You will remember our discussion (further down this blog) on the millenium challenges in Mathematics set by the Clay Foundation in 2000.
Read the following for an interesting update:
http://www.guardian.co.uk/world/2010/mar/23/grigory-perelman-rejects-1m-dollars
Any thoughts about this?
This is a very interesting happening.It just shows that, as i mentioned on the first post on the millennium challenges in Mathematics, that its just a matter of time. In as much as we human beings may not "know everything" this scenario is proof that we should not underestimate our intellectual abilities. Its however both shocking and interesting that a man who "is currently jobless and lives with his mother and sister in a small flat in St Petersburg." has refused a whole 1 million dollars...ONE MILLION AMERICAN DOLLARS which he dully deserves. Certainly his nonchalant reaction is not one that i or many people i know would have predicted again emphasizing that it is difficult to place human behaviour, emotions etc. in one box.
ReplyDeleteCongratulations Mr.Grigory Perelman
For me, this single case of totally unprecedented behavior from Mr. Perelman is evidence of the futility of the strife of human scientists to place a formula to human behavior. It brings back to focus the question of whether human sciences investigations should continue with the use of the scientific method or we should come up with a new method for studying the human sciences; say, a humanistic method, which takes into account the sporadic, extremely dynamic nature of the human being.
ReplyDeleteInteresting!
ReplyDeleteI think what's more interesting than the fact that this story highlights the unpredictablity of human beings, is the reason for his refusal. He refused it because he felt that his fellow Mathematics were unworthy to reward it.
I don't know much about the Mathematics community but feel able to sympathise with him a bit. I was distintly unimpressed after watching the Fermat's last Theorem videos over the mid semester break, i was struck by how quick the Mathematics community was to praise Andrew Wiley for his solution to the problem. I am not in the least suggesting that the Mathematics he did to solve the problem is simple, yet centuries after a Fermat stated a conjecture, which he claimed to have proved, should we really be jumping up and down because someone has validated the theorem using roundabout methods in the 21st century.
Of course Fermat's alleged proof may have been wrong, but the fact that Wiley validated Fermat's equation suggests otherwise.
Hi!
ReplyDeleteI believe this article has proved all of us who thought that such discoveries in this century in this century is impossible wrong! Many more of these discoveries are yet to be made.
Another interesting thing that this article presents is human behaviour and scientific psychology. As most people have already said, Mr. Perelman’s behaviour is odd and unexpected. It is very shocking that a grown man who lives with his mum will refuse such a reward for his hard work. This leads us to take a close look at generalisation. We all have at the back of our minds that every sane human will accept the offer without hesitation but this is not the case.
I will like to disagree strongly with Kojo that Andrew Wiles proving of Fermat’s Last Theorem just recently in 1994 is outstanding! It took him only seven years after 300 years to prove this theorem. This is a wonderful achievement that should be applauded. Did it not occur to you that some mathematicians in the past might have tried to prove it but weren’t successful?
Also we can really never be sure if Fermat really proved his theorem. His excuse for us not having evidence is that there wasn’t much space to write it down.
Hi!
ReplyDeleteI believe this article has proved all of us who thought that such discoveries in this century in this century is impossible wrong! Many more of these discoveries are yet to be made.
Another interesting thing that this article presents is human behaviour and scientific psychology. As most people have already said, Mr. Perelman’s behaviour is odd and unexpected. It is very shocking that a grown man who lives with his mum will refuse such a reward for his hard work. This leads us to take a close look at generalisation. We all have at the back of our minds that every sane human will accept the offer without hesitation but this is not the case.
I will like to disagree strongly with Kojo that Andrew Wiles proving of Fermat’s Last Theorem just recently in 1994 is outstanding! It took him only seven years after 300 years to prove this theorem. This is a wonderful achievement that should be applauded. Did it not occur to you that some mathematicians in the past might have tried to prove it but weren’t successful?
Also we can really never be sure if Fermat really proved his theorem. His excuse for us not having evidence is that there wasn’t much space to write it down.
Waow!
