Slashdot Mirror
Possible Proof of ABC Conjecture
submeta writes "Shinichi Mochizuki of Kyoto University has released a paper which claims to prove the decades-old ABC conjecture, which involves the relationship between prime numbers, addition, and multiplication. His solution involves thinking of numbers not as members of sets (the standard interpretation), but instead as objects which exist in 'new, conceptual universes.' As one would expect, the proof is extremely dense and difficult to understand, even for experts in the field, so it may take a while to verify. However, Mochizuki has a strong reputation, so this is likely to get attention. Proof of the conjecture could potentially lead to a revolution in number theory, including a greatly simplified proof of Fermat's Last Theorem."
Assuming the paper is correct and as impenetrable as the summary claims, this won't simplify the proof of FLT. It'd be a massive rug that the hard parts of of FLT would be swept under.
LMWTFY: http://en.wikipedia.org/wiki/Abc_conjecture#Formulations.
Obviously, that's the preliminary intuitive statement. Look further down the page for the formal statement.
That is precisely the point of the proof, to determine under which conditions the sum of 2 integers is less than the product of the prime divisors of the 3 original numbers. I hope that is less vague :P
...and solved. I think it was the early (19)70's. A researcher named Jackson
(with the help of his brothers) came to the conclusion that it was simple as 1-2-3.
Additional verification shown that do-re-mi fit the bill as well. At the time, people
were sing all about it - I'm surprised this has come up again.
"Rarely much smaller than"? What kind of mathematical statement is that? Are we to assume that most of the time, d is somewhat smaller than c? Are there conditions where d is larger than c? How are you supposed to get anything done with vague statements like "rarely much smaller than"?
There exists mathematical statements which sounds rather "unmathematical" at first, as an example, "almost everywhere" has a precise meaning in measure theory.
http://en.wikipedia.org/wiki/Almost_everywhere
Nobody's measuring anyone's penis--the truth is a lot more boring (and reasonable) than that. Wikipedia is a fantastic first reference for working mathematicians or grad students--I'm sure nearly all math article editors are in these groups--who just want to quickly find out e.g. what the hell an "ultrafilter" is. And so the articles are written in a way that makes them most useful to the people who donate their time to produce them. It's not that any (non-douchebag) mathematician gets off on throwing around smart-sounding jargon. It's just that you can't actually do anything with "intuitive" descriptions.
Yo dawg, I heard you like the Ackermann function, so OH GOD OH GOD OH GOD
Peter had a pretty good first glance reaction to the paper: http://www.math.columbia.edu/~woit/wordpress/?p=5104
I haven't seen any good discussions of the actual math content of the paper yet though.
Yeah, that "new, conceptual universes" line lit up my bullshit detector like a Christmas tree. But the author is well-established, so it's probably a bad translation and/or breathless hype inserted by the university PR office.
Yo dawg, I heard you like the Ackermann function, so OH GOD OH GOD OH GOD
Which makes it even more non-sensical to post it here, on slashdot, a general-interest geek site, where only very few are working mathemeticians or grad students.
A page like this: http://abcathome.com/conjecture.php would have been more apropos. No reaching for the jargon, and an actual mini-tutorial on what an ABC triple is and what the conjecture is.
--
BMO
Well WP math articles aren't designed so that every concept comes with a layman's introduction; that would involve massive duplication and bloat. And so, yes, the link you posted would be more appropriate here than a WP link. But I really don't see how you get from there to accusing the volunteer WP math editors of having a big willy contest. There's a reason those articles are written the way they are, and it's not just to make you personally feel stupid. They don't give a shit how smart you think they are.
Yo dawg, I heard you like the Ackermann function, so OH GOD OH GOD OH GOD
Wikipedia is a fantastic first reference for working mathematicians or grad students
As a physics graduate student, I can say this is not my experience. Wikipedia articles are terribly written because an encyclopedia is not the place to learn about concepts.
I did not read the article yet, but my guess is that it is some journalist's lame attempt to "explain" category theory to laymen.
AccountKiller
Sorry if it wasn't obvious, but I meant grad students in mathematics.
