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.
Gregori solved this question alone in his room which contains only a desk, a bed, a lamp, and a chair. And then quit all of mathematics after this. What a guy
Hardness of math problems: 0. I can solve the problem 1. I can understand the solution of the problem 2. I can't understand the solution of the problem 3. I can't understand the problem 4. I can't understand why it is not obvious
@@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.
@@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.
This video never mentions one major hero of the story, the inventor of the Ricci flow himself: Richard Hamilton. This is almost like talking about relativity without ever mentioning Einstein. Perelman's achievement is undeniable, of course, but Hamilton did a lot of heavy lifting beginning with the early 1980s. In fact, one of the reasons Perelman rejected the Fields medal and other prizes was that the people who were in charge of awarding them refused (apparently) to make the prizes shared with Hamilton.
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.
ignoring the money he just wants to show that there is something wrong with our world. Some of his ex-partners in math betrayed him, he thought that that the world of math is the only place where people are moral and pure in their thoughts. But it turned our that even a mathematical society is full of bustards craving for money and the fame. We are a dirt world, and he is a just a saint Man. That's it. I proud of that such a person lives in my county.
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.
While a very intriguing story, I'm surprised there were no reasons given why Dr. Perelman declined the money, fame, and accolades. His reasons, on some parts, I completely agree... many fields become doctrines that are devised by a very selected few. Science and mathematics are seriously suffering from a lack of openness to new ideas because of these centralized ideas (string theory, molecular quantum mechanics, and so forth). Unfortunately, not only is his intelligence and insight incredible but the his level of humbleness, unselfishness, and grace are far beyond most people.
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) ...
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.
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.
@@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
Poincare Conjecture is a fascinating problem because we start to make many questions about what are indicated equations to solve it. It sounds simple but there are many theorems we need to know and use to get it.
Perelman is a great character in the world of mathematics, thanks for this video. The millennium questions are very captivating, I wonder how long it will take for the next one to be solved.
The only thing I know about this particular brand of math is that a donut and a coffee mug are apparently mathematically the same thing. And this is because one of my math teachers was very creative about coming up with excuses why he had food in class, heh
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.
Came here to understand this, although an interesting video, i would have liked to have some brief explanation of what this proof actual stated and the basic logic behind what he was trying to do
Most brilliance languishes in obscurity. Unfortunately, this is the world we have fostered: people with few brains a tons of ambition usually take take the credit. People like Steve Jobs fit this example perfectly.
I saw a video on another channel about topology showing how a sphere could be turned inside-out following those same rules. It had a really cool animation but didn't explain very well how it was done.
Ooh... I just remembered an orange peeling question I had once which seems vaguely relevant to this video! *Is it possible to peel an orange such that its skin comes off in a donut type shape (as defined around **1:45**)? That is, one continuous loop that has a hole in it.* I have an answer to this question - a most elegant proof. But this comment box is too small to contain it.
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 speak Russian. From the few interviews on the web it becomes obvious that Perelman made very weighted and rational decision to refuse the money. Mostly because he thinks Hamilton made more for the solution. Actually, he hates when people think that he is some kind of a crazy genius. He is not.
There's a tiny piece of misinformation in the video. When mathematicians refer to a 2-dimensional sphere they mean the same thing as the laypersons sphere which exists in 3 dimensions (because its surface is 2 dimensional, just curved). This wouldn't be an issue since it's just a matter of convention, but the distinction became important when she talked about the conjecture having been proven for 5-spheres and up. In this case she meant the mathematicians "5-sphere," (which thus exists in 6 dimensional space) which is two more dimensions than the final case which Perelman proved, and not 1 dimension higher, which is what the video implied. It's a curious fact that it was eventually easier to prove the higher dimensional versions of the conjecture (7 was proven before 5), but an intuitive way to understand that is that you have more "elbow room" so to speak.
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.
He being a genius was treated poorly by his peers and hated people. He saw most as holding ego over the field and hated the behaviors of journalists and by extension the prizes.
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!
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.
I am a undergrad student in Mathematics and I know this video dumbs down the conjecture so that we all can comprehend it easily but i would appreciate if someone provides a guided path to form a basic background in understanding Perelman's proof . Just some directions to navigate forward (I have basic knowledge on real analysis and calculus )
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.