ReplyDeleteI believe this confirms the point in our TOK lesson that people do math just out sheer passion for the subject and not in this for 1 million dollars. His reaction to winning the money however astounds me. In line with lloyd said, considering his financial circumstances one would have thought that he would have undoubtedly taken the money and bought himself a life! "picking mushrooms"...really? Just like mentioned above I also believe this tells us that human behaviour is not as predictable as the human science make it seem. Oh, Ntiriwa I didn't understand you when you said you disagreed with Kojo about Andrew Wiles' acheivement being outstanding and yet you believe its "wonderful" and "should be appauled"
Here is an interesting link on this topic:
ReplyDeletehttp://www.nybooks.com/articles/archives/2010/apr/29/he-conquered-the-conjecture/?pagination=false
Although we all say that Perelman’s actions don’t conform to the “obvious” human thing to do (what in the world is he thinking!-$1million dollars!!!), it doesn’t make it “inhuman”. We only find it astounding because we have certain paradigms of human behavior in certain contexts. By boxing up the million complexities of human behaviour, we are always in for reality’s rude shocks!!!
ReplyDeleteYou’d realize that, it’s Perelman’s “non-conformist” actions that make the HEADLINES! In other words, he has become a STAR, because we cannot understand Why? How? and What made him do that. However, the fact that he is HUMAN is unchangeable, and thus, so are his actions!!! If you think about it like this, you’d see that the media makes more of a fuss about his behavior than what should be the central intrigue - His solution to a century-old mystery!
To Shawn: I think Mama disagrees with Kojo’s claim that Wiles’ proof is unspectacular and undeserving of the “hula-baloo” from the Math Community’s! But Kojo, why shouldn’t we be excited about one man’s accomplishment of a century-old problem in 7 years?! I also think it’s invalid to call his methods, “roundabout” (maybe to you… but not the Math Community). Again, the Mathematicians did not just accept his proof. They tested it rigorously, found loopholes, scrutinized it…until Wiles was able to justify himself! Probably, pursuing a higher level of Math in the future will show you how "implicitly” simple, and not “roundabout”, the proof is. I used the word “implicit” here because, if the explanation was so explicit, it wouldn’t have taken Mathematicians “forever” to unravel this! That’s the beauty of math - its IMPLICIT simplicity! As Wiles says (paraphrased): “Solving a problem is like entering into a dark room. You fidget around a lot, trying to define your surroundings, and then as time flies, you find the light switch, and EVERYTHING becomes so clear!”
However, Kojo, I must say that your opinion truly affirms that, we JUST cannot understand all possibilities of human thought and personality, just as I can’t comprehend how on Earth you could think of it that way!!!
That is indeed a shocking reaction from Mr Perelman. As my colleagues have already mentioned, this article reveals two very important things: the fact that humans are very dynamic and incomprehensible and also the fact that, there is “hope” for mathematical knowledge in the near future. Perelman’s actions have proved that, in as much as we may think some things can’t be solved, they probably can, since as time passes by, we learn new methods of figuring things out and find out other things which could be related to the subject in question.
ReplyDeleteIt took several years just to prove that Perelman was actually right. This again goes ahead to show the rigorous nature of mathematics and the importance of proof in maths.
Perelman’s refusal to reject the money is quite unusual but can be understood in the sense that, he “quit the world of mathematics in disgust four years ago.” However, this action is definitely not the norm. Further stressing on the beauty of the dynamic incomprehensible nature of human beings.
I just feel I should raise a counterclaim for those of you who point to Perelman as evidence for our lack of ability to understand and predict human behaviour.
ReplyDeleteIt has been claimed by several sources - here for example:
http://mathgradblog.williams.edu/?p=510
...though not confirmed, that Perelman has Asperger's syndrome (AS).
"Pursuit of specific and narrow areas of interest is one of the most striking features of AS. Individuals with AS may collect volumes of detailed information on a relatively narrow topic such as weather data or star names, without necessarily having genuine understanding of the broader topic. For example, a child might memorize camera model numbers while caring little about photography. [...] Although these special interests may change from time to time, they typically become more unusual and narrowly focused..."
Source: http://en.wikipedia.org/wiki/Asperger_syndrome
"Individuals with Asperger disorder have normal or even superior intelligence and may make great intellectual contributions while demonstrating social insensitivity or even apparent indifference toward loved ones. Published case reports of individuals with Asperger disorder suggest an association with the capacity to accomplish cutting-edge research in computer science, mathematics, and physics."
