Poincaré Conjecture - Numberphile 

any its at all levels of math.

Under rated comment.

Where is obvious things in math?

@@chabichabi3932 For me it seems "obvious", that Collatz Conjecture is true, because there is always a chance to hit a number that will bring the sequence down to the "known area" where sequence reaches 1. But greatest mathematicians of humanity can't solve it for decades, and say that the problem is so hard that it is completely out of range of modern mathematics. So obviously, the fact that answer is "obvious" for me, only reveals that I completely misunderstand math, related to the problem.

@@luck3949 you so smart

Really he quit all mathematics ?

@@pawankhanal8472 yep

@@thefakeslimshady8881 But people says he is working on Navier stokes equations- other millinium prize problem.

@@pawankhanal8472 I mean I'm just recounting what I've heard from other sources and they said he just quit

@@thefakeslimshady8881 doesn't matter. He proved to be genius and that's enough. History will remember him.

There are amazing people walking this world and I suspect that most of them we've never heard of.

Misterlegoboy he's probably pulling a gauss on us and after he dies we'll find fantastic work is left

That's not being a badass. That's being edgy

He is a great mathematician

You forgot to say that he isolated himself for seven years, working on nothing but this legendary problem, until the day he unveiled his discovery...and after that he disappeared again. Yes that's epic. No dragonborn or heir of Isildur ever lived with more epicness.

No. An interview with *Euler* would be the ultimate Numberphile video.

Gauss.

NuncFluens *Totally agree, bro but he didn't want it*

prabably he is not 100% mental healthy.

Прикладна Економіка, у него есть некоторые признаки синдрома Аспергера, но он не псих. Просто у него проблемы с социализацией.

Navier-Stokes was out this week! =D

Hodge conjecture might be hard to explain.

P=NP really intrigues me because I’m a computer scientist. I really wanna solve it!

@@epicswirl So here's what I've been thinking, since NP-class problems need Polynomial time to check the answer to, doesn't that mean that the problem of P vs NP is a question beyond NP itself? We haven't been able to prove that one of the two solutions are correct, but what if we're just going the wrong way?

Tazo Gochitashvili we can prove NP problems and even solve them in exponential time. The problem is we need an algorithm to do it in polynomial time like O(n^3). You may end up being correct that P=NP is unsolvable, but that needs to be proven and the $1 million will be awarded. If they can be solved in poly time then cancer could be cured theoretically. That is the solution we want. Perhaps we’re just looking at the problem from the wrong angle.

Dmitriy Soloviev 😂😂😂

Dmitriy Soloviev 😂

You will need to ask the psychologists for that conjecture. They need to know what was going on in his brain

I read somewhere that he thought he didn't deserve the prise any more than any other mathematician that made any contribution to the field before him

i.e.: the famous "standing on the shoulders of giants"

nice input 👍

You mean Poincare.

I'm not really trained as a mathematician, I'm an engineer. But I have developed immense fascination with the dynamics of the events that took place around the awarding of the prizes for the proof of the Poincare conjecture (No background in topology).. It is just fascinating to see that Hamilton wasn't selected to share the prize and I also read that the mathematical community didn't take any action against the Chinese who wanted to steal Grigori's work. All these things and dynamics just gives you a chill in the spine =O

***** (1) What you say is not relevant to what I said. (2) No, relativity was NOT discovered by Poincare. This is one of the standard claims by the anti-relativity crackpot crowd. Poincare came very close, true. This subject has been very well researched, I have no space here to dicuss it in more detail. Do your research. I'm not going to respond any further.

Perelman should simply have given half the prize to Hamilton. Who cares what the committee scrawls?

I see where this comes from. Love it.

👏 👏

he was being ripped off by the mathematicians at harvard. he's refusal to accept the prizes were designed to shine a spotlight on the inequities of academic research.

@@boriskogan666how can I learn more about this

TheUneuro 2+2=.?

3,999... repeating

@@naeemkuzco2525 4-1=3 quick maffs

@@kkiller1438 yeah

Mathematician with 17k subs and no vids

captain?

Lmoa

Well said. I think logic shouldn't be commercialized, though a symbol, like the medal, for his deeds might be in place. Or he might think that logic is above honor in that sense. Anyway he made the right choice with the money.

I would try to solve the problem just for the fun of it. I wouldn't turn down the prize money though. Not because I'm greedy, but because I have things I want to do in my life and money is a factor I would enjoy not having to worry about. Not to mention, turning a reward down just to be self righteous is ignorant and disrespectful imo. It'd be like joining a marathon, winning, and then rejecting the trophy. It's practically spitting in people's faces. If you don't want the trophy, don't join the marathon so someone else can enjoy the reward for the time and effort they put in.

