Slashdot Mirror

I'm thinking I should post these in HTML.

http://arxiv.org/PS_cache/quant-ph/pdf/0206/020608 9.pdf
http://www.ams.org/bull/2003-40-01/S0273-0979-02-0 0970-9/S0273-0979-02-00970-9.pdf
http://groups.google.com/groups?selm=b9401f8a.0302 062325.194d0c8d%40posting.google.com

This link from back in May purports the same news, not sure why its so delayed.

Over at the site of the AMS, there is an interesting overview article by J. Milnor on the ideas behind the Poincare hypothesis and Perelman's proof. You don't have to be an expert in low dimensional topology to read this...
Milnor's article

Secondly, the quality of Indian schools is no where to the same degree of western equivalents, and hence those diploma mills they call universities are no more than trade schools.

The admissions procedure for the Indian Institute of Technology (IIT) is rigorous and selective. There is a two-stage common procedure called the Joint Entrance Examination (JEE) for admission to one of the seven branches of the IIT and two other institutions. Last year 150,000 Indians applied for admission, and after an initial three-hour examination in mathematics, physics, and chemistry, 15,000 were invited to a second test consisting of a two-hour examination in each of the three subjects. Finally 2,900 students were awarded places, of which 45 were for computer science at the very renowned IIT in Kanpur. It is no wonder that good money is earned in India for preparing candidates for the dreaded JEE, and graduates of the IIT are eagerly hired worldwide.

You must admit this is a rather tiny niche market. Everyone should use Word because a couple of math lecturers have to?

Also, there are several math layout apps for this purpose -- such as Tex. It used to be the only acceptable format, IIRC. See American Mathematical Society TeX Resources for how Real Men lay out maths.

For matematics, computer science, applied mathematics, physics, statistics, and other things in that vein, the indespensible resource is MathSciNet, a service of the AMS (American Mathematical Society. Almost every article is reviewed, many have abstracts, and all have citations. Some have the full text of the article (or links to it).

You should also check out jstor.org, sciencedirect, and springerlink.

Speaking of LaTeX, look at this quote from the AMS (American Mathematical Society) website:

Authors who intend to publish a book or an article with the AMS are strongly encouraged to use LaTeX as described in the book LaTeX: A Document Preparation System 2nd edition, 1994 by Leslie Lamport.(emphasis mine, here is the source)

When visiting mathtutor one can see that even 200 years ago, many important discoveries were done in the later stages of the Mathematicians career. Stories like the ones about Abel or Galois distort the picture.

More and more discoveries of younger mathematicians are achieved through collaboration or by standing on the shoulders of people with more experience (who tend also to be more generous with sharing their ideas without expecting credit).

Mathematical knowledge continues to accumulate in a fast pace and only few of this knowledge has been absorbed in books. Chances grow that a young mathematician will discover something already known or to be a special case of a much more general result. Fortunately, there are better and better online databases but it also needs more and more time to dig through that material.

The most productive age for a mathematician will grow also in the future. The same will happen in physics or computer science (as a previous post has pointed out already).

But my favourite quote, from his homepage, is:

"Moreover, well known equations from mathematics like the Theorem of Pythagoras, the equations for conics and conics sections and the equation from Fermat's last theorem, are all special cases of this formula."

So... a guy who specialises in finding new ways to help bamboo propagate- and mind you, bamboo is pretty prolific on its own, don't let that 'lucky bamboo' (which is not actually bamboo, but a plant of another type entirely) fool you- has now found a new way to describe shapes. Yes, this is important, but it's not the next big thing. Folks have been trying to find ways to describe shapes by equations in images long before this, and while his rush to patent may cause some interesting snarls up ahead, i find it unlikely that he even understands Fermat's last theorem,

Cubem autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere.
Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caparet.

But if he does, he'd better post something more mathematical on his website, because he's just landed himself into mathematician waters- and it's sink or swim there, buddy. You don't get to try it again next growing season (Andrew Wiles' revisions notwithstanding), and contrary to what laypeople tend to believe, they still require proof when you walk in and say something crazy like 'Pi is 3.' Even mathemeticians are still arguing over the proofs available. And it's pretty cutthroat, with ten-day conferences, so i bet he's in for some entertaining phone calls.