Source: http://emedicine.medscape.com/article/912296-overview
If this is correct, then perhaps we know enough about the condition in order to predict, or at least explain, Perelman's behaviour quite well.
That is indeed a shocking reaction from Mr Perelman. As my colleagues have already mentioned, this article reveals two very important things: the fact that humans are very dynamic and incomprehensible and also the fact that, there is “hope” for mathematical knowledge in the near future. Perelman’s actions have proved that, in as much as we may think some things can’t be solved, they probably can, since as time passes by, we learn new methods of figuring things out and find out other things which could be related to the subject in question.
ReplyDeleteIt took several years just to prove that Perelman was actually right. This again goes ahead to show the rigorous nature of mathematics and the importance of proof in maths.
Perelman’s refusal to reject the money is quite unusual but can be understood in the sense that, he “quit the world of mathematics in disgust four years ago.” However, this action is definitely not the norm. Further stressing on the beauty of the dynamic incomprehensible nature of human beings.
wow!!
ReplyDeletePerelman's reaction indeed emphasizes the dynamic human nature. however, whether Perelman's ability to solve the math problem proves mathematics has a future or not is not certain.
congrats Perelman!
since i don't know the reason he quit the world of mathematics i can't judge him as to whether his reaction was the best or not. i personally don't think refusing ONE MILLION DOLLARS is strange. this accentuates the fact that humans are unpredictable and not strange! i think the headlines should have praised him for his achievement and not this..this goes on to prove that scientific predictions and hypotheses are not applicable in human sciences.
Mr. Kitching, the articles on Aperger's syndrome are indeed insightful, however, I do not find the information sufficient enough to rebut our statements about Perelman’s actions as confirmation of our inability to predict human behaviour. From what I read, Perelman has only been “stipulated” to have Asperger’s syndrome, it has not been confirmed. This stipulation was made by the fact that his actions seem to comply with the symptoms of this genetic disease. However the huge glitch in this claim is the fact that if it is genetic, then some hereditary pattern must justify this, in his family pedigree, which has not been found. Also, the criss-cross between Asperger’s syndrome and High-functioning Autism (HFA) predicts clumsiness and slowness in cognitive development however; a biography of Perelman proves otherwise. So what if he does not have Asperger’s Syndrome? What next for behaviourist theories? We should still accept the fact that his actions are a deviation from what is expected of “normal” human behaviour, and it is this very reason which propels scientists to investigate and try and qualify it as Asperger’s syndrome to provide insights about the future. It doesn’t necessarily contradict our claims about our inability to predict human behaviour.
ReplyDeleteFair points, Tori. I just wanted to draw attention to the dangers of a strict adherence to the idea that human behaviour is really unpredictable, even "random". We are all very attached to the notion that we are free agents with free will. A small and rather inconsequential example from class - if the bell is rung I can almost guarantee that someone in the class will immediately start packing their belongings away. I might even be able to predict exactly who in the class will do this. I am also confident in my prediction that the ringing of the bell will not result in everyone taking off their clothes. As I said, not a very profound example, but I think it shows that there are basic patterns in human behaviour. Just because my predictions might sometimes be wrong doesn't mean that it's all hopeless.
ReplyDeleteAnd we all thought Grigori Perelman would accept the $1m - who wouldn't? That's the kind of behaviour we expect! It's what you are calling "normal".
Wow, well this is amazing. Who on earth would refuse 1 MILLION USA DOLLARS? Considering the fact that this man lives on conditions that are portrayed to be poor. I always thought mathematicians are very unique people , very "normal" like what Mr. Kitching calls them!
ReplyDeleteI really cant believe this man would refuse such a huge amount of money, so much publicity, attention, promotions etc. Well humans are certainly UNPREDICTABLE. This one is for sure. Honestly, I could write a book on such people because I have never heard of a person refusing all these 'good things' especially in the 21 century!
And because such people are becoming rarer and rarer every time, we become very suspicious of them. We either call them "stupid" or "dumb". Honestly, this is the kind of behavior that I would see as 'beautiful'. I laugh when I hear that this man is seen as having Asperger’s syndrome and High-functioning Autism (HFA) predicts clumsiness and slowness in cognitive development, because it only proves that we humans have become so selfish and any act of unselfishness is seen as 'weird ' and unheard of. The symptoms of this syndrome are said to be clumsiness. My graciousness!!I totally disagree with this untrue conclusion, Have we put humans in different categories that if one human does not fall under a given category then they are seen as mentally disturbed or what? Are we not different in terms of our thinking, behavior? Should this man be given a category of being almost insane because he refuses an offer of wealth?
