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Open Mathematics Document

By HomeySmurf in Internet
Sun Dec 10, 2000 at 09:49:57 PM EST
Tags: Science (all tags)

I am wondering if anyone is interested in an open source mathematical reference document in hypertext similar to the now unavailable Eric Weisstein's World of Mathematics (Slashdot discusion about its demise here).

I know that the body of this work was by Eric Weisstein, but many of the math world submissions and corrections were by various knowledgeable individuals, much like an open source project. The information itself is fundamentally open, factual information about mathematics, and it is a horrible shame that there is no open contribution document project in mathematics. Or at least I haven't been able to find one. I know there is a GPL for documentation, and that it could really come into use here. I would certainly like to be involved in such a project, and there are many different directions this could take. For example, it could use kuro5hin scripts, and allow all the members of the project to vote on submissions (ie peer review) with a requisite number of positive submissions being required for insertion in the corpus, or it could me more like a cvs'ed set of html documents, or any number of different things. I would certainly like to be involved in such a project.


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Open Mathematics Document | 26 comments (19 topical, 7 editorial, 0 hidden)
I was wondering the same thing... (4.16 / 6) (#5)
by spectatorion on Sun Dec 10, 2000 at 05:58:54 PM EST

I think that a community-generated mathematics reference would be really great. I would be more than willing to contribute, but I don't think I would be able to run (or even oversee major parts of) a project of this magnitude. I am just a lowly undergrad, and while my knowledge of math is probably beyond that of most people my age, I'm no Eric Weisstein. Also, I have little experience with mathematical references. If an experienced, highly knowledgeable mathematician (or group of mathematicians) would be willing to collaborate on a task list of essential entries and information requisite to any mathematics reference worth looking at. Then people could inspect the task list and write up entries, examples, and construct graphics or whatever else might be necessary. This would be awesome, and we could keep CRC press's dirty hands off it.

Of course there is the issue of formatting. I think that most mathematicians who publish use some form of TeX or LaTeX or something like that. Once MathML is finallized, it would probably be the best format for publishing stuff, since it is specifically designed for making websites with formulae, which is what this website would be. Many kinks would have to be worked out, but this would be fantastic if it worked.

MathML (4.00 / 3) (#9)
by evvk on Sun Dec 10, 2000 at 06:53:19 PM EST

> Once MathML is finallized, it would probably be the best format for publishing stuff...

You are forgetting one thing: MathML is way too verbose to be written directly. Authors would still have to use an intermediate format that is meant to be written directly, such as LaTeX. It would then later get transformed into HTML+MathML for online viewing. Loose TeX math is pretty much the standard notation for mathematical formulas in ascii media (e.g. usenet and irc), as it is quite intuitive, and LaTeX the suggested format for many mathematical journals. I think mathworld was written in LaTeX as well and they used a modified version of LaTeX2HTML.
Of course one could create some SG/XML based format with tags for TeX-like math input but at least I prefer TeX syntax over SG/XML.

Oh, I also think that such a "community" generated reference would be great. There's just one major problem: how to get good enough people with the time involved. I don't think doctorial level people would be absolutely necessary but rather "good enough" people who have to time and are willing to do the research for reviewing and writing the more complex material. I'm also a lowly undergrad (well, almost a grad for you americans with lowly BS as the first academic degree :-P) and I'd certainly like to get involved in such a project but I have limited time.

[ Parent ]
Yes, true (4.33 / 3) (#14)
by spectatorion on Sun Dec 10, 2000 at 10:07:24 PM EST

I know that MathML is best generated from a TeX/LaTeX converted into XML (or whateverML). I was looking at the W3C's MathML page the other day and I noticed how much code there was and how inconvenient it would be to code that stuff by hand. Notice that I did say that mathematicians use TeX/LaTeX and that MathML would be the best way to present this (which it would be, assuming browsers will support it). Sure TeX/LaTeX would be best to write the stuff, but MathML is the best way to present it (even if it's generated from LaTeX source).