This is patently untrue. The percentage of people getting CS degrees has stayed relatively static over the past ten years. Take a look here to see that the number of CS majors who enrolled in the height of the dotcom boom of 1999 was the same as the the number in 1992. There were maybe 20% more than normal during the boom, but even by the next year it was only 5% more, then back to normal, even after the bust.

Sorry, but there are just fewer jobs available, and just as many qualified applicants.

I am curious:

• What surprises you the most about the computer lanscape of today?
• What you feel is especially/conspicuously lacking?

Conversely,

• what "Holy Grails" of today do you think are less than ideal?

For extra creidit, I'd love to see a computer software analogue to Hilbert's famous List of Questions, as a kind of to-do list of how computers could most benefit people (in their daily or creative life).

What do these folks think, seeing a nipple or the occasional double entry will mutate their kids into criminals?

Damn sure it will. It was youthful exposure to double entry that set the likes of Kenneth Lay and Robert Maxwell on the road to committing serious crimes. For the sake of our children we must block access to dubious sites like this, full of references to double entries.

It seems I messed up the link in my previous post.
The second article is here instead. Oops.

A detailed account of the mathematics of the mechanism, along with java animations, can be found at the American Mthematical Society: The Antikythera I and The Antikythera II.

A detailed account of the mathematics of the mechanism, along with java animations, can be found at the American Mthematical Society: The Antikythera I and The Antikythera II.

That being said, I disagree with a few points you made in your post, and I disagree with some quite strongly.

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The first point you made was about whether it's correct to view the BB as an explosion. There are two confounded issues here. The first is something like "what size was the universe at the inception", or "letting time go backward, what's the smallest the universe gets?". The second is whether or not the metaphor of explosion is correct to describe it.

The first issue was about "the size of the universe at inception", whatever that may mean. I don't think it really makes sense to differentiate between finite and zero size. I mean, look, at some timescale, and some temperature, all physical law will break down. Then what can we say? Let time run backward. Why should it continue to shrink to a 0-D point? Why not stop at 10^{whatever} m?

To the second issue, I think we must both agree that the question of a metaphor being "right" or "wrong" is tricky, and I may even go so far as to say the question is ill-posed. For example, you say

The point is that the idea of some sort of really tiny pellet of supercompressed matter exploding outward implies that space already exists

Here I disagree. As I said in my original post, "the universe started expanding", not "the stuff in the universe started moving outward". In fact, I think if I actually say that spacetime exploded, I really think that this is an accurate metaphor for what happened. Again, as I said, we can argue for infinite time whether or not this metaphor is good pedagogically, with no real end in sight. But, in my mind, when I think of nothing moving, then all of the sudden a bunch of shit moving, I'd call that an explosion. Never mind whether or not it's some matter, or spacetime itself.

You say that "explosion" implies space already existing, but you read too much into it. I mean, look, the theory is called the "Big Bang". Is that because we're supposed to think that there was a really loud noise when it happened?

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The second major point you raised with which I disagree is that there is no debate on the validity of the BB model. I could not disagree more. As you said:

If you can show me some evidence for such a serious debate within the community (journal cites, for instance), I'd like to see it. That's not to say that the cosmological community believes that there's nothing left to figure out; there's a lot to figure out. And that's not to say that the cosmological community believes, as a whole, that the Big Bang model will survive as it is without modification or supplement. But the consensus of the community is that whatever the correct description of the evolution of the Universe is, its evolution from a time when the age of the universe was about 10^-24 of what it is now and the average temperature of stuff in the univese was about a trillion degrees Kelvin, up to the present day, will look a lot like the Relativistic Hot Big Bang model.

There actually are quite a few references on this, but a good survey of an alternate theory is here. If you don't have access to the AMS site, the reference is

Daignault and Sangalli, "Einstein's Static Universe: An Idea whose Time has Come?", Notices of the American Mathematical Socity, (48), no. 1, pp. 1--16.

I grant you that this is a mathematics journal as opposed to a physics one, but this is as legitimate a journal as there is in the mathematics community. Notice the references in the paper to other papers on the topic in Astro. J. and Proceedings of the Nat'l Academy of Sciences. These are big-league journals that are publishing this stuff, and this is clearly a respected alternate theory.