Well, I could write more and more on this but have to go.
Thanks+
Hi Cynthia,
ReplyDeleteThanks for all your contributions. You have helped to bring this blog alive!
I would just point out that people with autism or Asperger syndrome are not "almost insane". It's just that in extreme cases there is sometimes a convergence of certain difficulties in social situations and brilliance in certain academic disciplines.
Whether this applies to Grigori Perelman is open to question, but I wanted to make a larger point - namely that the complexities of how real people behave has not left psychologists and social scientists totally baffled. Explanations and theories have been developed, however imperfect some of them may be.
I think there is a common thread running through quite a number of posts I have made on these threads in the last few days - and that is: be very wary of blanket statements. "All communication is language", "art is entirely subjective", "human behaviour is totally unpredictable", "morality is all about individual choice"... Be wary and consider the counterclaims. The truth is often (but not always) somewhere in between the extremes. And once again on a practical note, blanket statements, if accepted, often leave nothing further to be said. And that's a problem for your essay or presentation.
Thanks Mr Kitching.
ReplyDeleteJust a quick comment...for proving a conjecture that mathematical personalities have been trying to prove for YEARS,he was offered ONE MILLION US DOLLARS.
ReplyDeleteSimilarly, Picasso painted something in a SINGLE day, again years ago, and it sold for ONE HUNDRED AND SIX MILLION DOLLARS recently. 100X more than proving the conjecture.
Interesting contrast to the stereotype that subjects such as Math and the natural sciences have.
This is truly amazing ! One million dollars how many people get awarded such a substantial amount just because of their passion ? I was dumbfounded by the humble character of Grigory Perelman. For me this man proves to be one of the most down to earth people I have ever read or heard about. However, I make this comment with caution because his intentions are not clear , he may not want the money however he may have other motives behind his actions.In such a world we can never do anything without being criticized.I feel many people are shocked because he is jobless and still lives with his mother and sister.Many must think he is out of his mind ! Is he crazy ? I wonder !
ReplyDeleteHowever,his attitude to a news reporter proves that he is erratic he says "You are disturbing me. I am picking mushrooms." Generally, this is a bad answer , I would like to think he would enjoy his success and welcome the publicity. This proves a very important point as Shawn said Humans are unpredictable.
As the public we will never know the genuine reason why he refused the award.It does not matter what we think ! It is what he thinks that is important .As humans we always demand answers but sometimes it is better to stand back and reflect on the way different people reason. We do not know what runs through everybody's mind at every particular pint in their lives ! Opinions and actions must be respected not condemned.
Despite the fact that taking a multiple stance is not a good way to be focused, I will like to agree with both humans being predictable and unpredictable.
ReplyDeleteHuman behaviours are unpredictable.
In the case where we can predict students behaviours after a bell has been rang, is true but questionable. We are supposed to pack our bags and leave for the next class. It is a MUST. We are expected to do it. And it is only considered as "normal" to act that way. In that case, are we REALLY predicting human behaviours? YES but NO
We expect humans to behave in a certain "expected" or "normal" ways. Such as Mr Perelman accepting the money. In this case we could perhaps say that we can predict human behaviours.
However, why do we say that human behaviours are unpredictable? For example, businesses cannot predict what humans will purchase most or will wish to buy most so that they could increase sales. (excluding any external factors) Also, if we could predict human behaviours in sporst, that means that there will be no goals in soccer games.
Or could we say that since football players can predict other football player's move, they deceive each other in order to dribble past players or score goals? This could be very possible.
Thus, in my opinion, could we say that human behaviours are unpredictable due to the misconception of human nature which is actually predictable?
thank you
By the way, for Mr Perelman, they say he was "socially insensitive" Wouldn't that be the cause for the refusal of such amount of money?