@@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 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.
Please do videos on all 7 unsolved problems. Somewhere out there some 10 yr old kid is watching. yrs down the road will be one to solve them. Numberphile could influence human history! Thanks for what u do!
I bet he has solved other problems too, but since he hates attention and this gave him lots of it, he probably just destroyed the papers and kept his mouth shut.
Perelman on why he didn't accept the prize or medal: "I'm not interested in money or fame. I don't want to be put on display like an animal in the zoo." Ironically, this has made him much more famous and "on display" than if he would have accepted the awards.
I did not understand from this video what the conjecture was... just that it's premises were about a finite object with no holes like a sphere, but in any number of dimensions... what was the actual conjecture? why is this conjecture important? I really don't care about the personality or appearance of the one who proved it...
+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.
@@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?
He valued ethics and conceived maths the most ethical science whose community shared high moral standards. For him time proved that he had been sorely mistaken. One of the reasons why he parted company with maths and all the rest.
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.
Offering numbers to a mathematician as a token is what we call practical jokes. I mean that brain can invent a machine that prints money. Perel the great
What if I was allowed N "forbidden" operations for my topological transformations (e.g. N cuts or sphere closures)? I can imagine turning donuts into spheres with a single cut in the real world, so having a generalized topology for that kind of thing seems like it would make sense. Also, it seems like you could have classes of objects where one cannot be transformed into another even with infinitely many cuts.
Reminds me of a French philosophise who was offered a nobel prize but refused for some elevated reason. A problem like that takes years to solve, he's not just some genius who had an epiphany.
Poincaré is also famous for figuring out the field equations of General Relativity a short time before Einstein but he did not even try to take credit for that achievement because Einstein had been working on them for a decade.
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.
+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.
Temporal Infraction Developing a physical theory around the idea of "temporal infraction," where the day still has 24 hours, but the value of these hours decreases, involves a series of assumptions and extrapolations that mix theoretical physics, philosophical concepts, and the subjective perception of time. Let's explore this idea in a structured manner: 1. Definition of Temporal Infraction Temporal Infraction: would be a condition or phenomenon in which, despite the objective measure of time remaining constant (i.e., a day still has 24 hours), the "quality" or "value" of this time is perceived as diminished. This reduction in the value of time could be quantified in terms of efficiency, subjective perception, or capacity for achievement within a time period. 2. Initial Hypotheses Temporal Dilution Hypothesis: Propose that there is a dilution of temporal experience, where each unit of time (hour, minute) becomes less "dense" in terms of quality or utility, similar to the concept of entropy in thermodynamics, where the system tends towards a state of greater disorder. Subjective Compression Hypothesis: Suggest that there is a compression in the subjective perception of time, where the human brain processes time in an accelerated manner, making it seem like less time is available. 3. Mathematical Model We could model time not just as a linear dimension, but as a function that depends on psychological, social, and even cosmological variables. If T24 represents the 24 hours of a day, we could introduce a "temporal infraction" factor I(t) that modifies the perception or value of these hours: T24' = T24 × I(t) Where I(t) is a decreasing function of time (t), representing the decrease in the perceived value of time as days pass. 4. Physical Interpretation We can hypothesize that this temporal infraction is caused by external or internal interference: External Causes: A cosmological phenomenon that affects temporal perception, such as a variation in the expansion rate of the universe, which could influence how matter (including human brains) interacts with time. Internal Causes: A neurological or psychological change that, over time, alters how human beings process the passage of time, similar to how gravity can bend space-time in General Relativity. 5. Experiments and Predictions To test this theory, we could: Measure the subjective perception of time in different populations over time, observing if there's a tendency for people to feel they have less time as they age or in different seasons of the year. Investigate if there's a correlation between cosmic or geophysical events and changes in temporal perception. Develop computational models that simulate how time perception can be affected by psychological and physical factors, adjusting the I(t) factor to predict different scenarios of temporal infraction. 6. Conclusions and Implications If this theory proved true, it could have profound implications for how we understand time, both in a physical and subjective sense. It could also influence how we organize our lives, from structuring work time to valuing leisure time. This "Temporal Infraction" theory is an attempt to combine physical concepts with human perception of time, exploring new ways to understand how we experience and value time in our daily lives. Although still purely speculative, it offers an interesting field for future theoretical and experimentalexplorations.