Now, to be fair, I don't necessarily buy the alternate arguments and I am somewhat partial to Big Bang-like theories myself. But that being said, there most certainly is a debate going on in the community, as the above article shows.

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On the third point, you did in fact correct a mistake I made, but I would like to comment upon this further. I did say that "most cosmologists would say that the universe is closed", which I think, upon further reflection, is not quite accurate. The topic is quite debatable.

On the other hand, I would not go so far as you:

This would be correct if the data suggested that the topology/geometry of the Universe were that it were closed. That's not what the data say, and so that's not what the community believes.

Where I was too strong in my statement in one direction, I believe that you have overstated in the other direction. This is another topic which is even more debated than the validity of the BB itself. In fact, although I have heard arguments for an open topology, I've never heard a physicist express what you did with that much confidence. For example, I saw a talk by Frank Tipler a few years back in which he argued both sides of the coin. Also, I believe the cover story of the New Scientist (for whatever that's worth) was about this very issue. I do not think that there is a real concensus on this issue either. Sorry about the lack of explicit references here, but there's a lot of it out there, you should be able to find it.

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Anyway, like I said before: even though I don't agree with everything you said, you put some good stuff out there, and definitely made me think some shit through as I was writing this. It was quite enjoyable.

Here is an expository article from the Journal of the AMS about the Langlands program. Results of Lafforgue are used to prove some very nice theorems.

Here is a link to an article by Lafforgue in Inventiones Mathematicae, one of the world's most prestigious mathematics Journals. Malheursement, cet article est en français.

Here is the Mathematical Reviews citation for the Lafforgue paper. You can browse the articles cited by him.

Also, if anyone is interested, here is a paper by Voevodsky about some of his work in motivic cohomology.

Here is an expository article from the Journal of the AMS about the Langlands program. Results of Lafforgue are used to prove some very nice theorems.

Here is a link to an article by Lafforgue in Inventiones Mathematicae, one of the world's most prestigious mathematics Journals. Malheursement, cet article est en français.

Here is the Mathematical Reviews citation for the Lafforgue paper. You can browse the articles cited by him.

Also, if anyone is interested, here is a paper by Voevodsky about some of his work in motivic cohomology.

Here is an expository article from the Journal of the AMS about the Langlands program. Results of Lafforgue are used to prove some very nice theorems.

Here is a link to an article by Lafforgue in Inventiones Mathematicae, one of the world's most prestigious mathematics Journals. Malheursement, cet article est en français.

Here is the Mathematical Reviews citation for the Lafforgue paper. You can browse the articles cited by him.

Also, if anyone is interested, here is a paper by Voevodsky about some of his work in motivic cohomology.

Here is an expository article from the Journal of the AMS about the Langlands program. Results of Lafforgue are used to prove some very nice theorems.

Here is a link to an article by Lafforgue in Inventiones Mathematicae, one of the world's most prestigious mathematics Journals. Malheursement, cet article est en français.

Here is the Mathematical Reviews citation for the Lafforgue paper. You can browse the articles cited by him.

Also, if anyone is interested, here is a paper by Voevodsky about some of his work in motivic cohomology.

It is not the extremely low level garbage given in the article linked, but should be quite approachable as an introduction for anyone who hasn't done any serious advanced mathematics.

Jedidiah

Actually you can get a set of Adobe Type 1 fonts for LaTeX from the AMS. You can then make TeX use these standard PostScript Type 1 fonts in the PDFs it produces. More details here and here. You can also make LaTeX use the standard PostScript fonts for its body by using the \usepackage{times} directive in the preamble.

The people who do use Embed (and I have) are the ones who really need it for their work, in my case it's creating electronic documents (PDF or Corel Envoy) to send off to whomever needs this or that report within the organisation.

(Cavaets: I used to work for Goss and Varityper, and am well informed about the history of electronic-font theft by printing houses and the older copyright law surrounding fonts. I do not claim to be up-to-date on all aspects of modern font copyright. IANAL -- I Am Not A Lawyer.)

