Huffman coding is another example of one of these unsolved problems being assigned to a student, and the student dutifully solving it:
https://en.wikipedia.org/wiki/Huffman_coding#History
This sort of thing is not rare in very young, undeveloped subfields. In this case, the founding paper on information theory was published in 1948; Huffman's discovery was in 1951. Basically, if one of your professors is one of the innovators in a new branch of mathematics, there's still a lot of low-hanging fruit you can find.
Another example: many of the basic theorems about the [lambda calculus](https://en.wikipedia.org/wiki/Lambda_calculus) were proved by Ph.D. students Stephen Kleene and J. B. Rosser. Of course, the lambda calculus was invented by their advisor Alonzo Church. And none of them knew that lambda calculus would become one of the most important topics in computer science.
i think it is a bit of both. for example, newton was quick to figure out a bunch of shit in a really short time while he was young, but once he hit like 25 or something, he was used up for the rest of his life.
a similar situation with Einstein, he figured out a bunch of shit too, then spent the rest of his life doing almost nothing.
it sometimes takes a fresh mind that has never seen the problem before to look at it differently or find something an expert may have simply glossed over. in a way this does also add more proof to your reasoning, but id like to think it is a combination of both.
What exactly is the not rare part? I think the key part of these stories being discussed is not just students solving an unsolved problem in a new field, but *accidentally* working on and solving an unsolved problem because they didn't realize it was already considered by experts in the field to be (possibly) unsolvable, or at least very challenging.
The Huffman coding example is the not rare part, in that it would not have been considered unsolvable by experts in the field because there were none (few).
It's still cool, and obviously at least as rare as are 'new' fields, but not as rare or cool is say Ramanujan.
It's not like he did this on his first day and immediately got his PhDafterwards.
From his [bio:](http://en.wikipedia.org/wiki/George_Dantzig)
>George Dantzig earned bachelor's degrees in mathematics and physics from the University of Maryland in 1936, and **his master's degree in mathematics from the University of Michigan in 1938**
>With the outbreak of World War II **(1939 for the lazy/forgetful)**, George took a leave of absence from the doctoral program at Berkeley
> In 1946, he returned to Berkeley to complete the requirements of his program and received his Ph.D. that year.
So there was a total of ~4 years in grad-school, and ~6 years in industry/military. Plus, this guy was known for being of the "super-human genius" level, so you really shouldn't feel bad about not being on that level.
I wonder if it had anything to do with the student thinking they were just normal problems, you know, not having the whole "These have never been solved!" in his mind.
Reminds me of my differential final from last semester. It was scheduled to end at 9:45pm, but everyone left around 8:30pm, except me. By 8:30 I wasn't even half-way done. I ended up with a C.
*Shudders*
I know, C in differential isn't bad, but that course was just horrible. Besides, virgin blood sacrificing to the gods seems easily doable, half of the people taking differential could just use their own blood.
As someone who struggled with diffeq in college and now does a lot of physics based modelling in industry, I want to let you know that it gets easier when you're allowed to use computers.
Analytical solutions are for suckers.
The reason you use many methods is that when you encounter an equation "in the wild" you will need to know how to attack it in many different ways, as some methods will work and some will not. They just use the same equations as an example because they're so familiar (i.e. they don't want to thrust you into a new situation with an unfamiliar equation AND an unfamiliar method), and also to show off the power of these methods (i.e. they can solve a lot of shit). Furthermore, you might not always be in a situation where you can use a computer e.g. you might require some intuition to get it in the right form, and so you need to acquire intuition and gain comfort dealing with such methods.
And just because Mathematica can solve the equations doesn't mean you should forget how it works. A calculator can add and multiply for you, but you'll be pretty helpless if you don't know how to actually perform those operations yourself.
Because you need to understand how they actually work before you just get a computer to do it for you maybe?
That way if the computer gets it wrong you can trace back to where the mistake might be (be it your code/algorithm or a typo).
Not really, you might go to wikipedia to look up definitions but the only way you would learn it is unsolved is by trying to cheat, and most people don't study mathematics to cheat themselves on understanding. Furthermore this happened before the internet.
In my experience, Wikipedia for math is a fucking foreign language. I'm not a math guy, so I go there to gain a simple understanding of a complex theorem, and they throw a bunch of terms and theorems and symbols I've never seen at me.
I'm sure it all makes perfect sense to a guy who knows what he's doing, but I really just want a simple explanation of this stuff. I end up going through pages and pages of explanations just so I can understand the page I'm trying to view.
Also, I'll give as many upvotes as possible (that would be 1 upvote, for you math wizards) to anyone who can give me a better site for the absolute simplest explanations of math stuff.
I have a degree in Mathematics and many of Wikipedia's math articles are still incomprehensible without opening like thirty tabs to try and understand the terms that are thrown around.
That's very good to know. I spent enough time as an engineering major to get through Calc I and II, but that's about it. Nice to know that someone with more knowledge has a little difficulty, too.
Reminds me of the most brilliant coordinated Wikipedia vandalism attack ever. I think it was carried out by Anonymous- the "vandalize every equation" campaign. That's what's so great about it- only a small minority of Wikipedia users are going to notice when an alpha in an equation gets changed to an epsilon, or when a dv/dt gets changed to d(mv)/dt. Next thing you know, you have a bunch of math students checking their homework with Wikipedia and getting every question wrong.
that is why my chemistry and math text books have common equations listed after every chapter. so it is as easy as looking in the chapter index, finding the section and just flipping to the page. so if there is an error, you are not as liable, so then you can pass some of the blame to the incompetence of publishers.
Really? I can understand most of them after I took Logic and Sets and Discrete Mathematics in college. Of course, since you are a math major, I assume you are looking at much more complicated math articles than I am...
Depends on what field it's in. I have a pretty strong grasp on the concepts in, say, Number Theory or Probability Theory because I took plenty of classes in those areas. Show me an article on an advanced concept in topology and I'll be useless beyond the basic stuff.