Waji Deu Your view of the world is a very bleak. It's more likely than not that if he had your mentality, he wouldn't be in the position to solve that problem.

kabascoolr Everyone needs money. It makes the world go round. I'd rather be bleak and content than foolish and regretful.

Waji Deu You're already foolish. Not everyone holds your foolish views.

Yes, it should be the Poincare Theorem now.

Not necessarily. Perelman only solved a very specific case of P.C. 1. The General P..C. for the 3-Sphere still remains an open problem in Topology 2. Same goes for the 4-Sphere The only reason the don’t appear to mention this is because it would be most likely too difficult to explain to individuals who aren’t mathematicians. Even the standard definition of the P.C. won’t make much sense outside of those individuals who have ever taken a Topology class before, and that’s usually taken around 3rd or 4th year for Mathematics majors in College during their Undergraduate years.

SFLOVER94 Haha true I'm studying low Dimensional Topology and yeah it's truly difficult and requires a lot of abstract thinking ( compared to say an advance course in Algebraic Geometry ) but the biggest problem for me is Shortage of time because I have to write my papers and work in my area so finding additional time to read the proof just for the sake of knowing is just not possible..

I think when people have been calling a problem by one name for so long, they'll resist changing its name later. Besides, it wouldn't be the only problem to have an inaccurate name. Fermat's Last Theorem was called such long before it was ever proven.

@@NoriMori1992 agreed

he is not. he could have donated the 1 mln. to orphans. he is a crank.

MsBoredom22 Yeah, a little more formally, two spaces are considered to be "equivalent" in this sense if you can come up with a "nice" continuous function between the two spaces. A sphere and a donut are not "equivalent" in this sense because a sphere has no holes and a donut has a hole. This hole causes problems which makes it impossible for there to be this sort of "nice" function between the sphere and the donut. Of course, this can be described very rigorously and precisely, but that's the general idea of what's going on.

What topology is actually referring to is the local connections between points. Imagine you draw a circle on a sheet of paper, and you contract that circle down around a single point until it becomes a point. That circle defines what points are "adjacent" to the point. With topology, you can move points further away from each other and in different directions, but the locality is still the same: you can do the same circle contracting thing and it will collapse to the adjacent points in the same way. To add a hole though you're have to either remove points or break the connection between some, changing the locality. Imagine you have a sheet of a paper with a line running across it. You could tear a whole in the middle of the paper, but it would divide the line in half. It's not saying a donut and a coffee mug are the same thing, but that you can deform a donut shape into a coffee mug shape without changing locality, and they are said to be homeomorphic. It's similar congruence or similarity, only it's concerned with functions that preserve locality rather than distance or relative distance.

lol

Why, so you could talk to them at a party to seem cool?

NASA JET PROPULSION LABORATORY isn’t that why numberphile has so many subs?

Jakedesnake97 they should have taught us in school

@@nasajetpropulsionlaborator8727 bruh shut the f*ck up? then why do we learn anything? who said you need to watch them? but the 300 people who liked the OP's comment do like the idea

​@@nasajetpropulsionlaborator8727 nah he is just curious chill bruh

David Navarrete They were mathematically inevitable

Buhahaha

They should have warned us

Ball, donut, pretzel, fidget, fidget spinner.

I came into the comments just looking for someone to have said this.

Because he's a weird dude and weird dudes do weird things, the type of things a normal genius would think of as not normal.

