'None of the boys wore long party dresses, or if they did they weren't distinguishable from girls'. Best quote ever.

"I hope I'm getting it right..." I hope I get a constant named after me, only so that I can personally get it wrong.

"I couldn't get it", then proceeds to find an irrational root of a 71 degree polynomial and the 92 seeds of the sequence. Just when you thought you got him. RIP John Conway

John Conway passed away on 11 april 2020... A great mind has left us. :'(

That's so cute that instead of just skipping class they threw a party! 0:45 - "Some of the girls wore nice long party dresses. None of the boys wore long party dresses - or if they did they were indistinguishable from girls." The deadpan delivery nails it. XD

I actually "discovered" this series myself in middle school, and noticed that 22 was the only number that didn't generate a string...

Rest in peace. One of the most brilliant minds of our time...

1 1 was a race horse, 2 2 was 1 2, 1 1 1 1 race, 2 2 1 1 2.

Knew about this sequence before it got viral. like a boss.

Rest in peace Mr Conway. This was my favorite math “party” stumper as far back as the 8th grade and has always been a fun thing to look at and study (or even just to write down). Your work will live on in (in)famy for history as some of the most interesting problems-turned-games for even the those who least enjoy math. You’ve left an impression that is everlasting and we won’t soon forget.

Wow, nice nicee! The real question is how the heck did they find out the Conway constant is the root of that 71-degree polynomial?! The polynomial doesn't seem to have any structure in it really. The plus and minus signs alternate chaotically as well as the quantities of X's. I would really like to know more about this.

Did the student get credited in the paper?

I remember being given this problem as an extra credit problem in my geometry class. Of the ~25 students, two of us got it right (this was back in HTML1.1 days). That evening I got home and began playing with it. It consumed me for a whole month. Even writing my first REAL bit of code on a machine my uncle gave me to print out on screen the sequence and navigate it forwards and backwards and to store sequences and highlight them in other numbers. This stupid little puzzle my teacher gave me 5points of credit for solidified in earnest my fascination with computers and programming that has endured to this day. Ahhh the nostalgia, THANKS BRADY!

When I saw that some of the numbers contained 3113, for a moment I thought the 1's were Knuth up-arrows.

"none of the boys wore long party dresses, or if they did they were indistinguishable form girls" - So funny.

Reminds me of the "only number that describes itself": 10233221, with the hundreds thousands' place being independent. Read audibly, it says: " One Zero, Two threes, Three twos, Two ones.", describing itself. Sourced from some book somewhere.

Brady you should spend a week with this man!

R.I.P. John Horton Conway, born 26 December 1937, died of COVID-19 on 11 April 2020 (aged 82).

the PNG file format uses this technique to compress images. Let's say you have an image with a bunch of red pixels, and then a bunch of blue pixels. You can store the images as *amount**color*, so you would go for example 20Red, 40blue, etc. It uses some more tricks for stuff like gradients, but in essence it's the same technique.

Rest in peace, legend!

I don't care if Professor Conway reads the phone book, more please. Many more please :-)

I heard this puzzle long ago on a radio show called "Car Talk" - would have been 1987 or later, though, when the show went national.

The roman numeral "IIII" at the end made me think of counting in Unary (base one). If you count in Unary, all the numbers in this sequence are in exact sequential order.

I've tried this but a bit differently, instead of counting all the same consecutive digits I counted all the same digits in the whole number, and discovered that it eventually starts alternating between 2 numbers for a seed of 1: 1 11 21 1211 3112 (here is the difference, I count all the 1s in the whole number at once, not only the first one) 132112 311322 232122 421311 14123113 41141223 24312213 32142321 23322114 32232114 23322114

There's two mathematicians named John Conway born in the 30s. Stop it universe, just stop it.

The legendary John Conway on KZfaq! What great times!

Numberphile, you do a lot of videos on imaginary and complex numbers, but have you thought about doing on e about quaternions (a + bi + cj + dk)and their properties and uses?

This was really interesting! These kind of video's make me increasingly interested in the mystery of numbers.

I'm seriously loving this..

I fully admit I don't understand a lot of the videos on this page.... I can see the concept and believe the speaker. But I enjoy them all none the less. I was excited when this one started because I was on board and was keeping up right up until he started putting chemistry in it. Then I was only partially on board. lol.

COnway videos are the best! i really RELLY hope we will see more in the future!

Rest in peace John Conway.

Thank you for this fun and fascinating video. If I may make a suggestion, I think a Numberphile series on Surreal Numbers with Professor Conway would be an excellent topic.

This is fantastic! Thanks for sharing!

the fact that this recursion has a characteristic in another chaotic seeming recursive matrix(life or so , in conway's terms) is beautiful. and , such interlinks with no relations whatsoever, "catch my fancy". colouring such numbers, also brings them to life, bringing out patterns, with "no relation whatsoever".

This is a good version of the "petals around the rose" problem. Since I was already acquainted with that one, solving this one took me one second.

advent of code brought me here

Wow, i missed this one. Great episode!

When I first saw the sequence in the form of a problem I was around 11, and I though I was the only one who though deeply about it. Of course the only real conclusion my 11-year-old self reached was that there could never be a 4.

It's my favorite sequence of numbers and I spend many times in school after tests when I was bored and I had much fun with it.

Absolutely amazing!

I love this Conway stuff

Yay, I love this sequence!