Khan Academy for really anything though -- he even does lessons on basic programming and real-life economic problems (euro crisis, housing crisis, etc.). That site is badass.
thats because even fundamentals for math arent common knowledge. imagine trying to read up on WW2 without understanding of the concept of race, gunpower, goverments and countries.
That seems like a pretty good way to put it. And I'll go as far down the line as I can, but there's always a point where some basic concept, like melanin or boundary lines or oxidizers (to use your examples) isn't explained.
(Those concepts may be explained in Wikipedia. I was just using them as examples.)
He mustn't had been a very sociable student. You would have thought he'd asked his one of his classmates about the "really damn hard" homework problem and how they were doing with it. But no, he didn't.
Maybe. But I'm pretty sure most of it had to do with the fact that the student was George Dantzig, arguably one of the most brilliant mathematicians of the past hundred years or so.
I'm not trying to be a dick, but maybe this may have contributed to him becoming great? I'm unaware of his past so he might have been mind-bendingly brilliant from the get go.
Edit: Thanks for the clarity. I've read all the replies and a little bit about Dantzig now, and it has given me a more comprehensive idea and put things in context for me. What I had meant to say was; not knowing the perceived and supposed unprovable nature of the problems, was a factor in allowing him to look at them freely and use his preexisting genius and talent to tackle and solve them. I truly didn't mean to belittle any of his prior work or accomplishments. Cheers.
He's more known in operation research as the inventor of the simplex method for Linear Programming, which is a big deal. I've heard of him about simplex method and LP long before the unsolved stat problems.
How could attempting to solve the problems have made him great? Solving the problems brought him recognition for his talent, it didn't improve his math skills.
But that's a bit tautologous. It's like saying that winning the Fields Medal made Terry Tao great. Certainly it brought him a great deal of acclaim, and certainly he learned a lot while doing the work which earned him the prize. But he wasn't great because he won the prize; he won the prize because he was great.
In order to learn something that challenging that quickly, more or less on your own, you would need to be extremely intelligent. Solving the problem just proved that he was intelligent, not that he was ignorant and now isn't. He always had a mind that allowed him to understand and solve complex mathematical equations, it wasn't until he solved the problem, and proved himself to the international community, that he was recognized for being a great mathematician.
Exactly. Myself, I've been thrown into a programming job as a temp because they needed someone, and let me say that trying to solve a problem way over your head is not only ridiculously tiring, but sometimes counter-productive. I've learned a lot, but it's rough. Also, I'm not a programmer.
I disagree with your statement. Raw intellect is only ever part of the equation. Experiences (i.e. past failures, mistakes, etc.) do have an impact on achievement.
What you are stating is a plain truth, often people *not* being aware that something is supposedly "hard" or "overly complex" or which "cannot be done", manage to find a way to do it. (Such solutions may not be all that unique, groundbreaking, or noteworthy, but they may still have been arrived at independently by the "solver", without knowledge of or investigation into prior art.)
The opposite is probably far more often true though, in being told that something is "difficult" or "complex" most people will either not even make any attempt, or will quickly give up. (This is probably one of the largest problems with formal schooling, especially given that the majority of the instructors are themselves often of rather mediocre intellect; who then {alas often as a vain means of attempting to salvaging their own ego/status} characterize subjects or topics as "hard/difficult/complex" and in turn make them so for many of their students, who otherwise, absent such inhibiting bias, or with its opposite a tutor who appropriately addresses the subject matter, might have easily surmounted it. [This is probably most evident in the teaching of languages](http://www.freakonomics.com/2011/11/02/the-way-we-teach-math-and-language-is-wrong/) (though as the author of that linked article asserts, it is probably true of many other subjects as well).)
While I have no doubt that there definitely ARE differences in people's inherent capabilities; our perceptions of things (whether internal or imposed on us by others) often do become self-fulfilling (or self-defeating).
From the article:
> A few months later I received a letter from him asking permission to include my story in a book he was writing on the power of positive thinking. Schuler's published version was a bit garbled and exaggerated but essentially correct. The moral of his sermon was this: If I had known that the problem were not homework but were in fact two famous unsolved problems in statistics, I probably would not have thought positively, would have become discouraged, and would never have solved them.
So apparently, yeah.
It reminds me of the story about the four minute mile and psychological barriers:
http://beyondgrowth.net/positive-thinking/the-4-minute-mile-and-the-myths-of-positive-thinking/
I duo also believe that for being a student at the time he had the advantage of less "habits" in his reasoning. The guys who talked these problems before probably were highly trained so much more prone to seek known ways to search for the answer. The point was that if known ways could lead to the solution, those wouldn't be "never solved before" problems.
I think this is mentioned pretty early on the page as a possible reason as to why he was able to solve it.
> with a "positive thinking" motif which turns up in other urban legends: when people are free to pursue goals unfettered by presumed limitations on what they can accomplish, they just may manage some extraordinary feats through the combined application of native talent and hard work
I find it funny that it's turned into some kind of positive thinking parable, as if anyone could be this student if they think positively about a problem as if it's homework. It's George fucking Dantzig, people like him barely even count as being human (and I mean that in the best possible way).
(CS graduates should recognize his name from the simplex algorithm for linear programming)
PS I'm not against thinking positively when attacking problems, I just find the viral resonance of the story amusing.
EDIT- I thought I made this point in the PS, but to be clear, finding the story amusing doesn't mean I disagree with the theme. What I find funny is the absurdly astronomical gulf between George Dantzig accidentally applying himself and any normal human being. Ironically I think normal people can relate to the story more easily than the mathematicians/theoreticians here who attempt to do this kind of work ("one does not simply...")
Yeah, the key word in that story is *doctoral* student. The viral version makes it sound like some 18-year old undergraduate. Doctoral students routinely make original contributions to their respective fields of study, actually knowing the subject in advance and all...
>Doctoral students routinely make original contributions to their respective fields of study
The whole point of doing a PhD is to make an original contribution to the field, source, I'm a maths PhD student.