He's a weird dude

You have a deep point: Please check out my take on Perelman's refusal, which appeared in my column on the editorial page of The Economic Times: Man who said `No' to Million Dollars Imagine walking away from a medal regarded as the maths equivalent of the Nobel Prize. If that's easy, imagine solving a hundred-year-old conundrum ranked among seven of the world's greatest mathematical problems, each worth a million dollars. Grigory Perelman, a reclusive Russian mathematician, has done it all with the nonchalance of a nishkamya yogi. In shocking contrast, the conduct of the Fields Medal-winner Shing-tung Yau seems to accord well with the Iron Age of Kali: the Chinese mathematician has attacked his former protégé, tried to overthrow an aging mentor in a well-publicised attempt to grab credit for solving the million-dollar problem named after the French theoretician Henri Poincare. Perelman's otherworldliness was on display from his student days. In 1982, the year that Yau won a Fields Medal, he earned a perfect score and a gold medal at the International Mathematics Olympiad in Budapest. A Russian mathematician who later became his Ph D advisor said Perelman was different: "There are a lot of students of high ability who speak before thinking," he told The New Yorker. "(Grisha) thought deeply. His answers were always correct. He always checked very, very carefully and he was not fast. Speed means nothing. Math doesn't depend on speed. It is about deep." In 1992, when Perelman spent a semester in American universities some of his colleagues were taken aback by his fingernails, which were several inches long. If someone asked why he didn't cut them, he would reply in a manner echoing a Taoist sage, "If they grow, why wouldn't I let them grow?" He went back to a job in Russia that paid him less than a hundred dollars a month. He said he'd saved enough money in the US to live on for the rest of his life. He seemed obsessed by the Poincare Conjecture described as a kind of 20 th century Pythagorean Theorem. But after proving it, he didn't even mention it. "I didn't worry too much myself," he said. "This was a famous problem. Some people needed time to get accustomed to the fact this was no longer a conjecture." He turned down the Fields Medal conferred on him and broke away from his profession. A colleague described Perelman's logic thus, "To do great work you have to have a pure mind. You can only think of mathematics. Everything else is human weakness. Accepting prizes is showing human weakness. An ideal scientist does science and cares about nothing else." ENDS Vithal C Nadkarni 409 words (2014 characters without spaces, including byline) ...

@@danphillips8530 What a thinker you must be

Schrodinger, you sneaky boi

U from Russia?

@@ianleo3030 parents were born in st petersburg, i was born in america.

@@fio123 They are 2 different Perelmans.

@@stkelen9535 whos th anothr 1?

@@bustofpallasathena Yakov Perelman

No it's not; RU-vid updated the settings so that comments aren't limited in size.

The Real Flenuan Look up Fermat's last theorem :-)

Jay Brown I already know what it is. -.-

The Real Flenuan OK . . . sorry if I am being dense, I took Alankey86's comment to be a humorous reference - "I have an answer to this question - a most elegant proof. But this comment box is too small to contain it." - to Fermat's note in his margin. I thought your comment about the comment box size not being limited missed his joke, but as I say, maybe your sense of humor is too subtle for me and went over my head. Anyways, I just thought Alankey86's comment was funny :-)

I think I figured it out. May post a vid.

I loved that book on Simpsons maths

Me too. I saw Simon talking about it on one of the Numberphile videos then immediately checked my local library.

pseudo science it is then .. =D

So n-tiny Homer's approaching width 0 could make m-nibbles {m-> infinity}....hold on, "what were we talking about?"

Yui

thanks

Numberphile Idiot.

aspenbackwoods not true first chinese 2 they are one of the reason to why he rejected, they are frauds.

@@MachinimaCommentary1 why

I stopped the video to see how many likes would the person who would write a comment about fidget spinners get.

Dark_Lord 9 I did the same thing 😂😂😂😂😂

i just did the same :3

Tacky Yeah Don't be rude.

batterup98 I apologize if you're offended, but I was offended by what is a rather troll-type of question ... but I hope you appreciate the incredible wit that insult of mine showed ... sphere into torus by way of bullet!

durrr - you

"If you can put it in a box and close the lid, and it doesn't have any holes, than its a sphere, in any dimension"

It can be turned into a sphere in any dimension with only stretches squeezes and morphs* Is what I believe is the conjecture. Not necessarily that it is a sphere, which of course is ludicrous, because we can instantly disprove that in our 3 dimensions by looking at a cube.

impossible!!

+Luke Lebel Don't rock the boat.

binidra: How do you know?

Your wish has been granted

Also me

That's Mad Lad!

This is what is so interesting about the margins, when constraints and degrees of freedom are balanced in such a way that solutions either don't exist or are needles in the haystack.

I don't know if it's a relevant comparison, but proving the 5-or-more-color theorem was a lot easier than the 4-color theorem!

If it's a hollow sphere with thickness, then in classic 2-dimensional topology it would count as two distinct surfaces rather than one, because the inside is not connected topologically to the outside. But if you're working with 3-dimensional topology it would be considered a higher-dimensional torus.

Yes

A “hollowed” sphere is just two spheres. We’re just talking about 3d objects that have a single continuous surface.

Gibberish

I don’t want your likes, stop rewarding me.

@@warriormanhasdied6479You are disturbing me, I'm picking mushrooms

It's your boy... RAID SHADOW LEGENDS

Grigori refused the million dollars because he had mastered mathematics to such a degree that he could manipulate space time and create anything he desired. Thus money was worthless pieces of paper to him.