Yo dawg, I heard you like the Ackermann function, so OH GOD OH GOD OH GOD
Actually after reading a bit more, it turns out not to be as hyperbolic as it sounds. The author has come up with a whole constellation of new mathematical constructions to support his claimed proof. As the article points out, this means it'll take quite some time for mathematicians to understand these constructions before they'll be able to judge the correctness of the proof. This kind of thing would be dismissed out of hand if it came from Joe Nobody, but Shinichi Mochizuki's reputation in this case should ensure that it gets a good look. And before the crackpots hop on, no, that's not because of any ivory-tower prejudice, but simply because no sane (and busy) professional would judge that such a large personal time investment is likely be worthwhile, without some very strong past performance.
Yo dawg, I heard you like the Ackermann function, so OH GOD OH GOD OH GOD
This is one of the things I've always hated about the reporting on math, which is not only the fault of reporters but also of mathematicians.
...
But mathematics really needs to get less abstract in its terminology. The name needs to mean something, just like how in CS you call something "method_does_this()" instead of "method_x()".
Well, the names often are meaningful, but after a while one starts running out of words, and/or the concepts just get so specialized that there aren't any words that convey anything close to the right idea of what's happening.
Yo dawg, I heard you like the Ackermann function, so OH GOD OH GOD OH GOD
Perhaps the Rhythm of the Primes has a new conductor.
---- Teach Peace. It's Cheaper Than War.
NBC , CBS, and FOX say about this conjecture?
That's what mathematics is—obscure and non-obvious stuff is everywhere. Sorry if you're only interested in arithmetic, but math is a huge, complicated subject. One of my math professors said that he'd never found an error in a mathematics article in Wikipedia, which is true in my experience.
Use of the words "good", "bad" or "evil" is almost invariably the result of oversimplification.
This kind of thing would be dismissed out of hand if it came from Joe Nobody, but Shinichi Mochizuki's reputation in this case should ensure that it gets a good look.
I wonder how many interesting insights we miss due to such bigotry.
No, you can't actually learn abstract mathematical ideas by basing your understanding on intuitive descriptions. If you think you have learned a concept that way, I can almost guarantee that your understanding is faulty. (I've learned this the hard way: I happen to be a mathematician who is particularly adept at providing comfortable metaphors that cause non-mathematicians to believe they've understood something when they really haven't.)
For anyone with a suitable background (say, a first-year graduate student or better), Wikipedia's math articles are generally the best, most accurate and most comprehensive free source of basic mathematics information available. If you don't have that background, no article of any kind is going to be explain to what a "scheme" is, for example. To think so is as naive as believing that you can understand all the nuances of Baudelaire's poetry without learning French; you may think you learn something from a translation into your language, but you actually don't.
See http://mathoverflow.net/questions/106560/philosophy-behind-mochizukis-work-on-the-abc-conjecture for a discussion on the mathematical content by experts.
Because if you look in all other commercial encyclopedias (encyclopediae?), you get a more english (well, natural language) translation of the concepts of a math article. But not even that, Wikipedia on this subject fails even at the post-secondary textbook level. I don't count myself among the dumbest of the population, but when I go to a Wikipedia page for something that is on my level for math, the articles on things like cycloids and such are much better explained by Machinery's Handbook or any other source, really, than there.
I am not saying that Wikipedia should dumb its articles down to the point where even the most innumerate among us would understand all of them, but the "spam equations on the wall with little explanation" model doesn't work very well unless you are immersed in the subject. For example, concepts covered in Algebra I and II in high school should be written for that level.^1 Also, this "write for the grad-student and mathemetician for everything" model does little to help people who use applied mathematics. Indeed, this whole focus on grad-student and up writing in the math articles is at odds with the rest of the Wikipedia.
As a result, anyone wishing to *learn* anything about math is better off using anything but Wikipedia.
Your response to me that the articles are written by grad students and mathemeticians (not all mathemeticians are jerks, btw) for grad students and mathemeticians reinforces the fact that it certainly seems like a giant circle jerk.
--
BMO
Footnotes:
1. I had to explain to a high school student that she should not be using Wikipedia for help in her Algebra II class. Because all it did was confuse her. I mentioned that Wikipedia math pages are a "dick measuring contest for experts on the subject" and the light went on behind her eyes and she laughed and agreed. There are far better resources and I suggested she ask her teacher for them.