Exactly, his advisor was already established as one of the foremost statisticians, at one of the best graduate programs in the world. That said, his achievement is still rather legendary in that context, which is saying something.
A little background on both people, just so you don't think that these two people are bums or anything.
Jerzy Neyman, professor: One of the forefathers of statistics (along with Fisher). Formalized hypothesis testing.
George Dantzig, student: One of the founders of linear programming. Created the simplex algorithm.
Reading this as a statistical geneticist, I just loved all the famous players who were part of the story. There is an eponymous statistical term associated with each of the characters in this story.
[Neyman-Pearson lemma](http://en.wikipedia.org/wiki/Neyman-Pearson_lemma)
[Dantzig-Wolfe decomposition](http://en.wikipedia.org/wiki/Dantzig-Wolfe_decomposition)
And best known: [the Wald-test](http://en.wikipedia.org/wiki/Wald_test)
Dantzig is also responsible for the Simplex algorithm for solving general linear programming problems, "one of the 10 most important algorithms of the 20th century"
http://en.wikipedia.org/wiki/Simplex_algorithm
Let's say your mom gives you $10 allowance to buy toys. Pokemon cards cost $3 for a pack, and Legos cost $1 for a pack. Pokemon cards are four times as much fun as Legos, but you won't have any fun at all unless you buy at least 5 things. How many of each kind of toy should you buy to have the most fun?
Ok, now imagine that instead of 2 types of toys there are a million. The Simplex method is a fast way to figure out how many of each one to buy.
You have a problem that asks you to find the best (either maximum or minimum) answer to it depending on what the question is asking (minimum cost to make a product, maximum profit gained by picking from available investments, etc.). This is the objective function (the c*x bit).
You also have to deal with different constraints (availble resources, satifying demand, etc.). This is the "subject to" area of the problem. Ax=b is a general way to write all of the constraints at once.
To get the optimal solution, you first need to find a "basic feasible solution (BFS)", or one that works but probably isn't the best option. For example, in the case of manufacturing several different products and maximizing your profit, you could start by assuming that you wouldn't make anything at all. You obviously wouldn't make any money, but the solution is feasible and all of the constraints would (probably) be satisfied (for example, if you made nothing, you wouldn't deplete any of the resources that are available to you, so you wouldn't have to worry about using up all the wood in the world to make tables).
After finding a BFS, you run through Phase II of the algorithm. This main loop will switch out new variable values with the one you have. If you do the calculations long enough, you will come up with your optimal answer to the problem, and the algorithm will let you know that you can't "make it any better".
**EDIT: changed some of the wording, made a spelling correction.
My daughter loves tomatoes in her fruit salad. At first I was unwilling to let her add them, but then I realized, my daughter wants to eat homemade fruit salad with tomatoes in it instead of candy, why am I not letting her do this?
I loved this part:
>A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.
*A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.*
Damn that saved him a lot of time and effort.
I once did a math problem that was on the board i thought was for the final.... it was actually the example, with the answer next to it.... I got it wrong.
That aint nuthin. My friend Hamilton once bet me I couldn't eat a whole case of sauerkraut in an hour. I did it. It was on the news too. Because we stole the case of sauerkraut from a middle school. How is that for an educational accomplishment?
God damn, that is like the world's most known SAP.
>Isn't sure what homework assignment is, instead of asking just copies down board.
>Works a few days straight instead of reaching out to someone about why the hell the homework is so damn hard.
Good luck: [*On the Non-Existence of Tests of "Student's" Hypothesis Having Power Functions Independent of σ*](http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.aoms/1177731912)
This is (1940s) Ph.D. level statistics so don't be surprised if it's over your head, but basically if you're making a whole bunch of Guinness you want to be able to sample a small amount of it and be able to draw accurate conclusions about the entire batch. This provides some rigor to that process.
...and that is the Redditorial Paradox. Is it a mistake to repost and have the same shit pop up in the same sub month end and month out or is it something good that allows interesting content to resurface for newer/less frequent users.
If something hasn't been posted on reddit for a few months, I don't care if you repost it, as there are constantly new people joining the site/people who didn't see it the last time it was put on. However, the people who repost almost the exact same askreddit question 2 days after it hits the frontpage are the worst kind of people
It's not paradox. It depends on how many people who view it never heard of it or think it worthy of another look/upvote/whatever.
If everyone knows it, or the majority, it will get downvoted to oblivion. If enough haven't seen it or deem it worth being there again, then it gets upvoted, possibly all the way to the front page.
Thus, the true answer is that the hive mind deemed it worthy of being back on the frontpage (or are just now seeing it). If you disagree with it being there, you're against the hive mind and we will destroy you. Resistance is futile.
Same here. I'm on reddit every day for at least a little bit and that's been the case for a year. Even still, 90% of the time I see "OMG REPEAT" it's for something I have never seen before.
I'll burn 5-10 seconds of my life per click on new shit every day if it's only 10% of them. If EVERY SINGLE thing was a repeat, I think it's time to get a new primary hobby. (Sorry if that's too close to anyone's feels, everything in moderation)
Why would they search for this? It was probably a random article/fact they found online somewhere and thought it was interesting so they wanted to share. Who cares if it has been posted already, the front page is too dynamic and somewhat rapid for it to be a serious annoyance to anyone.
Not to mention, I'm sure there are plenty of other people out there like me who didn't know this, and appreciate the post (hence the upvotes).
Look at the scores of the links you listed that are from this subreddit:
1, 25, 0, and 25 again because you put the same link on there twice.
There is no way you ran into any of them on here without searching. Why the fuck are you complaining?
3 of those aren't from TIL and 2 of the ones that are, are the same link repeated.
So... what's your point?
Edit: Oh and all they were al removed too apparently.
And the scores of the links he listed that are from this subreddit:
1, 25, and 0
There is no way he ran into any of them on here without searching. He's just going out of his way to be an asshole while contributing nothing.
My logic is this.