1 MILLION SUBCRIBERS! Congratz, guys!

I'm happy he got to talk about something other than the Game of Life.

Congrats On 1 Million Subs!

Fascinating!

Rest In Peace

I managed to work out the sequence before Conway revealed the secret, but to be honest, I think the title "Look-and-Say Numbers" somewhat made it easier to deduce, than it would have been for Conway in the original setting, not having a snazzy video title to clue him in :)

Very cool. I'm gonna try this on my friends.

I wish the name of this sequence wasn't in the video title; I've never run across it before, and it ruined the puzzle :(

I'm so glad I'm alive at the same time this man is.

this channel consists of the nerdiest of nerds... I love it

I like videos like this, they give me a rare glimpse into just how smart some people are.

SURPRISE!!

Grats on 1 million subs!!!

Brilliant video as always! If you've got John Conway handy for any upcoming filming sessions, would you mind asking him to explain that Blue Eyed Islander riddle? Would you film a Numberphile on the topic with the man himself? As far as I know Mr. Conway provided the first solution (certainly one of the most accepted solutions), he used a concept of common knowledge. I've read solutions, they go: “if you know a person knows, you know he's got blue eyes”, and then I can't understand anything. It's rather logic-based, as opposed to arithmetic. It's an excellent riddle and the solution is genius. If Mr. Conway and yourself have time to film such a session, it would be a historic moment in the riddle's history, and something I think the world would cherish forever. Either way, thanks for all your work Brady and Mr. Conway!

Really awesome results for such a simple math game-like problem.

@delwoodbarker, the precise words to explain the logic, chapeau...

I had fun typing this out over several rows. And if you align the text, you also see a nice curve (or curves it's centre align) appear.

Is there any meaning associated with the other (complex) roots of the Conway polynomial?

wow, I didn't know this one, but when he showed the 4th one, I knew it already :D this is a cool sequence

I like John. This may seem rude, but I'd like to see more old mathematicians on here. They're like wise, yet befuddled, wizards. There is something about minds like that that I would like to find a connection too. Beyond the adorableness of it. Maybe it's their personality, still intact, their lack of common characteristics of communication, shining through coupled with the deterioration of their bodies, in this case, the vocal cords and the face. However, I imagine there is something more going on upstairs, inside. Maybe they've spent their lives investing in the neocortex, and I recall that being the first thing to go as the brain deteriorates. While it's the newest part of the brain for mammals like us, and the one that makes us so richly complex, it doesn't seem to stay intact as long as the older, more basic parts. My apologies if that sounds morbid or disrespectful, but I like brains. All brains are interesting but it's the outliers that are particularly fascinating.

Came on 1/11/21 (to us Americans) to pay respects. RIP Professor Conway

RIP. A legend

It turns out this is a really boring sequence in unary.

A teacher put this on the board when I was in high school. Took me about a minute to get up and add the next line, and no one else in the class seemed to get it.

Rest in peace, John Conway.

Wow... this was very interesting... Thx

RIP 😭

RIP professor Conway. A truly great man.

I’m guessing it’d be impossible to have a 4 in the sequence because that would require say “1111” which would require you to count the same number twice back to back when you could just say “21”.

...spark of curiosity ignied the flame of ingenuity. It's interesting to see how mathematicians mind thinks over a number "problem" by relating it to a known physics phenomena...:)

A genius ! Thanks

He has a wonderful sense of humor.

RIP John Conway, what a ledgend

I really wasn’t expecting this 😂

We played this in 6th-7th grade a lot, starting with different numbers... Never thought there was hard math behind! XD

John Conway-Rest In Peace

Rest in Peace Mr. Conway...

so close to 1,000,000 cant wait for their number vid on 1 million :D

If you put a gun to my head and demanded that I explain how to recreate this sequence. I think I'd end up with a new hole in my head. I don't understand how you get the third sequence.

I think of John Conway as a mathematical mystic. What a mind.

You'll be missed, sir...

I really need to start playing with the ideas in my head like prof.conway lol :)

It's very funny to me that someone could do a whole lecture (and have it attended by highly educated people) on the interesting mathematical properties of a riddle.

This man is really a genius!

WOW they just hit 100,000,000 subscribers!!!

My dad showed this to me when i was in junior high. I filled a note book. There is also a growing pattern in the front of the number as well as the back. In the front it's every other. In the back it's every third. This pattern grows from the inside out. Try coloring the pattern green as you go down you will see what i mean.

I think the name ot the video gave it away for me. Or maybe i have just seen it before.

This was already my favorite pattern but now my fave mathematician over analyzed it and nade it better

Seeing a relationship between different number bases would be cool too! like with hex, e.g. 4dd8 has 142d18, that could make the polynomial constant representation enourmous!!!

This sequence appeared in a video game called "Please Don't Touch Anything".

6:55 - I went to Acadia University in Nova Scotia. Too bad I was able to be at this lecture. RIP Conway.

He was a legend , Rest in peace sir

the question is, at witch number will you see the first 4

Nice, I've never seen this sequence before. Also: Will you maybe make a video with John Conway about FRACTRAN? Would be awesome :)

We need more of the wizards! (Conway, the heptadecagon man whose name I don’t know, and Stoll.)

Brady can you make a video with John Conway talking about his 'chained arrow notation'? It's like a much bigger version of Knuth's Arrow Notation.

what would happend if you start doing chemistry with math elements? HOw does the H20 looks like?