For anyone with a suitable background ..., Wikipedia's math articles are generally the best, most accurate and most comprehensive free source of basic mathematics information available. If you don't have that background, no article of any kind is going to be explain to what a "scheme" is, for example. To think so is as naive as believing that you can understand all the nuances of Baudelaire's poetry without learning French; you may think you learn something from a translation into your language, but you actually don't.
Goethe's comment is relevant here:
Mathematicians are like Frenchmen: whatever you say to them they translate into their own language, and it immediately becomes something entirely different.
Good question. Why don't you devote twenty years or so to becoming competent to judge, then spend all your time reading every crackpot's theory on trisecting angles or why pi isn't really transcendental, and let us know what you find out?
Yo dawg, I heard you like the Ackermann function, so OH GOD OH GOD OH GOD
Probably extremely few.
A friend of mine knew Shin (as he was known then) when he was an undergraduate. The guy was obscene insane-clown-level genius prodigy. Not the prodigy in the sense of the people who can shoot the lights out of the Putnam Competition but even far deeper than that, and jumping into very difficult and profound concepts by age 17 or 18. He did a small stint doing independent research with Ed Witten before moving up to pure mathematics. By 2nd or 3rd year undergrad (age 17 or so), he was already at an advanced graduate level.
I think he may be a different species.
Oh yeah and for fun he learned ancient Sanscrit.
thinking of numbers not as members of sets (the standard interpretation), but instead as objects which exist
Of course he was able to solve the problem; he used an Object Oriented framework!
Although exploder's explanation may be accurate, it in no way justifies the massive uselessness that most of the math articles -- including ones about subjects that are fully capable of being explained to the laymen (as the Encyclopaedia Britannica has done for years).
There is nothing wrong with the technical math being included. There is everything wrong with the intuitive explanations not being included when they are feasible.
The major problem is a bunch of pompous mathematicians (and as a mathematician I am happy to say that these are only a small subset of all mathematicians) who are unclear on the concept of an encyclopedia having written much of the material in Wikipedia's math articles.
But fortunately, there are wiser mathematicians who comprehend the concept of an encyclopedia, and who have a knack for making things understandable to laymen, who are working to remedy these flaws in many of Wikipedia's math articles.
If you're a mathematician who sees math articles in WP which are missing intuitive explanations that could feasibly be added, then by all means be bold and add them! Just, please, if it's an important one like "manifold", read the talk page first to see if there's already a consensus about the technical level. There's a lot of thought and effort put into striking the right balance that may not be apparent from just reading the articles.
Yo dawg, I heard you like the Ackermann function, so OH GOD OH GOD OH GOD
Because if you look in all other commercial encyclopedias (encyclopediae?), you get a more english (well, natural language) translation of the concepts of a math article. But not even that, Wikipedia on this subject fails even at the post-secondary textbook level. I don't count myself among the dumbest of the population, but when I go to a Wikipedia page for something that is on my level for math, the articles on things like cycloids and such are much better explained by Machinery's Handbook or any other source, really, than there.
I am not saying that Wikipedia should dumb its articles down to the point where even the most innumerate among us would understand all of them, but the "spam equations on the wall with little explanation" model doesn't work very well unless you are immersed in the subject. For example, concepts covered in Algebra I and II in high school should be written for that level.^1 Also, this "write for the grad-student and mathemetician for everything" model does little to help people who use applied mathematics. Indeed, this whole focus on grad-student and up writing in the math articles is at odds with the rest of the Wikipedia.
As a result, anyone wishing to *learn* anything about math is better off using anything but Wikipedia.
Your response to me that the articles are written by grad students and mathemeticians (not all mathemeticians are jerks, btw) for grad students and mathemeticians reinforces the fact that it certainly seems like a giant circle jerk.
The problem is that these topics aren't what you'd see in high school algebra. In fact, upper level undergraduate courses would probably just touch on these. So yes, encyclopedias would have more easily understood articles but they almost certainly don't cover theorems like the ABC theorem or topology in any depth. In fact, most articles in encyclopedias will probably give you a very cursory explanation. To make an analogy it'd be like explaining people as living things with 2 legs, 2 arms and which breath air. It's not useful for any in depth topic and when you really want to understand, you'll need to go into details. And in math, those details come in the form of definitions and equations explaining how the definitions interact together.