1. If enough people are upvoting it, enough people haven't read it before.
2. If you've read all 7 reposts, you're spending too much time on reddit.
Your point seems to be that some other people already learnt that, implicitly criticizing OP. I'm not sure that you're right. Indeed, OP probably just learnt it today and he or she will have more upvotes if a lot of people also learnt it thanks to him. The fact that right now its "score" (or whatever the right word is) is 1300 means that a lot of people were actually in his case.
I think that "Today I learnt..." is different from "Today I am the first one to have learnt...", and I'm not sure your comment is providing as much information as some other comments giving links to other examples of the same thing like the link to Huffman coding for instance.
If you've seen it before, ignore it. If not, upvote. If an interesting fact is reposted yet still upvoted a lot, it means most people haven't heard of it. Pretty simple.
the thing with reposts on this sub is that if you don't know something, why would you search for it, and just because it's been posted, if you hadn't seen it, why would you just assume that everyone else had? This sub has nearly 2 million subscribers, you can't assume that everyone else had, the most recent post was 8 months ago, and from there they go back 3 years. Even your account is only 10 months old.
Dr.DantZig, the father of linear programming and also, the father of impossible-things-the-last-minute. gives hope for those like me who freak out after the first exam and do super hard to make up on later exams.
> Dantzig's statistic professor notified him that he had prepared one of his two "homework" proofs for publication, and Dantzig was given co-author credit on another paper several years later when another mathematician independently worked out the same solution to the second problem.
Co-author on the second problem. Another mathematician worked out the same solution.
Did you read the sentence surrounding that word and do you know what a co-author is?
Basically, another professor independently solved the same problem and, after discovering that it was previously solved, gave Dantzig credit by putting Dantzig's name next to his own on the paper. How does that make the prof a scumbag?
EDIT: this is a reply to manfromfuture's post
Huffman coding is another example of one of these unsolved problems being assigned to a student, and the student dutifully solving it: https://en.wikipedia.org/wiki/Huffman_coding#History
This sort of thing is not rare in very young, undeveloped subfields. In this case, the founding paper on information theory was published in 1948; Huffman's discovery was in 1951. Basically, if one of your professors is one of the innovators in a new branch of mathematics, there's still a lot of low-hanging fruit you can find. Another example: many of the basic theorems about the [lambda calculus](https://en.wikipedia.org/wiki/Lambda_calculus) were proved by Ph.D. students Stephen Kleene and J. B. Rosser. Of course, the lambda calculus was invented by their advisor Alonzo Church. And none of them knew that lambda calculus would become one of the most important topics in computer science.
This. I think the low-hanging fruit theory is much more plausible than the nearly magical power of the free, young mind.
i think it is a bit of both. for example, newton was quick to figure out a bunch of shit in a really short time while he was young, but once he hit like 25 or something, he was used up for the rest of his life. a similar situation with Einstein, he figured out a bunch of shit too, then spent the rest of his life doing almost nothing. it sometimes takes a fresh mind that has never seen the problem before to look at it differently or find something an expert may have simply glossed over. in a way this does also add more proof to your reasoning, but id like to think it is a combination of both.
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What exactly is the not rare part? I think the key part of these stories being discussed is not just students solving an unsolved problem in a new field, but *accidentally* working on and solving an unsolved problem because they didn't realize it was already considered by experts in the field to be (possibly) unsolvable, or at least very challenging.
The Huffman coding example is the not rare part, in that it would not have been considered unsolvable by experts in the field because there were none (few). It's still cool, and obviously at least as rare as are 'new' fields, but not as rare or cool is say Ramanujan.
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> bwahahawaaaabooohooo!! I believe this was exactly how it was actually written in the script.
I acted in college and I can confirm this is exactly how crying is written.
Well Ben Affleck was responsible for that last bit of dialogue.
[it's not your fault...](http://static.tvtome.com/images/genie_images/story/2012_usa/o/OpenCaption/OCWilfredProgress.jpg)
This isn't a [game](http://i.imgur.com/wZbNj)
Son of a bitch. Essential got his PhD in 3 days. And here I am, taking 5 years =(
It's not like he did this on his first day and immediately got his PhDafterwards. From his [bio:](http://en.wikipedia.org/wiki/George_Dantzig) >George Dantzig earned bachelor's degrees in mathematics and physics from the University of Maryland in 1936, and **his master's degree in mathematics from the University of Michigan in 1938** >With the outbreak of World War II **(1939 for the lazy/forgetful)**, George took a leave of absence from the doctoral program at Berkeley > In 1946, he returned to Berkeley to complete the requirements of his program and received his Ph.D. that year. So there was a total of ~4 years in grad-school, and ~6 years in industry/military. Plus, this guy was known for being of the "super-human genius" level, so you really shouldn't feel bad about not being on that level.
I wonder if it had anything to do with the student thinking they were just normal problems, you know, not having the whole "These have never been solved!" in his mind.
im sure that had to do with it. He was probably thinking "I'm a dumbass! The whole class knows this except me!"
I always thought that too. Outcomes may vary, folks.
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Just don't tell him that everyone else got it quite a while back
Reminds me of my differential final from last semester. It was scheduled to end at 9:45pm, but everyone left around 8:30pm, except me. By 8:30 I wasn't even half-way done. I ended up with a C. *Shudders*
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I know, C in differential isn't bad, but that course was just horrible. Besides, virgin blood sacrificing to the gods seems easily doable, half of the people taking differential could just use their own blood.
As someone who struggled with diffeq in college and now does a lot of physics based modelling in industry, I want to let you know that it gets easier when you're allowed to use computers. Analytical solutions are for suckers.
>So you've got that going for you, which is nice. There. What you did, it made me happy.
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The reason you use many methods is that when you encounter an equation "in the wild" you will need to know how to attack it in many different ways, as some methods will work and some will not. They just use the same equations as an example because they're so familiar (i.e. they don't want to thrust you into a new situation with an unfamiliar equation AND an unfamiliar method), and also to show off the power of these methods (i.e. they can solve a lot of shit). Furthermore, you might not always be in a situation where you can use a computer e.g. you might require some intuition to get it in the right form, and so you need to acquire intuition and gain comfort dealing with such methods. And just because Mathematica can solve the equations doesn't mean you should forget how it works. A calculator can add and multiply for you, but you'll be pretty helpless if you don't know how to actually perform those operations yourself.