As I said before human beings are extremely unpredictable. Who would have thought that such a man who can hardly be called middle class publicly refused the money offered to him? We “the public” and them ”his society “would have expected him to accept such a huge amount of money with OPEN hands. But not all humans are unpredictable, take for instance a group of fans watching their favorite team playing when they go and score, it would be very disturbing to see the fans start weeping not because they are happy but because they are sad. In such a case, I would expect them to rejoice and be glad. So humans are predictable. But if I say humans are totally predictable then I am wrong so they are predictable to a certain extent depending on how we know the m and how they behave. Well, humans are so complex………..
ReplyDeleteOne million dollars.... I'm trying to put myself in his shoes and figure out what I would be thinking if I was in this situation. And I'm thinking that maybe human behaviour is not completely unpredictable. Go with me here..if i was him, after winning such an amount of money I have gained something which could be worth more than a million dollars; international recognision. Tv appearances, i.e., interviews on talk shows (i would be looking forward to meeting Larry King if i was him), my name being mentioned in history books probably for years, maybe a few sponsors (free clothes and stuuf , you'll never know)...and by rejecting the money, making people wonder..(look at us, we're still talking about him), he is probably becoming a household name, famous in his own right.....Ok , I'm not saying this may be his true agenda but think about if we try and look a little deeper, observing certain 'patterns' in his decisions could help us predict his intentions, maybe even his next action...i mean he lives with his mum, that just makes him a topic of discussion...
ReplyDeleteHi everyone. I am really enjoying some of the arguments here and I would like to share my thougths on the matter. Firstly, yes we all admit that it is really suprising that he did not accept the 1 Million Dollar prize. Now as to why he did not accept it is quite debatable. As Mr. Kitching commented earlier I do not think it is right to make extremist claims like "humans cannot be predicted" it is neccessary to consider other possibilities. We have to realise that humans can actually be predicted to a certain extent. Some things humans do are innate and as a result can be predicted. For example if a hot iron accidently touched your hand you would automatically pull your hand away. It is relfex. This may not be the best example but I feel this example could be likened to other things humans do. Just as we may be able to predict this we should be able to, with an appropriate means, determine human behavourial patterns to a certain extent.
ReplyDeleteI would like to introduce a different possible reason for him not accepting the prize money. As a mathematician solving a great problem could be something more than just a hobby or a means of making money. Infact I feel to be able to solve such a problem it must be something that you are truly passionate about maybe even to the point of obsession. It must be an integral part of your being. Andrew Wiles who solved Fermat's Last Theorem actually stopped research at the university he was working at to dedicate himself full time to solving the problem and he did this for seven good years until he got the solution. This occurence should automatically tell us that it was something he had the upmost dedication for. There should be some real 'love' for the problem before you can solve it. Now if Mr.Perelman had this amount of 'love' for the problem, solving it and collecting a prize for it would in effect nullify his 'love' for the problem. It would be almost like finally succeeding in courting the love of your life but to only have done it for other benefits she might come with. In this case money being the benefit. I feel a mathematician who has great passion for a problem like this might not see the point in collecting a prize for it. He would have great joy in knowing that he was able to solve his problem. That would be the pinnacle of his success for him and not the prize money. Many people might not be able to understand this but I have tried to put myself in his shoes and this is how I interpreted it.
Football is something I am also very passionate about and if i was able to become a proffesional footballer it would most certainly not be for the fame or money. The mere fact that I have acheived my goal and I am doing something I 'love' would be all the satisfaction I need. Just like how Mr Perelman may have gotten his satisfaction from actually solving his problem and didn’t want to cloud his purpose by accepting a "small"(I choose my words carefully here)prize. “Small” because that is how HE may see it in relation to solving HIS “Great” problem. Ironically in this case the money has no value where as his solution is priceless!
I think this is a good example of true passion. When you are passionate about something, you care for that thing alone and nothing else. I hope you guys can see the angle I am coming from and hpefully reflect on it. As I sit here i have studying to catch up on but I came accross this and I decided to give my input.... I wonder what I am truly passionate about and if i can ever be as passionate about something as Mr Perelman was about this problem. Can you? Food for thought...
I hope that our deliberations on mathematics have given you some insight into the nature of that profound intellectual endeavour. It is perhaps in this area of knowledge that deep questions emerge most quickly.
ReplyDeleteI am aware that the everyday experience of learning mathematics sometimes appears a far cry from some of the questions about it we have tried to pose in TOK, but I am confident that we have contributed towards a deeper understanding of what mathematics is about and how it might or might not relate to the world in which we live.