"When you sit with a nice girl for two hours, it seems like two minutes. When you sit on a hot stove for two minutes, it
So an entry about poems, should lust list the rules, and be done. Actually, a lot of knowledge is contained in the examples, the reason why the concept was needed, how it evolved, and ways to make the concept clear to one that isn't in the field but is generally smart. If you ARE in the field, you likely have specialized books. I don't go to Wikipedia for economic or finance related issues. I got to books that I trust and are solid.
So...I don't agree. Math in wikipedia is useless to me. I don't go to wikipedia to understand any math problem, concept or proof. But I go there for almost anything else as one quick reference. For math, as a non-mathematician, I may go to some of the sites that focus on making concepts useful, comprehensible as well as accurate.
unfinished: (adj.)
I agree with exploder. Wikipedia math articles are surprisingly useful.
Battles?
Well, you know what they say: The penis mightier than the sword.
Have gnu, will travel.
>The problem is that these topics aren't what you'd see in high school algebra.
But the fact is that I was able to pull up a *better* explanation of what ABC triplets are and what this conjecture is by linking to a project dealing directly with this problem run by an actual mathemetician. And it was in terms that anyone in algebra I or pre-algebra, if they slowed down and took it step-by-step, could comprehend and it was accurate.
And if you clicked through to the other pages, on the site, you found clear common-english explanations as to why it's important.
Really, go look at the other page I linked.
http://abcathome.com/conjecture.php
And nothing anyone said defending the Wikipedia math pages contradicts my initial claim that you shouldn't link those pages to explain math, especially to a bunch of non-mathemeticians on Slashdot.
--
BMO
The best way I can describe this is to say this:
When you see a cube, you define it's boundaries in this universe by it's sides and edges,
In this theory primes, q 1 make up the "dimensions" if you will.
Want an easier explanation? The abc conjecture is a universal equation through which (seemingly) all other equations can be refactored to make them comparable and translatable. Great for number theorists and programmers, not sure who else will use it. Maybe physicists.
Where genius and insanity become confused true wisdom is found
The thing is though, there are mathemeticians who are good at writing articles on math that *can* explain things so that people not necessarily immersed in higher math 24/7 *can* understand what is being talked about.
The page I cited earlier was written by a mathemetician running a project called "abcathome" - a BOINC project looking at abc triples. And it's understandable. And it gives you an method how to discover whether 3 numbers are an abc triple. It also doesn't resort to any fancy formulas or jargon - rather you can do it with a pencil and paper and arithmetic. Someone back there said "well, it's not something covered in HS math" while failing to understand that abc triples and the conjecture are understandable to HS students if you bother to take the time to actually explain it like he did.
Such mathemeticians are a gift to society.
They just aren't on Wikipedia.
--
BMO
The Penis Measuring Armageddon will be fought on Pen Island.
http://www.penisland.net/
--
BMO
I agree with your perspective 100% on this. I have been reading a lot of WP math articles lately, and many of them are really difficult to follow. A Google search usually brings up a different site within 2-3 results which has a 10x better, easier to read explanation of the same concept. I'm not stupid, I have a 135+ IQ...but blaming the reader and making excuses is par for the course at WP.
The funny thing is, most of these concepts I've read about are at their heart quite simple. It's the people who have no clue how to explain things which makes it complicated and difficult to understand.
Wikipedia has its uses, but overall it's shit.
Your response to me that the articles are written by grad students and mathemeticians (not all mathemeticians are jerks, btw) for grad students and mathemeticians reinforces the fact that it certainly seems like a giant circle jerk.
I wrote a couple of the original pages on wikipedia dealing with some comp-sci type topics not usually taught in a 4 year program (back in ~2000). I thought they were fairly clear and understandable, complete with short pieces of pseudo code, and algorithmic explanations. I gave up on those pages because of the idiots editing them. I couple years ago I looked at them, and frankly was shocked, its like some grad students have been trying to out do each other on writing the most esoteric mathematical description of the problem/solution. In fact the Wikipedia pages probably should just be wiped and replaced with references to the original authors (of the algorithms/mathematics) works, because they are a far more accessible resource.
Basically, I would call the Wikipedia pages a complete failure on any metric other than a competition to obfuscate with math something that is fairly accessible.
And nothing anyone said defending the Wikipedia math pages contradicts my initial claim that you shouldn't link those pages to explain math, especially to a bunch of non-mathemeticians on Slashdot.