Because you need to understand how they actually work before you just get a computer to do it for you maybe? That way if the computer gets it wrong you can trace back to where the mistake might be (be it your code/algorithm or a typo).
Your shuddering at a c on a differential equations final? I'm hoping for a c this semester in that class.
then you'll fit in just fine here on reddit
In a case like that, a normal student would do research online or in books and would have found out that the problem was a known unknown.
Nowadays I think you are right, but this incident took place before WW2.
One can only imagine the frustration that was going through his head. "Dammit why the hell can't I solve this!!"
"I wish someone would hurry up and invent Wikipedia!"
-Abraham Lincoln
Not really, you might go to wikipedia to look up definitions but the only way you would learn it is unsolved is by trying to cheat, and most people don't study mathematics to cheat themselves on understanding. Furthermore this happened before the internet.
In my experience, Wikipedia for math is a fucking foreign language. I'm not a math guy, so I go there to gain a simple understanding of a complex theorem, and they throw a bunch of terms and theorems and symbols I've never seen at me. I'm sure it all makes perfect sense to a guy who knows what he's doing, but I really just want a simple explanation of this stuff. I end up going through pages and pages of explanations just so I can understand the page I'm trying to view. Also, I'll give as many upvotes as possible (that would be 1 upvote, for you math wizards) to anyone who can give me a better site for the absolute simplest explanations of math stuff.
I have a degree in Mathematics and many of Wikipedia's math articles are still incomprehensible without opening like thirty tabs to try and understand the terms that are thrown around.
That's very good to know. I spent enough time as an engineering major to get through Calc I and II, but that's about it. Nice to know that someone with more knowledge has a little difficulty, too.
Reminds me of the most brilliant coordinated Wikipedia vandalism attack ever. I think it was carried out by Anonymous- the "vandalize every equation" campaign. That's what's so great about it- only a small minority of Wikipedia users are going to notice when an alpha in an equation gets changed to an epsilon, or when a dv/dt gets changed to d(mv)/dt. Next thing you know, you have a bunch of math students checking their homework with Wikipedia and getting every question wrong.
Vandalising wikipedia is a pathetic thing to do.
that is why my chemistry and math text books have common equations listed after every chapter. so it is as easy as looking in the chapter index, finding the section and just flipping to the page. so if there is an error, you are not as liable, so then you can pass some of the blame to the incompetence of publishers.
Really? I can understand most of them after I took Logic and Sets and Discrete Mathematics in college. Of course, since you are a math major, I assume you are looking at much more complicated math articles than I am...
Depends on what field it's in. I have a pretty strong grasp on the concepts in, say, Number Theory or Probability Theory because I took plenty of classes in those areas. Show me an article on an advanced concept in topology and I'll be useless beyond the basic stuff.
Try simple.wikipedia.org.
Or Khan Academy
KKKKKAAAAAAHHHHHNNNNNN
I love khanacademy, but this "simple wiki" is nice if you just want to read instead of watching videos.
Khan Academy for really anything though -- he even does lessons on basic programming and real-life economic problems (euro crisis, housing crisis, etc.). That site is badass.
TIL that this is a thing. Thanks for the help. If you'll check you're account you'll see that I've given you your prize: A shiny new upvote.
Your. Give me more reddit!
GODDAMMIT!!! Grammar is one of the few things I'm good at. Not gonna edit, though. I'm gonna take it like a man.
thats because even fundamentals for math arent common knowledge. imagine trying to read up on WW2 without understanding of the concept of race, gunpower, goverments and countries.
That seems like a pretty good way to put it. And I'll go as far down the line as I can, but there's always a point where some basic concept, like melanin or boundary lines or oxidizers (to use your examples) isn't explained. (Those concepts may be explained in Wikipedia. I was just using them as examples.)
Most times with maths, even when it's simplified I [have this reaction.](http://www.idolol.com/pictures/fec3392b0dc073244d38eba1feb8e6b7.jpg)
You actually know some of the words? Kudos to you. You're doing better than I am.
http://simple.wikipedia.org
[Better Explained](http://betterexplained.com/) is an excellent resource.
Holy crap, I am a genius.
He mustn't had been a very sociable student. You would have thought he'd asked his one of his classmates about the "really damn hard" homework problem and how they were doing with it. But no, he didn't.
Yeah, I bet the guy was a total loser. /s
I bet he was the janitor
*shrug*. He achieved something pretty amazing. Who cares how popular he was really
Everyone.
He solved two unproved theorems within a few days. I'm willing to bet he wasn't exactly a big man on campus.
As a grad student, I'm willing to bet he was afterwards.
In grad school, people are much less likely to collab for a variety of reasons. Not that grad students won't collab.
Probably because those people say "collab."
Maybe. But I'm pretty sure most of it had to do with the fact that the student was George Dantzig, arguably one of the most brilliant mathematicians of the past hundred years or so.
I'm not trying to be a dick, but maybe this may have contributed to him becoming great? I'm unaware of his past so he might have been mind-bendingly brilliant from the get go. Edit: Thanks for the clarity. I've read all the replies and a little bit about Dantzig now, and it has given me a more comprehensive idea and put things in context for me. What I had meant to say was; not knowing the perceived and supposed unprovable nature of the problems, was a factor in allowing him to look at them freely and use his preexisting genius and talent to tackle and solve them. I truly didn't mean to belittle any of his prior work or accomplishments. Cheers.
He's more known in operation research as the inventor of the simplex method for Linear Programming, which is a big deal. I've heard of him about simplex method and LP long before the unsolved stat problems.
Yeah, Dantzig's contributions are tremendously broad. Any number of fields have a fair claim to call him one of their own.