It is about the intersectionality- id 0 = blob id 1 = blob + punchblob (-blob). By defining displacements, we can assign dimensionality of measure, and spot the difference is a bounded philospphical method which limits a posteriori experimental science methodologies. Socrates likes this.
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.
I thought Fermats Last Theorem had more wrong proof attempts than any other. In the words of mathematical historian Howard Eves, "Fermat's Last Theorem has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published."
A 3-ball has -1 (minus one) hole. A solid circle (a 2-ball) has -1 (minus one) hole. Proof. An infinite (2D) sheet missing a solid circle has 1 hole. That solid circle is the hole, so give it -1. A -1 hole is a hole on the outside. A sphere is defined as the covering of a ball. It has one less dimension than the ball.
+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 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
It took people more to acknowledge his solution than what it took him to solve it, Perelman was also treated as liar and thief by the community that's why he wanted to have nothing to do with it anymore.
I love reading and gaining knowledge of maths and science all the time. The more I know, the more dangerous it gets. After watching this video, I asked my mate what my name is? 😂 Great work Lad. Need to read more about this conjecture, not completely clear.
what a badass- he solves one of the 7 hardest problems in the world and then just drops the mic and leaves
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.
Gregori solved this question alone in his room which contains only a desk, a bed, a lamp, and a chair. And then quit all of mathematics after this. What a guy
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.
An interview with Perelman would be the ultimate Numberphile video.
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.
Hardness of math problems:
0. I can solve the problem
1. I can understand the solution of the problem
2. I can't understand the solution of the problem
3. I can't understand the problem
4. I can't understand why it is not obvious
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
do a video on every millenium prize problem
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.
This video never mentions one major hero of the story, the inventor of the Ricci flow himself: Richard Hamilton. This is almost like talking about relativity without ever mentioning Einstein. Perelman's achievement is undeniable, of course, but Hamilton did a lot of heavy lifting beginning with the early 1980s. In fact, one of the reasons Perelman rejected the Fields medal and other prizes was that the people who were in charge of awarding them refused (apparently) to make the prizes shared with Hamilton.
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?
Perelman refused to take any prize, thereby create Perelman Conjecture. Now mathematician trying to understand why.
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"
ignoring the money he just wants to show that there is something wrong with our world. Some of his ex-partners in math betrayed him, he thought that that the world of math is the only place where people are moral and pure in their thoughts. But it turned our that even a mathematical society is full of bustards craving for money and the fame. We are a dirt world, and he is a just a saint Man. That's it. I proud of that such a person lives in my county.
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.
As a mathematician, I respect so much what you do Brady ! Thank you :)
TheUneuro 2+2=.?
3,999... repeating
@@naeemkuzco2525 4-1=3 quick maffs
@@kkiller1438 yeah
Mathematician with 17k subs and no vids
" Some people can't be bought or bargained with, they just want to see the world learn. "
I see where this comes from. Love it.
👏 👏
He has a gold heart. Humble, and sincere.
he is not. he could have donated the 1 mln. to orphans. he is a crank.
While a very intriguing story, I'm surprised there were no reasons given why Dr. Perelman declined the money, fame, and accolades. His reasons, on some parts, I completely agree... many fields become doctrines that are devised by a very selected few. Science and mathematics are seriously suffering from a lack of openness to new ideas because of these centralized ideas (string theory, molecular quantum mechanics, and so forth). Unfortunately, not only is his intelligence and insight incredible but the his level of humbleness, unselfishness, and grace are far beyond most people.
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)
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@@danphillips8530 What a thinker you must be
Schrodinger, you sneaky boi
So Perelman basically did the world's greatest ever hold my beer followed by an epic mic drop.
Legend.
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
[takes drag of cigarette] "I was with a bunch of people in San Diego who were really into Ricci Flow..."
captain?
Lmoa
I would watch this movie 💯
2:15 OMG they predicted fidget spinners 3 years ago 😱
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.
Shouldn't we stop calling it a "conjecture" now that it has been proven?
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
Hey Brady, could you make a series of videos explaining every millennium problems please?
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
Perelman was my dad's classmate! From what I've been told, he's a super-nerd but is also a genius!