Nobody's really disputing that. You kept reiterating that Wikipedia Math articles are written by jerks. They're most unhappy about that. To support your point, you basically compared the Wikipedia article to a webpage that's simple enough to suit curious junior high pupils, but it is not up to your own opinion whether one shall cater Wikipedia to this level of pedagogy. It is wrong to say something's absolutely bad just because something else is better (for a different purpose). For example, I can easily find other people who can talk much more politely in a discussion; does that make you a jerk?
Of course wikipedia isn't a great teaching resource, it is ostensibly a databank for knowledge (and crazy admins). Teaching resources take that knowledge and convey it in some meaningful and understandable way to someone who doesn't know what it means.
It is by no means a dick measuring contest, at least not in the way you are saying. Math, computer science, and physics are areas I am very well versed in and articles written about those subjects on wikipedia are very easy for me to read and comprehend. However, if you point me to an article in a subject matter that I'm weak in I find it very difficult to read. Take the article on photosynthesis for instance. There are so many words in that article that I can barely pronounce let alone know the meaning of that I could easily assume it was a giant circle jerk by the biology community to include as much technobabble as possible. Yet it isn't a circle jerk and would be easy to read for someone well versed in that subject matter.
What you should have told that high school student was that wikipedia is secondary reference material, not a learning aid. If you need help learning a subject matter you should be asking for help from a tutor, teacher, instructor, or educational textbook, not wikipedia.
What you should have told that high school student was that wikipedia is secondary reference material, not a learning aid. If you need help learning a subject matter you should be asking for help from a tutor, teacher, instructor, or educational textbook, not wikipedia.
Then Wikipedia math articles should never *ever* be referred to in a general context to introduce an unfamiliar subject to anyone.
it is ostensibly a databank for knowledge (and crazy admins)
This is a damning indictment of Wikipedia's mission. What good is information if it cannot be understood? It may as well be Viking runes.
>crazy admins
>deny dick measuring
Dohohoho.
The http://abcdathome.com/ website provides an explanation of what ABC triples are, how to figure them, and what the conjecture is, its implications, and all that, in plain, understandable English, because ABC triples are just mere arithmetic when you get down to it. But you wouldn't know that from the Wikipedia page, which is a disaster.
--
BMO
Maybe you can't "learn abstract mathematical ideas" from intuitive descriptions, but 99% of the public don't need to explore all the implications of mathematical ideas. Frankly, the attitude that "everybody should know as much of my art as I do" is quite elitist.
Intuitive descriptions will help the rest of us to a) communicate with the expert who actually understand the implications and b) apply them to real life problems without the need to have a whole understanding. People consulting an encyclopedia don't want full understanding, otherwise they'd be looking a course instead.
What a Wikipedia mathematical article should contain is:
1- who developed the concept, when it happened, and to which problems it was applied at first.
2- in what fields it is applied nowadays, and what benefits it provides.
3- basic intuitive explanations.
4- links to references with the mathematical formal definitions.
You know, encyclopedic content. Unfortunately, few people writing mathematical articles at Wikipedia want to develop them for a *general* public as they're supposed to be.
Singularity: a belief in the "God" idea with the "demiurge" relation inverted.
Then Wikipedia math articles should never *ever* be referred to in a general context to introduce an unfamiliar subject to anyone.
Given that most readers on this website are in the software engineering field who haven't studied advanced mathematics (though a lot probably have), I'd say you're right in this context. If this was posted on a math forum the wikipedia article would probably be an appropriate explanation. Similarly I probably wouldn't link to the wikipedia article "P versus NP problem" on a chemistry centric website as it wouldn't explain much since they probably lack the necessary background. It's all a matter of what your audience is.
This is a damning indictment of Wikipedia's mission. What good is information if it cannot be understood? It may as well be Viking runes.
Even though number theory wasn't my area of study I understood the article well enough. It's not indecipherable, merely specialized.
The http://abcdathome.com/ website provides an explanation of what ABC triples are, how to figure them, and what the conjecture is, its implications, and all that, in plain, understandable English, because ABC triples are just mere arithmetic when you get down to it. But you wouldn't know that from the Wikipedia page, which is a disaster.
The website you linked (even though it has a typo in it) is a teaching resource. Like I said, it's far better at conveying the meaning in an understandable way to someone who is unfamiliar with the subject matter. I also agree that something like that should have been used rather than the wikipedia article given the demographic on this website.