[ Parent ]
Another option and the time factor... (4.66 / 3) (#17)
by evilquaker on Sun Dec 10, 2000 at 11:38:34 PM EST

In addition to LaTeX2HTML, there's also the neat TtH, which seems to work better in some cases. It's free for non-commercial use, so that would be an option here as well.

here's just one major problem: how to get good enough people with the time involved.

I think graduate students are generally "good enough" here... and math grad students have plenty of time on their hands (at least they do where I'm a grad student). But even professors could be urged to contribute, by donating lecture notes on particular subjects, which can be broken down or expanded (as necessary) by others. There are tons of lecture notes handed out in graduate classes, it's just a case of getting these donated, instead of either being used in a book eventually, or simply discarded when they're no longer of use.

"Die, spork user! And burn in fiery torment!" -- Handy, the Handpuppet of Doom
[ Parent ]

Not only open, but free . . . (3.66 / 6) (#6)
by discoflamingo13 on Sun Dec 10, 2000 at 06:25:12 PM EST

In the course of my research as an undergrad, the amount of mathematics papers and journals available on-line for a fee is becoming more and more disturbing. If the whole point of education is to raise the bar for the field as a whole, and only the wealthy can pass, is this acceptable?

The more I watch, the more I learn ---
If you set yourself on fire, the world will pay to watch you burn.
--- Course of Empire

Re: Not only open, but free (4.66 / 3) (#11)
by evvk on Sun Dec 10, 2000 at 07:04:17 PM EST

> In the course of my research as an undergrad, the amount of mathematics papers and journals available on-line for a fee is becoming more and more disturbing.

Errmm.. I have, infact, met very few totally free online journals. Most of the online papers are just PDF versions of the dead-tree published versions, which have always had a price. Universities (at least here) have subscriptions to the dead-tree and online versions of many of these journals (so as a student you shouldn't have to pay for online access and you can probably find the paper versions at the university library at least).

[ Parent ]
Mathematicians have kids too you know. (4.33 / 3) (#22)
by Robby on Mon Dec 11, 2000 at 04:00:25 PM EST

If the whole point of education is to raise the bar for the field as a whole, and only the wealthy can pass, is this acceptable?

personally, while I do prefer getting things for free, I realise that getting mathy stuff for free is pretty unlikely.

The simple reason is that many of the 'high' level mathematics (i'm talking past first year college) is not at all popular. I have been sitting in classes where the lectures are packed full of 10 people (only) - I think my largest mathematics class this year has has 80 people in it - thats pretty special. This is a big deal because the amount of work for the lecturer is no less, and publishing papers is the same: The amount of work is very high compared to the palpable 'output'. As such, the few that want to read it have to pay for the mathematicians time. As long as the fees aren't extremely high, I don't have a problem paying for highly specialised papers - what constitutes 'extremely high' ? Well, of course, in a market economy, it's determined by the market.

Anyway, just trying to diss the myth that all papers should be 'free' simply because you don't want to pay for them.

[ Parent ]

Very much so (3.70 / 10) (#12)
by antizeus on Sun Dec 10, 2000 at 08:34:24 PM EST

I thought mathworld had some serious problems in the higher level information (especially in my favorite topic, ring theory), but it was a good resource when helping people out in the undernet #math channel. You could find an appropriate page and spit out a URL instead of getting into a long, drawn-out description in channel.

I've been thinking about this very idea since mathworld got killed by the dead-tree publishing company. Here are some of my thoughts:

All write-ups should be released under a nice license which allows free (credited) reproduction for non-commercial use.

There should be a mechanism for having multiple write-ups of the same topic, with some sort of voting system so that the best write-ups can get pushed to the top and become the "default" writeup. For example, the mathworld statement of Hoelder's Inequality lacked the (1, infinity) case. Similarly, their definition of the Jacobson Radical was less complete than I thought it should be (it was missing quite a few of the equivalent ways to obtain the radical). It would have been nice if I could have submitted complete versions of these.