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
Poincare Conjecture is a fascinating problem because we start to make many questions about what are indicated equations to solve it. It sounds simple but there are many theorems we need to know and use to get it.
Perelman is a great character in the world of mathematics, thanks for this video. The millennium questions are very captivating, I wonder how long it will take for the next one to be solved.
Your last videos are amazing Brady ! Excellent choices.
thanks
Numberphile Idiot.
aspenbackwoods not true first chinese 2 they are one of the reason to why he rejected, they are frauds.
@@MachinimaCommentary1 why
-comes
-Solve one of the hardest math problem
-resisting the prize
-refuse to elaborate
-leaves
Thank you so much for this Brady. I love these Millenium Problems.
The only thing I know about this particular brand of math is that a donut and a coffee mug are apparently mathematically the same thing. And this is because one of my math teachers was very creative about coming up with excuses why he had food in class, heh
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
Came here to understand this, although an interesting video, i would have liked to have some brief explanation of what this proof actual stated and the basic logic behind what he was trying to do
2:17 Numberphile predicted fidget spinners before anyone else
Most brilliance languishes in obscurity. Unfortunately, this is the world we have fostered: people with few brains a tons of ambition usually take take the credit. People like Steve Jobs fit this example perfectly.
Gibberish
Grigori is no bs
I saw a video on another channel about topology showing how a sphere could be turned inside-out following those same rules. It had a really cool animation but didn't explain very well how it was done.
It amazes me that so many people watch your videos, always thought that math is not that popular.
Ooh... I just remembered an orange peeling question I had once which seems vaguely relevant to this video!
*Is it possible to peel an orange such that its skin comes off in a donut type shape (as defined around **1:45**)? That is, one continuous loop that has a hole in it.*
I have an answer to this question - a most elegant proof. But this comment box is too small to contain it.
No it's not; TH-cam 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.
Who's here after count dankulas video?
Also me
That's Mad Lad!
2:16 what kind of fidget spinners are those
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
I guess if you can solve the hardest mathematical problems for humanity, you really don't think too much about money or prizes.
I speak Russian. From the few interviews on the web it becomes obvious that Perelman made very weighted and rational decision to refuse the money. Mostly because he thinks Hamilton made more for the solution. Actually, he hates when people think that he is some kind of a crazy genius. He is not.
There's a tiny piece of misinformation in the video. When mathematicians refer to a 2-dimensional sphere they mean the same thing as the laypersons sphere which exists in 3 dimensions (because its surface is 2 dimensional, just curved). This wouldn't be an issue since it's just a matter of convention, but the distinction became important when she talked about the conjecture having been proven for 5-spheres and up. In this case she meant the mathematicians "5-sphere," (which thus exists in 6 dimensional space) which is two more dimensions than the final case which Perelman proved, and not 1 dimension higher, which is what the video implied.
It's a curious fact that it was eventually easier to prove the higher dimensional versions of the conjecture (7 was proven before 5), but an intuitive way to understand that is that you have more "elbow room" so to speak.
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!
But, according to Homer Simpson, if it's a real donut then nibbles are allowed.
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
He being a genius was treated poorly by his peers and hated people. He saw most as holding ego over the field and hated the behaviors of journalists and by extension the prizes.
Next video: Navier-Stokes equation!
impossible!!
+Luke Lebel Don't rock the boat.
binidra: How do you know?
Your wish has been granted
So... what is the Poincaré Conjecture?
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.
I can't even imagine how difficult this girls course was
Brady, you should make a video with Perelman himself.
I am a undergrad student in Mathematics and I know this video dumbs down the conjecture so that we all can comprehend it easily but i would appreciate if someone provides a guided path to form a basic background in understanding Perelman's proof . Just some directions to navigate forward
(I have basic knowledge on real analysis and calculus )
0:45 There is a certain relationship between geometry and topology. Lol I always thought topology is just big daddy of geometry.
What about a hollowed sphere? Can that be made into a solid sphere or does that count as a "hole"?
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.
who is here after count dankula.
I don’t want your likes, stop rewarding me.
@@warriormanhasdied6479You are disturbing me, I'm picking mushrooms
It's your boy... RAID SHADOW LEGENDS
I love how you have James wearing a Red Sox hat the whole video and Brady at the end wearing a Yankees hat.