How would that work? In mathematics, the intuitive interpretation is about as conjectural and unsourced as it gets. The whole *point* of doing mathematics rigorously is because the intuitive ideas are unreliable as a guide to the truth. Given wikipedia's insistence on sourcing interpretations and skirting controversy, it seems natural that adding intuition (especially if the contributor is a random web surfer) is not appropriate for the majority of math articles.
I am not a mathemetician. I know my way aronud a reasonable bit of maths as part of my day job (engineering of sorts), but I never studies maths apart from in my engineering course and what I have had to pick up from books since.
Ocasionally random bits of maths interest me (like involution matrices) so I read about them. I find wikipedia a very useful resource.
Because if you look in all other commercial encyclopedias (encyclopediae?), you get a more english (well, natural language) translation of the concepts of a math article.
If it exists at all. Which it usually doesn't.
Also, when it comes to maths, natural languages peter out quite fast. It turns out that maths can be quite difficult and you have to sit down and actually think hard about it in order to gain understanding.
But not even that, Wikipedia on this subject fails even at the post-secondary textbook level.
It's an encyclopedia, not a textbook, but...
but when I go to a Wikipedia page for something that is on my level for math, the articles on things like cycloids and such are much better explained by Machinery's Handbook or any other source, really, than there
Well, it's wikipedia. Quit complaining and write a better article! If you can't be bothered... then why complain that noone else can be bothered either.
For example, concepts covered in Algebra I and II in high school should be written for that level.^
Please bear in mind that wikipedia is very much an international site. There is no "Algebra I" or "Algebre II" outside of some specific educational syllabus. Maths tents to be entertainingly interconnected and even the most unlikely things turn out to be related. Keeping articles dumbed down to the level of the syllabus of a particular education system would be a shame.
Also, this "write for the grad-student and mathemetician for everything" model does little to help people who use applied mathematics. Indeed, this whole focus on grad-student and up writing in the math articles is at odds with the rest of the Wikipedia.
Not really. the whole point of wikipedia is that anyone can write it. It starts off with someone splatting something down and then others refine it. It is not terribly surprising that the initial articles on maths are written by working mathemeticians.
As a result, anyone wishing to *learn* anything about math is better off using anything but Wikipedia.
Well, of course a good text book is going to be a better place for learning than encyclopediea. It should be full of explanations, worked examples, exercises designed to stretch knowledge etc. But to claim wikipedia is worse than everything ele is, frankly, absurd.
And yes, I have learned stuff from wikipedia.
Your response to me that the articles are written by grad students and mathemeticians (not all mathemeticians are jerks, btw) for grad students and mathemeticians reinforces the fact that it certainly seems like a giant circle jerk.
And it's that comment that makes you sound like a grade A whiny entitled asshole. So a bunch of people working hard to provide free encyclopedic content are in a "circle jerk" because the level they have written (and to which you have not contributed" does noe exactly match the level you want out of it?
SJW n. One who posts facts.
There are enough books on mathematics that are worth reading by the general public. There's no reason why wikipedia's math section should follow suit. It fills a gap that is visible to, and only affects, highly trained professionals in scientific fields. It's a niche reasource, and as such it's pretty good as it goes.
And nothing anyone said defending the Wikipedia math pages contradicts my initial claim that you shouldn't link those pages to explain math, especially to a bunch of non-mathemeticians on Slashdot
Actually, it does. The wikipedia article in this case is a really good example of encyclopedic content. It gives a brief description of the ABC conjecture which is quite easy to understand. It then goes into a little more depth and gives a nice bunch of further reading links.
It's a great refersher for anyone who may have forgotten it.
It is a clear explanation for anyone who understands what a prime factor is.
And there are lots of further reading links.
what more do you want out of an ecyclopedia?
SJW n. One who posts facts.
I mentioned that Wikipedia math pages are a "dick measuring contest for experts on the subject"
Please check out the comment above by exploder (should be easy to find - it is rated +5 Insightful). In particular:
the articles are written in a way that makes them most useful to the people who donate their time to produce them
I just want to briefly provide an example as to why this is a good thing. I'm a math/stats guy. For me, the free and easily accessible Wikipedia pages are always my first port of call when looking into a new topic/method.