I would very much like to get involved with such a project. I've been thinking of taking a couple months off after quitting my current job, and was thinking about starting to build a framework for such a project during that time. It would be nice if I could collaborate with other interested individuals.

it already exists (4.50 / 4) (#13)
by vsync on Sun Dec 10, 2000 at 09:23:17 PM EST

What you describe sounds very similar to Everything2. Why don't you head over there and start noding up some math?

"The problem I had with the story, before I even finished reading, was the copious attribution of thoughts and ideas to vsync. What made it worse was the ones attributed to him were the only ones that made any sense whatsoever."
[ Parent ]
Isn't it better? (3.66 / 3) (#16)
by darthaya on Sun Dec 10, 2000 at 10:54:19 PM EST

To have some kind of web forum devoted to math problems? It is a little difficult to read mathematical equations in pure text, much like reading mandarin in pinyin. :)

Btw, does anyone know a URL for somewhat advanced graph theory?

[ Parent ]

reference document or text? (4.75 / 4) (#15)
by evilquaker on Sun Dec 10, 2000 at 10:50:08 PM EST

I've been thinking about this too, but from a different angle. How many times have you taken a course which is taught mostly -- but not completely -- from a certain textbook? I just finished an OS course taught mostly out of Silberschatz & Galvin, but with additional material (lecture notes and lectures) furnished by the professor. My question is: why couldn't there be an online textbook (of everything mathematical) which anyone can use, and which asks for and accepts submissions of additional material? It could be much like the reference book you describe, except more complete. Given the number of university courses taught all over the world, it could reach critical mass (i.e. be useful as a textbook for a course) extremely quickly, given some high-profile donations of unpublished lecture notes.

As someone else mentioned, Everything2 offers the kind of functionality that could be used for a reference project. However, I think that such a document should be run more like an open source project, with multiple maintainers of the set of documents, each accepting "patches" to their fiefdom of documents. There should also be a mechanism so that if you submit a patch which is not accepted, and you feel you're being treated unfairly, you can fork the documents. After a time, the two versions can be voted on to choose a new "official" version. Of course, one would hope that maintainers wouldn't force this to happen...

The main advantage of this system over the Everything2 system is that it allows easy incremental changes (e.g. the (1,infinity) case of Holder's that someone else talked about), without having to submit a completely new document each time. It also allows a somewhat more consistent style, since submissions can be reworded by the maintainer.

One of the problems that needs to be dealt with is the same problem that crops up with documenting an open source project: no one is going to want to do the boring stuff. Who wants to spend a few days writing up the definition of a "set", when it would be so much more fun (and impressive) to write up the section on graph-self-similar sets as defined by Mauldin-Williams graphs? Hopefully, someone (perhaps a high school student or an undergrad) will step up to take over the more "mundane" stuff that others don't want to do...

In any case, let us know if something ever comes of your idea... I'd be glad to contribute what my time will allow...

"Die, spork user! And burn in fiery torment!" -- Handy, the Handpuppet of Doom

Two things (4.00 / 5) (#18)
by spectatorion on Mon Dec 11, 2000 at 01:25:27 AM EST

First, I think you're missing the point (to some degree). Mathworld was a free resource for everyone that did not aim to be a text. Texts are boring and stupid and useless (at least, all texts I've come across). Hopefully, we could create a reference (concise, informative, interesting) which could be used by anyone doing their math homework in high school algebra/geometry and forgot what a parabola looks like to anyone who was doing some advanced research at the graduate level and needed to check a reference to make sure his/her definitions were right and everyone in between. A reference with entries in all levels of mathematics, freely available to all, is what we are aiming to provide.

As for who would write the "mundane" stuff, I would think there are plenty of people like me who are just starting to get the formal definitions and mechanics of the precise language of mathematics. People for whom this material is (somewhat) new, but who have a solid understanding of it would probably be willing to write up entries that others find uninteresting. Also, think of it this way: a lot of professors teach introductory classes (even though going though the definition of a limit, derivative, open set, or whatever is way below their level of expertise) and some enjoy it because hopefully they can get students interested in math and can get them to take more classes, pursue more knowledge. Although some are really conceited and would take the "That is below me," attitude some might say, "If I can write this up very well, adding interesting examples, illustrations, and applications then someone who is looking this up might become more interested in this topic and in mathematics in general." Hopefully this would be motivation enough for good submissions. Others would want to write advanced entries in their respective fields, and others would want to write the basic stuff because that's all they know.