Go Blue Jays ;)
Katie explained it so well
Convinced Perelman has been working since he left the math community. the questions are; on what, and is it even finishable?
Perelman.
Solves one of the hardest problem ever.
Refuses to take the prize money.
Leaves.
🗿
this is called actual genius and not those who claim their IQ is of 100 or 200 or say they have cleared some entrance exams.
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.
Please do videos on all 7 unsolved problems. Somewhere out there some 10 yr old kid is watching. yrs down the road will be one to solve them. Numberphile could influence human history! Thanks for what u do!
π million subscribers, very satisfying.
Well. In words of Perelman: " if the proof is correct, then no other recognition is needed."
I bet he has solved other problems too, but since he hates attention and this gave him lots of it, he probably just destroyed the papers and kept his mouth shut.
Solves 16-body Schrodinger equation... crumples script and uses it to light a Hibachi.
OMG hi Katie! I finally came across your video! :)
Grisha is a living genius. What a brain! I wished I could speak to him, but it is even less possible than solving another unproved conjecture.
Perelman on why he didn't accept the prize or medal: "I'm not interested in money or fame. I don't want to be put on display like an animal in the zoo." Ironically, this has made him much more famous and "on display" than if he would have accepted the awards.
I would love to know what his Mum said about the million dollars.
I cannot believe I got two Millennium problems done, and this dude, whom is smarter than me, only got one. That makes me so proud of myself.
Grigori loves the purity of maths, everything else is expedient. I hope he’s still working.
I did not understand from this video what the conjecture was... just that it's premises were about a finite object with no holes like a sphere, but in any number of dimensions... what was the actual conjecture? why is this conjecture important? I really don't care about the personality or appearance of the one who proved it...
+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?
Grigori Perelman is not a strange man. He just doesn't think like a "western" man.
He valued ethics and conceived maths the most ethical science whose community shared high moral standards. For him time proved that he had been sorely mistaken. One of the reasons why he parted company with maths and all the rest.
@Floofy shibe It's sad, but not unjustified.
Grigori Perelman you absolute genius
Grigori conjecture: *why Grigori refused one million dollars*
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.
Offering numbers to a mathematician as a token is what we call practical jokes. I mean that brain can invent a machine that prints money. Perel the great
What if I was allowed N "forbidden" operations for my topological transformations (e.g. N cuts or sphere closures)? I can imagine turning donuts into spheres with a single cut in the real world, so having a generalized topology for that kind of thing seems like it would make sense. Also, it seems like you could have classes of objects where one cannot be transformed into another even with infinitely many cuts.
Reminds me of a French philosophise who was offered a nobel prize but refused for some elevated reason. A problem like that takes years to solve, he's not just some genius who had an epiphany.
Poincaré is also famous for figuring out the field equations of General Relativity a short time before Einstein but he did not even try to take credit for that achievement because Einstein had been working on them for a decade.
I love her Doctor Who shirt and robot necklace. The robot fits perfectly in front of the TARDIS.
:)
It would just be so great if every one of the Millennium Math Problems' Solvers refused the million dollar prize.
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.
I Love this channel with all my heart.
Another awesome video! Are there gonna be videos on all the millennium problems?
Temporal Infraction
Developing a physical theory around the idea of "temporal infraction," where the day still has 24 hours, but the value of these hours decreases, involves a series of assumptions and extrapolations that mix theoretical physics, philosophical concepts, and the subjective perception of time. Let's explore this idea in a structured manner:
1. Definition of Temporal Infraction
Temporal Infraction: would be a condition or phenomenon in which, despite the objective measure of time remaining constant (i.e., a day still has 24 hours), the "quality" or "value" of this time is perceived as diminished. This reduction in the value of time could be quantified in terms of efficiency, subjective perception, or capacity for achievement within a time period.
2. Initial Hypotheses
Temporal Dilution Hypothesis: Propose that there is a dilution of temporal experience, where each unit of time (hour, minute) becomes less "dense" in terms of quality or utility, similar to the concept of entropy in thermodynamics, where the system tends towards a state of greater disorder.
Subjective Compression Hypothesis: Suggest that there is a compression in the subjective perception of time, where the human brain processes time in an accelerated manner, making it seem like less time is available.
3. Mathematical Model
We could model time not just as a linear dimension, but as a function that depends on psychological, social, and even cosmological variables.