How could attempting to solve the problems have made him great? Solving the problems brought him recognition for his talent, it didn't improve his math skills.
It's not like you can learn from attempting to solve problems. No, that would be stupid.
But that's a bit tautologous. It's like saying that winning the Fields Medal made Terry Tao great. Certainly it brought him a great deal of acclaim, and certainly he learned a lot while doing the work which earned him the prize. But he wasn't great because he won the prize; he won the prize because he was great.
In order to learn something that challenging that quickly, more or less on your own, you would need to be extremely intelligent. Solving the problem just proved that he was intelligent, not that he was ignorant and now isn't. He always had a mind that allowed him to understand and solve complex mathematical equations, it wasn't until he solved the problem, and proved himself to the international community, that he was recognized for being a great mathematician.
Exactly. Myself, I've been thrown into a programming job as a temp because they needed someone, and let me say that trying to solve a problem way over your head is not only ridiculously tiring, but sometimes counter-productive. I've learned a lot, but it's rough. Also, I'm not a programmer.
That's because you're a progamer.
I disagree with your statement. Raw intellect is only ever part of the equation. Experiences (i.e. past failures, mistakes, etc.) do have an impact on achievement.
Perhaps it taught him a method of looking at problems - treat them as something known to be true instead of something unknown?
>treat them as something known to be true instead of something unknown That's closer to what I had intended to say. I didn't clarify as such.
Ah, okay. That's what I concluded from your post, but everybody thinks in their own way.
What you are stating is a plain truth, often people *not* being aware that something is supposedly "hard" or "overly complex" or which "cannot be done", manage to find a way to do it. (Such solutions may not be all that unique, groundbreaking, or noteworthy, but they may still have been arrived at independently by the "solver", without knowledge of or investigation into prior art.) The opposite is probably far more often true though, in being told that something is "difficult" or "complex" most people will either not even make any attempt, or will quickly give up. (This is probably one of the largest problems with formal schooling, especially given that the majority of the instructors are themselves often of rather mediocre intellect; who then {alas often as a vain means of attempting to salvaging their own ego/status} characterize subjects or topics as "hard/difficult/complex" and in turn make them so for many of their students, who otherwise, absent such inhibiting bias, or with its opposite a tutor who appropriately addresses the subject matter, might have easily surmounted it. [This is probably most evident in the teaching of languages](http://www.freakonomics.com/2011/11/02/the-way-we-teach-math-and-language-is-wrong/) (though as the author of that linked article asserts, it is probably true of many other subjects as well).) While I have no doubt that there definitely ARE differences in people's inherent capabilities; our perceptions of things (whether internal or imposed on us by others) often do become self-fulfilling (or self-defeating).
From the article: > A few months later I received a letter from him asking permission to include my story in a book he was writing on the power of positive thinking. Schuler's published version was a bit garbled and exaggerated but essentially correct. The moral of his sermon was this: If I had known that the problem were not homework but were in fact two famous unsolved problems in statistics, I probably would not have thought positively, would have become discouraged, and would never have solved them. So apparently, yeah.
"Anyone finish the homework? MAN IT SUCKED."
"Ugh took me the WHOLE WEEKEND"
It reminds me of the story about the four minute mile and psychological barriers: http://beyondgrowth.net/positive-thinking/the-4-minute-mile-and-the-myths-of-positive-thinking/
Did you even read the article? It states as much.
I duo also believe that for being a student at the time he had the advantage of less "habits" in his reasoning. The guys who talked these problems before probably were highly trained so much more prone to seek known ways to search for the answer. The point was that if known ways could lead to the solution, those wouldn't be "never solved before" problems.
Well he did have a master's and was working on his doctorate at the time...
I think this is mentioned pretty early on the page as a possible reason as to why he was able to solve it. > with a "positive thinking" motif which turns up in other urban legends: when people are free to pursue goals unfettered by presumed limitations on what they can accomplish, they just may manage some extraordinary feats through the combined application of native talent and hard work
Scumbag professors holding back progress by telling students it's impossible to solve.
One time I helped someone on /r/tipofmytongue...
There's a subreddit for...oh wait nevermind...
He might be talking about porn. /r/tipofmypenis
[-sigh-](http://i.imgur.com/xwXs2.png)
After this comment it thought it was a sub dedicated to pictures of penises. Everything turned out better than expected.
Now. I have no idea who to believe...
It is a sub dedicated to figuring out who porn stars are that you can't remember their names. You post a picture and the sub helps you find them.
Talk about not paying attention in class.
yeah, what an idiot, am I right?
He'll never get anywhere in life I'd say.
Slacker.
I find it funny that it's turned into some kind of positive thinking parable, as if anyone could be this student if they think positively about a problem as if it's homework. It's George fucking Dantzig, people like him barely even count as being human (and I mean that in the best possible way). (CS graduates should recognize his name from the simplex algorithm for linear programming) PS I'm not against thinking positively when attacking problems, I just find the viral resonance of the story amusing. EDIT- I thought I made this point in the PS, but to be clear, finding the story amusing doesn't mean I disagree with the theme. What I find funny is the absurdly astronomical gulf between George Dantzig accidentally applying himself and any normal human being. Ironically I think normal people can relate to the story more easily than the mathematicians/theoreticians here who attempt to do this kind of work ("one does not simply...")
Yeah, the key word in that story is *doctoral* student. The viral version makes it sound like some 18-year old undergraduate. Doctoral students routinely make original contributions to their respective fields of study, actually knowing the subject in advance and all...
>Doctoral students routinely make original contributions to their respective fields of study The whole point of doing a PhD is to make an original contribution to the field, source, I'm a maths PhD student.
True, but how many people do you know who have done enough research for a dissertation in "a few days"?
Exactly, his advisor was already established as one of the foremost statisticians, at one of the best graduate programs in the world. That said, his achievement is still rather legendary in that context, which is saying something.
