 ... 🤔 What is this video actually about???
@WrathofMathАй бұрын
😂 Ramsey Theory!
@vindi167Ай бұрын
167 likes (it is the number of the
@matthijsheblyАй бұрын
πz²a
@hazevthewolf178Ай бұрын
I like my pepperoni pizza with a topping a pineapple on it.
@tomkerruish2982Ай бұрын
HERESY!
@hazevthewolf178Ай бұрын
@@tomkerruish2982 :}
@hazevthewolf178Ай бұрын
@@tomkerruish2982But tastsy.
@hazevthewolf178Ай бұрын
@@tomkerruish2982:)
@WrathofMathАй бұрын
Well you know i have a rich history with pineapple, but I've actually never had a pizza with pineapple. On the other hand I have had pizza with apple on it, and it was one of my favorite pizzas. Short Rib BBQ, with short rib, bbq sauce, onions I think, and candied apples.
@vampire_catgirlАй бұрын
This is cool, but may I take a bite of your pizza?
@WrathofMathАй бұрын
Unfortunately I ate the whole thing :(
@hancockiАй бұрын
mmmmmmm pizza
@tristanridley1601Ай бұрын
"translate to English" lol
@This_used_to_be_my_momsАй бұрын
5 hours ago
@AavyanTiwariАй бұрын
Something 'bout that pizza Fifth!
@WrathofMathАй бұрын
Shaq-a-roni, looking for that papa johns sponsorship