Yes, this is a huge undertaking, but it seems a worthwhile one. The web would greatly benefit from a free mathematical resource that will not be stolen from the people by corporate evil.

[ Parent ]
Texts vs. references (4.00 / 2) (#24)
by evilquaker on Tue Dec 12, 2000 at 12:08:40 AM EST

I realize that what you're talking about above is a reference book, but my question was: why a reference book instead of a text book? To some degree, you answered this question by saying:

Texts are boring and stupid and useless

This may be true of all of the texts you've come across, but it isn't true for all texts. Moreover, I'm not sure why you think the same things aren't true of reference books. The main problem with reference books is that you can't use them to learn anything from. The examples you cite acknowledge this. On the other hand, anything you can do with a reference book, you can do with a sufficiently voluminous textbook.

In addition, your second example also points out a failing of a reference book model. Important concepts are often defined differently in different works, and the theorems presented depend upon the definitions given. (The dichotomy is usually "easy definitions => hard proofs, hard definitions => easy proofs") Choosing definitions and theorems willy-nilly from different text books is a recipe for disaster. Similarly, using an online reference book to get a definition may or may not give you the definition you need. With a textbook style, you can (ideally) see which versions of the theorems result from the given definitions.

But perhaps our visions aren't so far apart after all... What I envision is something like Mathworld, but with the individual nodes about 1-4 pages in length. Ideally, they'd be about the length that can be covered in one 50-minute lecture, covering perhaps an important definition and its consequences. Further, the nodes would be arranged in an acyclic tree, and ordered by dependencies. This way, if you're interested in learning about the solution to the heat equation, you can go to that section, and quickly find out which sections you need to read (solutions of second order ODEs with constant coefficients, separation of variables, Fourier series, etc.) to understand the material of that section. In addition, after reading a section, you could be given a set of sections which you are now able to understand. Something like the Technology help viewer in Freeciv is what I've got in mind, only much larger, of course.

This type of system can be used as a reference book (provided a searchable index is kept), or as a basis for a text book for a course. The dependency information should make it easy to plan a course, and the granularity of the sections should make it easily extensible.

Finally, I'll note that you appear to argue for my position in the second paragraph. You write:

some [professors] might say, "If I can write this up very well, adding interesting examples, illustrations, and applications then someone who is looking this up might become more interested in this topic and in mathematics in general."

I agree that this could generate some high quality submissions. However, what you're describing here is a textbook, not a reference book. There's no way to incorporate a lot of examples, illustrations and applications into a reference book without turning it into a textbook.

"Die, spork user! And burn in fiery torment!" -- Handy, the Handpuppet of Doom
[ Parent ]

How to do this... (3.00 / 3) (#19)
by mwright on Mon Dec 11, 2000 at 07:49:51 AM EST

If we really want to do this (I do!), someone here should probably make an email list for it for further discussion. Anyone?

Perhaps we could even start a sourceforge project for the code.

Me too (+suggestions) (3.50 / 2) (#21)
by Duckman on Mon Dec 11, 2000 at 11:20:41 AM EST

I'd really like to help out in such a project, really, although I don't know too advanced mathematics. But then again you've gotta start somewhere, don't you? Something like this is on my personal wishlist for things to become avaiable on the net.

I assume that making it MathML would also let you hyperlink to derivations or underlying assumptions, which would come in quite handy. It might as well contain a multilangual list of mathematical jargon, because few things are as annoying as coming across stuff you know already but don't recognize because you don't know the Engish term for it.

Maybe it could also contain some physics stuff (especially the not too advanced stuff). Just because it's fun.