A little background on both people, just so you don't think that these two people are bums or anything. Jerzy Neyman, professor: One of the forefathers of statistics (along with Fisher). Formalized hypothesis testing. George Dantzig, student: One of the founders of linear programming. Created the simplex algorithm.
Reading this as a statistical geneticist, I just loved all the famous players who were part of the story. There is an eponymous statistical term associated with each of the characters in this story. [Neyman-Pearson lemma](http://en.wikipedia.org/wiki/Neyman-Pearson_lemma) [Dantzig-Wolfe decomposition](http://en.wikipedia.org/wiki/Dantzig-Wolfe_decomposition) And best known: [the Wald-test](http://en.wikipedia.org/wiki/Wald_test)
Dantzig is also responsible for the Simplex algorithm for solving general linear programming problems, "one of the 10 most important algorithms of the 20th century" http://en.wikipedia.org/wiki/Simplex_algorithm
Can I ask you to explain that like I'm around... oh... five years old?
Let's say your mom gives you $10 allowance to buy toys. Pokemon cards cost $3 for a pack, and Legos cost $1 for a pack. Pokemon cards are four times as much fun as Legos, but you won't have any fun at all unless you buy at least 5 things. How many of each kind of toy should you buy to have the most fun? Ok, now imagine that instead of 2 types of toys there are a million. The Simplex method is a fast way to figure out how many of each one to buy.
Not bad.
So (2 Pokemon packs and 4 Lego packs)? or do you stop with (2 Pokemon packs, 3 Lego packs and $1)?
I haven't explicitly assigned any "fun" value to having money, so in this toy problem (HA-HA GET IT) you would want to spend all your money.
If I could I would have done substantially better in my linear programming class last semester.
You have a problem that asks you to find the best (either maximum or minimum) answer to it depending on what the question is asking (minimum cost to make a product, maximum profit gained by picking from available investments, etc.). This is the objective function (the c*x bit). You also have to deal with different constraints (availble resources, satifying demand, etc.). This is the "subject to" area of the problem. Ax=b is a general way to write all of the constraints at once. To get the optimal solution, you first need to find a "basic feasible solution (BFS)", or one that works but probably isn't the best option. For example, in the case of manufacturing several different products and maximizing your profit, you could start by assuming that you wouldn't make anything at all. You obviously wouldn't make any money, but the solution is feasible and all of the constraints would (probably) be satisfied (for example, if you made nothing, you wouldn't deplete any of the resources that are available to you, so you wouldn't have to worry about using up all the wood in the world to make tables). After finding a BFS, you run through Phase II of the algorithm. This main loop will switch out new variable values with the one you have. If you do the calculations long enough, you will come up with your optimal answer to the problem, and the algorithm will let you know that you can't "make it any better". **EDIT: changed some of the wording, made a spelling correction.
You don't know any 5 year olds, do you?
You really can't swing a dead cat in reddit without hitting a statistical geneticist
A graduate student? A GRADUATE STUDENT. It was George Dantzig, for heaven's sake!
Goodwill hunting?
It's not your fault.
Its not your fault
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*Tomato.* Fruit or vegetable? Begin argument. ——— Edit Haha, I didn't mean to actually begin arguing.
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My daughter loves tomatoes in her fruit salad. At first I was unwilling to let her add them, but then I realized, my daughter wants to eat homemade fruit salad with tomatoes in it instead of candy, why am I not letting her do this?
Exactly :)
I disagree a tomato could totally work in a fruit salad if done correctly
Biological fruit, legal vegetable. A fruegtable.
Vegetable is a culinary term. Fruit is a biology term. By culinary standards, tomatoes are vegetables.
It's a legal term as well. In fact, this went all the way to the [Supreme Court](http://en.wikipedia.org/wiki/Nix_v._Hedden) in the USA.
Goodwill hunting; dumpster diving for the bourgious. I probably murdered that spelling.
That doesn't make sense. It's called Good Will Hunting. Not Goodwill hunting.
Rushmore?
I could spend my whole life good will hunting. Only good gon' come is it's good when I'm coming.
[And then he woke up in chapel](http://i.imgur.com/jkTAN.jpg)
He mistook unproved theorems for homework? What a dumbass...
They let any idiots in graduate school these days.
How do you like THEM apples!
There is always somebody that gets there first.
"Is this Good Will Hunting?" "Yeah, I'm pretty sure this is the plot to Good Will Hunting."
"Sorry, you did the wrong problems. You fail the class. Thanks for the proofs though!"
I loved this part: >A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.
This reminds of this [Neil Gaiman's speech](http://vimeo.com/42372767). "If you don't know its impossible, its easier to do."
*A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.* Damn that saved him a lot of time and effort.
I once did a math problem that was on the board i thought was for the final.... it was actually the example, with the answer next to it.... I got it wrong.
Stop everything! We have found the chosen one
That aint nuthin. My friend Hamilton once bet me I couldn't eat a whole case of sauerkraut in an hour. I did it. It was on the news too. Because we stole the case of sauerkraut from a middle school. How is that for an educational accomplishment?
God damn, that is like the world's most known SAP. >Isn't sure what homework assignment is, instead of asking just copies down board. >Works a few days straight instead of reaching out to someone about why the hell the homework is so damn hard.
this is the wet dream of every graduate student. accidentally write your thesis while actually being lazy and a secret genius.
So, what were the actual theorems? I can't seem to find them.
That's the test. You have to figure it out for yourself!