+Truetheist Don't, this kind of mathematics is purely abstract it has no real use in the real world it's more like seeing if something can be done or not 95 % of the people will never get this kind of math myself included

+Ynse Schaap A huge chunk of pure mathematics has applications on physics.

Kevin U It has but how close is physics to the real world of most people I believe just as far as math, try explaining entanglement to the average joe

cious li Would have done a lot for me that's for sure

+Ynse Schaap well it's not exactly like that,people try to prove some of the problems,which are non-relevant,as you say,to the most of the things,but in fact,they derive new problems,which are more relevant and some day i'm pretty sure that P vs NP problem(one of the millenium problems,and the most important one,actually) will be solved and then there will be total turn over in whole science or non-science industry

+MrWorshipMe The conjecture is: If you have any such object, i.e. any shape you can imagine but without holes in it and not "infinitely large", then there is always a way to push it around and deform it into a sphere. The inifitely large part is simply to avoid things like an infinite plane. It certainly has no holes but you won't be able to deform it into a sphere!

+MrWorshipMe 2:23 "If a object which don't have hole on it and it's finite then it's a sphere (or can be made into a sphere)". Seems trivial on 3d space, but mathematician needs a proof so it can made generic.

+MrWorshipMe Agreed, this was more about the person who solved it and not much about the actual conjecture, difficulties, solution, applications, etc.

I looked into it, and the sphere was actually the final case to be solved.

@@RosarioLeonardi so maybe I understand it correctly...if I have a rope and i travel with a spaceship around a cricle..i reach the end of the rope and i try to tighten the rope...if it really gets tightened then the universe is finite? If it doesn't get tightened then the universe is infinite? Or did I miss something?

I disagree respectfully. These are once in a lifetime problems that require year if not decades of dedicated work. People have to feed their families. Ideally we would pay our mathematicians better.

Nilesh Jambhekar Yes. The amount of time and work that goes into these millennium problems would be worth far more than a million dollars if in the actual market anyway.

The Vidlets Nah, I just think it's hilarious that he didn't take it, and it would be funny if everyone refused it. Has nothing to do with morals.

MetroAndroid Oh.... You should have said so bro

+Nilesh Jambhekar I am totally agreeing with your statement. My turbulence professor said that even for the navier stokes equation people should pay 10 million or more because not everybody knows how much work behind such theories is! It is so hard to understand and grab at some point.

agreed.

His reasoning is beyond our comprehension

Perhaps he has read "The Pearl" by Stienbeck

Perelmans IQ is over 175

@@membersonly807 I am not sure if this is true but I have heard that IQ has factors involving wealth and quality of life which ofcourse don't contribute to how smart you are.

@@hexa3389 income and iq correlate with each other , people with higher iq earn more money on average

@@membersonly807 but children? Do they earn money? Or what about people who live on poor countries but are smart any way?

@@hexa3389 While in the typical range wealth and IQ are correlated, once you reach a certain level of IQ that correlation disappears and even reverses. At some point you become intelligent enough to realize that nothing in this material world means a damned thing.

It doesn't matter that it is obvious, you need to proof it, in any branch of science.

That sort of argument isn't rigorous enough. One could simply ask Why wouldn't it be different as well.

There are lots of things that are obviously true, but it's a different thing to actually prove it. For example, there are 48 known perfect numbers, and every one of them is even. It's not a huge leap to guess that all perfect numbers are even. However, in order to say something like that, it needs to be proven, which involves rigorous mathematics (Whether there actually exist any odd perfect numbers is currently unknown).

Mike, not only is every known perfect number even, every known perfect number ends in either a 6 or a 28.

it's magic, man :) there are things, that sound pretty general, yet are true for only some certain dimentions. the simplest and at the same time the most illustrious example is right polytopes. they are 5 in 3D as you know, but it is true only for 3D. in 4D we have 6 of them. but in 5D and more, there are only 3 of them -- WHY? because the math we know is ordered this way. and if you ask "WHY", you probably should take a phylosophy path. nowdays brain-dead phylosophy's body positively requires some... handling. either you will revive it, or bury it at last.

One of the versions: taxes. The other one: he wanted to live a quite life but got huge attention and now everyone kniw where he lives. Imagine what could happen to him if he decided to take the money.

who told he were the first! take it easy baby, and relax you are not defending your doctorat thesis..

I wouldn't be able to win it...

At least take the money and give it to charity.

Take the money and set it as a prize for another troubling conjecture.

Nah

@@Felixr2 Smart move.