[ Parent ]
Let's start it up. (3.50 / 2) (#20)
by Garc on Mon Dec 11, 2000 at 10:32:21 AM EST

I am interested in this also. I am somewhat math inclined, but probably not enough to help beyond some basic number theory, trig, or calculus. I have not seen Eric's page, so I am unaware of the format that he used or anything like that.

What I can do though is fire up a mailing list, create a cvs server, and have it do nightly transforms from TeX to html, mathML, or whatever. I wouldn't want to be the sole administrator, so I'd probably need some help with that too. Would people be interested in this? If so email me. If enough people are interested, maybe we can get started.

Tomorrow is going to be wonderful because tonight I do not understand anything. -- Niels Bohr

GNU/Math (2.50 / 2) (#23)
by SIGFPE on Mon Dec 11, 2000 at 08:22:04 PM EST

Document management and the Open Library (4.33 / 3) (#25)
by zerowolf on Tue Dec 12, 2000 at 12:54:13 AM EST

I like this idea. I really, really like this idea, because I don't see why we should limit it to just mathematics. The opportunities to do this with other fields like music, computer science, literature/literary criticism, and just about anything else are enormous. In fact, you might even be able to do collaborative open research like this. So, why not found the Open Library?

I'd love to see references built the way MathWorld was, only better. I think it could do a lot to enhance the basic educational utility of the 'Net. I'm not much of a math guy (Advanced Calculus took me three tries), but I can think of several other topics that I might be able to contribute to (computer science, mythology, etc). However, we're going to need a system that's a lot more robust and complete than Everything2. Wouldn't it be nice to have a true and well-organized collection of free knowledge that could do the following:
  • Maintain a complete and reconstructable history of the resource, so that the progress of ideas and the correction of errors is fully visible. This is akin to an author being able to completely reconstruct their process, or a scientist keeping detailed records of an experiment. The reasons why this would be so important should be obvious...
  • See annotations from other users and authors, commenting on and improving the document. These too would need to be completely versioned to expose the community process.
  • Link between documents, and manage those links along with the versions.
  • And lots more stuff - I'm sure y'all can think of some...
This would not be a small task, and in order to do it we'd need to write a pretty serious document management system. Something that could manage document versioning, link versioning, different file/media types, author/viewer permissions, and a half-dozen other things. We'd also want to put in some way for an individual Open Library to maintain comprehensive links, link management, and indexing between all the other Open Libraries that may be out there, in a distributed and indexable fashion (I've got some ideas on how to do this in a relatively low-overhead fashion). I know of several commercial systems that do or try to do this stuff, but no open source systems that even come close. With the recent proliferation of XML-based tools, I think an open-source effort to build this, both the tool and the resource itself, could work.

Was someone going to start a mailing list for this idea? If so, I'd like to get on board...


Great minds think alike (4.00 / 1) (#26)
by THEWeirdo on Fri Dec 15, 2000 at 06:11:07 PM EST

This sounds a lot like some thing I've been working on: an open-access database with CVS-style revision history, commenting system (so content useful to the reader and additional comments/corrections/what-nots willn't get muddled together; see E2), links (of course!), and, an addition to what you mentioned, a hierarchial structure. It wouldn't go by E2's one-user-one-write-up modal, but instead have a single write-up for each node, as in a WikiWikeWeb. (Hence the need for the revision history.) And I would not let this system become a jokes database.

I'm currently trying to write such a system in C/C++. Only thing I need to do is learn a lotta C/C++. :-) Hopefully the time it takes to bring up my C skills up to par will allow me time to fully plan this project through.

People keep saying what would be cool and saying "E-mail me if you're interested." I think I'll E-mail a few people; maybe getting things rolling will be as easy as a few pieces of E-mail. If this comment gets a high enough rating, the Gods send me a sign, or some body (that means you!) sends me some supporting E-mail, I'll even set up a project at SourceForge. C'mon people, let's get serious here!

  - THEWeirdo

"Better paranoid than sorry" -- Me
[ Parent ]

Open Mathematics Document | 26 comments (19 topical, 7 editorial, 0 hidden)
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