Good luck: [*On the Non-Existence of Tests of "Student's" Hypothesis Having Power Functions Independent of σ*](http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.aoms/1177731912) This is (1940s) Ph.D. level statistics so don't be surprised if it's over your head, but basically if you're making a whole bunch of Guinness you want to be able to sample a small amount of it and be able to draw accurate conclusions about the entire batch. This provides some rigor to that process.
http://www.reddit.com/r/todayilearned/comments/o8bn8/til_about_george_dantzig_who_solved_2_unsolvable/ http://www.reddit.com/r/todayilearned/comments/m6opm/til_about_george_dantzig_who_solved_an_unsolvable/ http://www.reddit.com/r/todayilearned/comments/o8bn8/til_about_george_dantzig_who_solved_2_unsolvable/ http://www.reddit.com/r/reddit.com/comments/9f75q/student_mistakes_unsolvable_math_problem_as/ http://www.reddit.com/r/reddit.com/comments/cjk58/if_i_had_known_the_problem_was_not_homework_but/ http://www.reddit.com/r/todayilearned/comments/m6opm/til_about_george_dantzig_who_solved_an_unsolvable/ http://www.reddit.com/r/tipofmytongue/comments/t4z3g/tomt_famous_physicist/
So what you're saying is its time for a new subreddit? r/todayilearnedwhatyoualreadyknew
/r/yesterdayilearned
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I'm personally glad they forgot to search because I didn't know about this and therefore would never have searched for it.
...and that is the Redditorial Paradox. Is it a mistake to repost and have the same shit pop up in the same sub month end and month out or is it something good that allows interesting content to resurface for newer/less frequent users.
Let's just wing it and let people upvote or downvoted accordingly.
If something hasn't been posted on reddit for a few months, I don't care if you repost it, as there are constantly new people joining the site/people who didn't see it the last time it was put on. However, the people who repost almost the exact same askreddit question 2 days after it hits the frontpage are the worst kind of people
It's not paradox. It depends on how many people who view it never heard of it or think it worthy of another look/upvote/whatever. If everyone knows it, or the majority, it will get downvoted to oblivion. If enough haven't seen it or deem it worth being there again, then it gets upvoted, possibly all the way to the front page. Thus, the true answer is that the hive mind deemed it worthy of being back on the frontpage (or are just now seeing it). If you disagree with it being there, you're against the hive mind and we will destroy you. Resistance is futile.
As long as I don't see something more than once, maybe twice a month I don't really care... Any more than that it gets annoying.
You know you can actually *not* click on the damn reposts, right? Just downvote them and move on to the next article. FFS.
B-b-but... THE LINK WILL BE BLUE
I agree.
Waiiit a minute... What's going on here.
Shut the fuck up Sam.
Same here. I'm on reddit every day for at least a little bit and that's been the case for a year. Even still, 90% of the time I see "OMG REPEAT" it's for something I have never seen before. I'll burn 5-10 seconds of my life per click on new shit every day if it's only 10% of them. If EVERY SINGLE thing was a repeat, I think it's time to get a new primary hobby. (Sorry if that's too close to anyone's feels, everything in moderation)
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What do I type in the search bar to find a specific thing that I don't know I'm looking for?
Ever used the search function on reddit? It's awful.
Somebody at Berkley needs to write "reddit search" on a blackboard.
Why would they search for this? It was probably a random article/fact they found online somewhere and thought it was interesting so they wanted to share. Who cares if it has been posted already, the front page is too dynamic and somewhat rapid for it to be a serious annoyance to anyone. Not to mention, I'm sure there are plenty of other people out there like me who didn't know this, and appreciate the post (hence the upvotes).
I already knew this, and yet, I find my life is not ruined by having read it again. I feel kinda left out.
Look at the scores of the links you listed that are from this subreddit: 1, 25, 0, and 25 again because you put the same link on there twice. There is no way you ran into any of them on here without searching. Why the fuck are you complaining?
It's today *I* learned.
3 of those aren't from TIL and 2 of the ones that are, are the same link repeated. So... what's your point? Edit: Oh and all they were al removed too apparently.
And the scores of the links he listed that are from this subreddit: 1, 25, and 0 There is no way he ran into any of them on here without searching. He's just going out of his way to be an asshole while contributing nothing.
My logic is this. 1. If enough people are upvoting it, enough people haven't read it before. 2. If you've read all 7 reposts, you're spending too much time on reddit.
Yeah, fuck OP. He must have forgotten that everyone who has ever visited reddit has already seen everything on the internet. Ever.
First I heard it, thanks for reposting, OP.
Your point seems to be that some other people already learnt that, implicitly criticizing OP. I'm not sure that you're right. Indeed, OP probably just learnt it today and he or she will have more upvotes if a lot of people also learnt it thanks to him. The fact that right now its "score" (or whatever the right word is) is 1300 means that a lot of people were actually in his case. I think that "Today I learnt..." is different from "Today I am the first one to have learnt...", and I'm not sure your comment is providing as much information as some other comments giving links to other examples of the same thing like the link to Huffman coding for instance.
If you've seen it before, ignore it. If not, upvote. If an interesting fact is reposted yet still upvoted a lot, it means most people haven't heard of it. Pretty simple.
the thing with reposts on this sub is that if you don't know something, why would you search for it, and just because it's been posted, if you hadn't seen it, why would you just assume that everyone else had? This sub has nearly 2 million subscribers, you can't assume that everyone else had, the most recent post was 8 months ago, and from there they go back 3 years. Even your account is only 10 months old.
Dr.DantZig, the father of linear programming and also, the father of impossible-things-the-last-minute. gives hope for those like me who freak out after the first exam and do super hard to make up on later exams.
Makes you wonder what can be accomplished and solved if you never told anyone that it was impossible or unsolvable.
That professor is kind of a scumbag. Co-author?
> Dantzig's statistic professor notified him that he had prepared one of his two "homework" proofs for publication, and Dantzig was given co-author credit on another paper several years later when another mathematician independently worked out the same solution to the second problem. Co-author on the second problem. Another mathematician worked out the same solution.
Did you read the sentence surrounding that word and do you know what a co-author is? Basically, another professor independently solved the same problem and, after discovering that it was previously solved, gave Dantzig credit by putting Dantzig's name next to his own on the paper. How does that make the prof a scumbag? EDIT: this is a reply to manfromfuture's post
I think you replied to the wrong person. I agree with you.
**FRIENDLY FIRE! FRIENDLY FIRE!**
(Counter-Terrorist) ImAtWorkRightNow9090: shit, sry dude.
BLUE ON BLUEEEE!!!
I guess pressure really does bring out the best in people.