If T24 represents the 24 hours of a day, we could introduce a "temporal infraction" factor I(t) that modifies the perception or value of these hours:
T24' = T24 × I(t)
Where I(t) is a decreasing function of time (t), representing the decrease in the perceived value of time as days pass.
4. Physical Interpretation
We can hypothesize that this temporal infraction is caused by external or internal interference: External Causes: A cosmological phenomenon that affects temporal perception, such as a variation in the expansion rate of the universe, which could influence how matter (including human brains) interacts with time.
Internal Causes: A neurological or psychological change that, over time, alters how human beings process the passage of time, similar to how gravity can bend space-time in General Relativity.
5. Experiments and Predictions
To test this theory, we could: Measure the subjective perception of time in different populations over time, observing if there's a tendency for people to feel they have less time as they age or in different seasons of the year.
Investigate if there's a correlation between cosmic or geophysical events and changes in temporal perception.
Develop computational models that simulate how time perception can be affected by psychological and physical factors, adjusting the I(t) factor to predict different scenarios of temporal infraction.
6. Conclusions and Implications
If this theory proved true, it could have profound implications for how we understand time, both in a physical and subjective sense. It could also influence how we organize our lives, from structuring work time to valuing leisure time.
This "Temporal Infraction" theory is an attempt to combine physical concepts with human perception of time, exploring new ways to understand how we experience and value time in our daily lives. Although still purely speculative, it offers an interesting field for future theoretical and experimentalexplorations.
"Is any smooth, finite shape with no holes a sphere?"
Can somebody just tell me whether it's true or false already...
just watching this has done physical damage to my brain. Thank you
I would have taken the money.
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.
I would take the money and make a sphere out of it
It is about the intersectionality- id 0 = blob id 1 = blob + punchblob (-blob). By defining displacements, we can assign dimensionality of measure, and spot the difference is a bounded philospphical method which limits a posteriori experimental science methodologies. Socrates likes this.
Am I the only one with audio problems on this video. All other videos seem to be fine. :-/
you guys should do a video on the difference between rimman integral and lebesgue integral
she's wearing a doctor who shirt.
Yes I want to listen to Dr. GrigoriPerelman!
2:15 its a figit spinner, 3 years ahead of its time. TRIGGERED.
great video :D
I looked at Perelman's paper - I could only recognise the full stops !!! The stuff in between was a blur !!!
The 8th millennium problem by CLAY Institute: Perelman money declining
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.
Grigori's eyebrows are worthy of worship!
Anytime I feel that my coding job is too hard I go and watch some math videos and my life seems easy again
who doesn't like these videos? I mean not many, but really? why??? they are so much fun.
Math is so cool! I love the TARDIS shirt!
Harder to solve than the Poincaré Conjecture is to find the solution to reward the one who solved it.
Do you know that Poincaré discovered the pixel (picture element : square point) !!!
who told he were the first!
take it easy baby, and relax you are not defending your doctorat thesis..
I thought Fermats Last Theorem had more wrong proof attempts than any other. In the words of mathematical historian Howard Eves, "Fermat's Last Theorem has the peculiar distinction of being the
mathematical problem for which the greatest number of incorrect proofs have been published."
anyone else notice the disguised fidget spinner at 2:12
A 3-ball has -1 (minus one) hole. A solid circle (a 2-ball) has -1 (minus one) hole. Proof. An infinite (2D) sheet missing a solid circle has 1 hole. That solid circle is the hole, so give it -1. A -1 hole is a hole on the outside. A sphere is defined as the covering of a ball. It has one less dimension than the ball.
I feel stupid lol
+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
It took people more to acknowledge his solution than what it took him to solve it, Perelman was also treated as liar and thief by the community that's why he wanted to have nothing to do with it anymore.
I love reading and gaining knowledge of maths and science all the time. The more I know, the more dangerous it gets.
After watching this video, I asked my mate what my name is? 😂
Great work Lad. Need to read more about this conjecture, not completely clear.
heisenberg?
Wow Katie is intelligent and beautiful. I didn't understand the concepts so much but I enjoyed the narrative.
0:44 Heisenberg anyone?
Yes
Are you... certain?
Another Topology video! That's amazing... more people should be interested in these stuffs!