Mathematician Paul Erdős once said that if aliens landed on Earth and demanded a precise Ramsey number for 5 or they'd destroy the planet, humanity should divert all of its computing resources to figure out the answer. But if they demanded the Ramsey number for 6, humans should prepare for war.
What a great quote! This is a great field of research. I haven't studied Ramsey numbers in particular, but I have looked in to Anti-van der Waerden numbers and Schur numbers!
@@hunterrehm6165 i don't understand how they don't know the ramsey numbers for 6, can't you just brute force the solution with programming? I mean, with enough computing power, you can surely make an algorithm to check every possiblity for each number.
it seems very interesting! I don't know much about it just happened to come across your channel because we used it in analysis as part of a proof of Bolzano weierstrauss
@@maxdemuynck9850 Wow that is interesting. It has been a bit since I have seen Bolzano-Weierstrass, but I am surprised to here Ramsey theory was in the proof. Would love to hear more!
@hisocar I think of the colors as the bins and the edges as the pigeons. This way, by the (generalized) pigeonhole principle, three of the edges must be colored the same. Does that make sense?
The idea is that nobody forces you to pick 3 red and 2 blue, you can try doing 5 red 0 blue, but no matter what, there always will be at least 3 people connecting to first person, that have same color, lets call them A B and C. This allows constructing the white triangle, at which point we are helpless, no matter what you color the triangle, you either create same color edge between first person and 2 from ABC, or if you try to avoid this situation by not giving same color at all... the white triangle becomes what you wanted to avoid, it has only one color!
A bit late, but if you're still having trouble, I think I got what Rehm meant. So for 1 person knowing or not knowing 5 others, from their POV, they can only have any one of the following possible mutually exclusive options: 1. Know all 5 2. Know 4, and not know 1 3. Know 3, and not know 2 4. Know 2, and not know 3 5. Know 1, and not know 4 6. Not know all 5 At 3:19, Rehm claims that using Pigeonhole principle, that person knows at least 3 people or not know at least 3 people. You can go through all 6 options listed above and see that, in every case, Rehm's claim is true. I'm not fully sure how the Pigeonhole principle is used here, but the ultimate claim is correct.
The theorem states that with 6 people in a room, either 3 people know each other, or 3 people do not. So if 3 people do not know each other, then the theorem is satisfied and we should consider the next case. That proof really just shows that there will necessarily be a monochromatic K_3 in every 2-edge-coloring of a K_6.
Mathematician Paul Erdős once said that if aliens landed on Earth and demanded a precise Ramsey number for 5 or they'd destroy the planet, humanity should divert all of its computing resources to figure out the answer. But if they demanded the Ramsey number for 6, humans should prepare for war.
What a great quote! This is a great field of research. I haven't studied Ramsey numbers in particular, but I have looked in to Anti-van der Waerden numbers and Schur numbers!
@@hunterrehm6165 i don't understand how they don't know the ramsey numbers for 6, can't you just brute force the solution with programming? I mean, with enough computing power, you can surely make an algorithm to check every possiblity for each number.
Honey, you’d best get ready to hit the bad lands for that one.
this explanation is simpler than the one i read on the book. thanks dude
Love to hear it!
Great vid. Thanks for sharing!
Thanks! I hope to post more soon.
So glad I found your videos!!
I am so glad you did!
beautiful video! just started learning this ,Thank you!
Thank you! I’ll be coming out with a new video soon I hope
wow, super underated. subscribing time!
Welcome aboard! I just finished my PhD, so I will be making video more now. What would you like to see? More videos like this one?
This was so good and helpful, thankyou 😄
Love to hear it! I am currently getting my PhD so video production is slow, but I hope you subscribed!
Banger video man I love math
Very simple and clear explanation, thanks!
Glad you said something! It means a lot!
Great video!! Nice to see people using the manim engine.
Thanks! Yeah it’s nice and easy to make some really great animations. Have you tried it?
@@hunterrehm6165 Not really. But its nice to see the community making good of it.
background music is fire🔥10/10 vid
I thought so too.
Thank you! Now I understand!
Glad I was able to help! =D
Very good video!
Thanks @clonebin0!
excellent clear explanation
I’m glad you thought so!
Thanks Hunter. Good video
You bet! Let me know if there is a topic you are interested in seeing. I can try to make something on it.
Such a great video
Glad you think so!
this is amazing
Thanks Fatima Zahra!
Thanks for the simplest presentation.:)
Oh its my pleasure. Are you interested in graph theory?
@@hunterrehm6165 I've taught graph theory on my youtube channel already 😊
@@pcmtutorials Awesome! I just checked it out! Love it!
Great video
Thank you so much! Let me know if there is another topic that interests you!
Awesome
Thank you!
awesome video!!
Glad to hear you enjoyed it! Are you interested in graph theory like me?
it seems very interesting! I don't know much about it just happened to come across your channel because we used it in analysis as part of a proof of Bolzano weierstrauss
@@maxdemuynck9850 Wow that is interesting. It has been a bit since I have seen Bolzano-Weierstrass, but I am surprised to here Ramsey theory was in the proof. Would love to hear more!
thanks!!
Glad you enjoyed it! Let me know if there are any other topics you would like to see!
If I claim R(5,5) = 72 what can be used to prove it wrong?
very helpfull
Thank you! Stay tuned for more videos!
riveting 🧐
It doesn't get much better than this!
5:50 You forgot to put the link :(
I just added the link in the description! It's just the wiki page, but it does a good job summarizing the known values.
I don't understand how the pidgeon hole principle helps us with the coloring at 3:40
@hisocar I think of the colors as the bins and the edges as the pigeons. This way, by the (generalized) pigeonhole principle, three of the edges must be colored the same. Does that make sense?
The idea is that nobody forces you to pick 3 red and 2 blue, you can try doing 5 red 0 blue, but no matter what, there always will be at least 3 people connecting to first person, that have same color, lets call them A B and C. This allows constructing the white triangle, at which point we are helpless, no matter what you color the triangle, you either create same color edge between first person and 2 from ABC, or if you try to avoid this situation by not giving same color at all... the white triangle becomes what you wanted to avoid, it has only one color!
A bit late, but if you're still having trouble, I think I got what Rehm meant.
So for 1 person knowing or not knowing 5 others, from their POV, they can only have any one of the following possible mutually exclusive options:
1. Know all 5
2. Know 4, and not know 1
3. Know 3, and not know 2
4. Know 2, and not know 3
5. Know 1, and not know 4
6. Not know all 5
At 3:19, Rehm claims that using Pigeonhole principle, that person knows at least 3 people or not know at least 3 people.
You can go through all 6 options listed above and see that, in every case, Rehm's claim is true.
I'm not fully sure how the Pigeonhole principle is used here, but the ultimate claim is correct.
Use extended form of Pigeonhole principle i.e. [(n-1)/m] +1...... n=5 and m=2 .. Therefore, [(5-1)/2] +1= 3
Well, I um. I'll try watching again without drink in my brain.
Haha let me know if you have any questions! Happy to help.
Where is the link below?
My bad. I just added the link to the wiki page in the description. There is a table there which summarizes the known values!
Please use the regular way to show your text.thx
I will do this for future videos probably!
Why can't everyone not know eachother though? Ie, all blue?
The theorem states that with 6 people in a room, either 3 people know each other, or 3 people do not. So if 3 people do not know each other, then the theorem is satisfied and we should consider the next case. That proof really just shows that there will necessarily be a monochromatic K_3 in every 2-edge-coloring of a K_6.
Thank u sir love and support from Pakistan ❤