On the other side of the coin is my best mate. He is a med science guy. He avoids Wikipedia like it has the plague and instead uses a resource that is behind a paywall. Why? Because the Wikipedia med science topics are not written for guys like him. They're written to be more accessible. Unfortunately, this makes them of little use to researchers in the field, so they don't bother contributing.
So, what would you prefer? Personally, I think it is better to put up with a little jargon if it ensures a free and open resource that is constantly being peer-reviewed and updated by the top players in a given field. Surely this is preferable to a system where those top players instead choose to contribute to a resource that is behind a paywall?
I find these titbits about number theory absolutely fascinating... I followed a few courses at undergraduate level that touched on this material - without giving me a solid grounding. What I'd like to know is this: Is there a good textbook that would bring me up to speed with this material? I like Wikipedia articles - but I find them disjointed.. what I'd like from a textbook is something that leads me through the subject from undergraduate level onwards. Can anyone make any recommendations?
I am a mathematician, and I agree most of what you say.
One quibble -- the "dick-measuring contest" claim smacks of conspiracy theory -- the more prosaic and correct reason is that it is far easier for a mathematician to write the true mathematics into a Wiki article than it is for him or her to create a translation suitable for more general audiences.
(May I suggest you could improve the impact of your writing by spelling the word "mathematician" correctly?)
Explaining mathematics accessably is hard (much harder than merely providing a correct formal description), takes a long time, and is often only possible with a test audience. If you're willing to spend the time to add such explanations to wiki you're quite welcome.
Until then I'm going to be grateful for the already large amount of time and effort put in to providing what is already there.
The historical dead paper encyclopedia wouldn't even have entries on these kinds of things. It is true wikipedia's math articles are written at a graduate or higher level, though. Personally, my response was to stop settling for less than the real deal and become a math grad student - one course at a time (taking my third now).
For great justice.
I think I disagree a little. I see it as unfortunate that the people expressing their frustration walked into the trap of one of the logical fallacies (which one?) of using the Four-Star laden words (NSFW denoted as ****) in doing so. However there is a point under that flawed frustrated presentation. Put in a fancier manner, the rest of Wikipedia is indeed at a generalist level, meant for people who just want to know what something is, and then go back to their life. In those cases, the "Encyclopedia is only the start" surely applies. As a random example, let's use the article on "Bioavailability", which (intuitively) means that a nutrient is useless if your body in fact cannot absorb and process it. Still at the intuitive level, it was an old criticism of vitamin pills, whereupon your body removed them before the stomach could finish peeling off the layers of nutrients all the way to the middle of the pill.
http://en.wikipedia.org/wiki/Bioavailability
That's as tricky a topic as any, but the Wiki article is in fact generalist. What the frustrated people are saying is that the content level isn't stable across all of Wikipedia. They're reacting to the wide difference in tone between that article and the math (or sometimes other engineering ones etc.)
My first Journal Entry ever, in 8 years! http://slashdot.org/journal/365947/aphelion-scifi-fantasy-horror-poetry-webzine
Nice article to spur a bit of recreational math. They even have a nice little "quality" formula to use for rating your finds. It's obvious that the place to look is powers of small numbers, especially primes.
I used a few command line tools, bc and factor, and some bash shell scripting to check a few combinations. Skimmed through the results of commands like this:
for ((i=1;i < 25;i++));do echo -n "$i "; echo "13^15-5^$i"|bc|factor;done
With that, I found a few decent quality combinations:
5 + 2^10*227^2*970060037 = 13^15, quality = 1.2417
3^28 + 2^7*5*137*4804889 = 13^12, quality = 1.1716
For sums less than 10^17, fewer than 2*10^4 combinations exist that are above a quality of 1.2. A brute force search might take a long time to find just 1.
Intellectual Property is a monopolistic, selfish, and defective concept. It is "tyranny over the mind of man"
Lot's of professional mathematicians. If you sit in the back row of a conference a third of the laptop screens have wikipedia open to get a good quick first idea. Often enough so to be able to work with it afterwards.
The problem is when the "links right in the intro" form a loop and none of the articles gives a sensible explanation of the field, only unintuitive formal definitions with no practical application.
Singularity: a belief in the "God" idea with the "demiurge" relation inverted.
But...
ABC triples are not a complex subject. They are arithmetic.