I would only advise you to try to connect what we have discussed in class and here on this blog as best you can to your classroom experiences, using examples from there wherever appropriate.
Perelman's actions are indeed astonishing and unbelievable! A grown man who still lives with his mum in a small flat, refusing a golden ticket out of poverty!However, his actions reveal a lot about human behavior and psyche. Perelman may have haboured an intense passion for mathematics, prompting him to indulge himself fully in the mathematical realm. His persistent manipulation of axioms and conjectures, may have enabled Perelman arrive at the solution of this century-old problem,and in the process, attain a degree of satisfaction, that could not be valued by any monetary figure. This topic in particular showcases human irrationality at its finest. A rational economic opportunity, being turned down by one's ulterior sentiments for a certain subject. Perelman appears to derive innate joy by witnessing the his efforts, fueled by his mathematical passion, come into fruition. This is common characteristic trait for mathematicians, who attain inner fulfillment by by solving complex problems. Thus this topic on the whole, raises the questions of man's ability to make do internal satisfaction and contentment, against the rewards of external, worldly benefits.
ReplyDeletei think that there is a difference between having the passion to do something and doing something to gain something in the return. Grigory is one who has the passion for mathematics and this passion drove him to solve the mathematical question. As humans, it is only right that we hesitate on his actions because the amount of money he is to receive is very huge. Any other person would have taken this amount but Grigory, though not very well to do declined because he believes in satisfying his passion. i think as individuals, we owe it to him to understand and accept his decision and try not to criticise him too much.
ReplyDeleteEsther
I’m sure the first thought that struck most of us was, “how on earth would someone refuse a well-deserved million dollars?” But then, Perelman’s action illustrates an important point about humans. First of all, humans are very complex subjects and not wholly predictable. There may be some patterns to human behaviour but I won’t advise anyone to bet his last penny on anyone. At least, with this insight, we can attempt to understand the huge challenge posed to the human sciences. Is there even a point to human sciences that attempt to predict human behaviour?
ReplyDeleteMost of us would consider that the ‘normal’ thing would be to accept the million dollars for a good job done. However, the idea of ‘normal’ can be very relative. I’m sure that if we were all ascetics, we would probably regard Perelman’s action as ‘normal’ and expected. Hence, surprise at the refusal is unwarranted, in a sense. We don’t know his culture, his religious affiliations and his personal standards.
Most people were shocked when he refused the money. However, this illustrates an important point about us. Even though, most of us agree that humans are very complex subjects, not wholly predictable and can be very random, we’re still shocked when a person engages in something considered ‘abnormal’. This may indicate that we accept this fact rationally (in our heads), but not REALLY.
I’m sure the first thought that struck most of us was, “how on earth would someone refuse a well-deserved million dollars?” But then, Perelman’s action illustrates an important point about humans. First of all, humans are very complex subjects and not wholly predictable. There may be some patterns to human behaviour but I won’t advise anyone to bet his last penny on anyone. At least, with this insight, we can attempt to understand the huge challenge posed to the human sciences. Is there even a point to human sciences that attempt to predict human behaviour?
ReplyDeleteMost of us would consider that the ‘normal’ thing would be to accept the million dollars for a good job done. However, the idea of ‘normal’ can be very relative. I’m sure that if we were all ascetics, we would probably regard Perelman’s action as ‘normal’ and expected. Hence, surprise at the refusal is unwarranted, in a sense. We don’t know his culture, his religious affiliations and his personal standards.
Most people were shocked when he refused the money. However, this illustrates an important point about us. Even though, most of us agree that humans are very complex subjects, not wholly predictable and can be very random, we’re still shocked when a person engages in something considered ‘abnormal’. This may indicate that we accept this fact rationally (in our heads), but not REALLY.
SAM SARP
Who knows, he might have had a strong reason for rejecting that $million prize. But I seriously think was a stupid decision to make in this 21st century. There is something that opportunity comes but once. I agree totally with Shawn said, that math is just sheer passion for the subject. This brings out the unpredictable nature off humans. I mean how he can reject this huge sum of money considering his financial status should blame him for not accepting the $1million price? I think the journalists should still keep on finding out form him why he rejected the offer.
ReplyDelete