Case law following the 1972 copyright changes made it clear that the actual letter shapes are not subject to copyright, and a cursory look at the various amendments to the Copyright Acts since 1992 indicate there has been no statuary change in this area. What is protected by copyright is the digital description of a font -- the electronic file. The contents of such files go beyond the description of how to draw the character; it also includes information concerning the placement of characters in relation to other characters, sizing information, and "hints" as to how to modify the rendering as you change size, among other things.

What a lot of people tend to forget is that the name of a font is protected by trademark law. That's why Apple used place-names for a number of its in-house-developed fonts, and why "Helvetica", "Swiss", "Ariel", and "Megaron" appears to be synonyms for essentially the same typeface. They are. The difference between the fonts they name is the source of the font.

So, by using "Helvetica" in your document, a trademark, you are acknowledging the source of the font. Helvetica is a registered trademark of Linotype-Hell AG and/or its subsidiaries. Adobe, for example, licenses the face from Linotype-Hell, and is most likely required by that license to limit distribution of the outline files to people who have paid for a license to use.

If your license for the font "Helvetica" does not include the right to embed the font in Portable Document Format files, then you are guilty of copyright infringement.

Unfortunately, the embedding of the outline information in a PDF does not meet the tests for fair use. Others have listed the requirements in this discussion; I leave it to you, Dear Reader, to apply the tests and see how they fail.

The DMCA implications of "embed" is, frankly, just icing on the cake. At the base of the problem is copyright infringement, and the unjust enrichment that comes from the infringement. One person made it clear that he "needs" to embed fonts to ensure that the correct outline, kerning, and master-modification information is used when reading the document, or the result is a "mis-proportioned document" that looks ugly. The person derives a financial benefit from embedding fonts, and this can be viewed in court as "enrichment." By exceeding the boundaries imposed by the font license, s/he is profiting from the copyrighted work of another. The fact that the infringement is internal to an organization is of little weight, as the company may be the one considered guilty of the infringement, not the individual, if the copyright holder can show that the infringer is working within the scope of his/her employment.

The argument that there is no copyright infringement when the document is printed on paper, and therefore there can be no infringement because PDF is "like paper," isn't going to hold up in court. The problem is that the letterform itself is not subject to copyright, and the version of the type on paper is the letterform. Contrast this to the version of the letterform in the electronic PDF document is in its original copyrighted form. If the PDF document were to be in the form of a compressed pixel map, like a fax, then there would be no infringement because the copyrighted work would not be embedded in the electronic document. Unfortunately, such a pixel map, even heavily compressed, would be considerably larger than the desired PDF form, and the resolution of the resulting document would be fixed at the one used to render the page.

This suggests one way to avoid infringement: render the document as an image. It meets most of the original requirements, although the resulting file will be bloated. Because the outline file is not distributed in any way, there is no copying, therefore no copyright infringement. For purely inside distribution over a fast LAN, the bloat issue isn't as much of a problem. Mail servers may need to be upgraded to deal with the larger file sizes, but with the cost of mass storage plummeting the delta shouldn't be painful at all. It's definitely cheaper than lawyers and lawsuits and damages.

The more direct path to avoid infringement is for that person needs to enter into a license with the original holder of the copyright for each typeface s/he uses to specifically permit embedding those fonts s/he uses into PDFs. There may be a license fee per font to do so -- this is a good thing, to reduce file bloat from too many font outline files, not to mention the cleaner documents that will result from reducing font clutter. If there is a distinct business necessity to use specific, copyrighted type faces, the cost of entering into a license agreement should be tolerable. After all, type foundries are in business to sell type, not to bleed customers dry. For that reason, shop around. Every type house/foundry has their versions of a Times newspaper face, a san-serif block face [Helvetica/Swiss/Megaron/&c], a mono-spaced typewriter face, and useful display faces, and their licensing requirements may be more in line with your needs than what Linotype offers. That's competition.

Don't like paying cash for the right to use a letterform? The shapes of the letterforms are not subject to copyright. There is nothing I'm aware of that says you can't print a font, letter by letter, scan the printed pages, and encode them into your own font outline file using any of the many font development packages available. Then you can embed to your heart's content. (Check with a competent intellectual property attorney before doing this.) Don't forget to use your own completely made-up name for the resulting font outline.

For those not willing to put in that kind of time, there is yet another alternative: investigate other type face sources. Donald Knuth has designed a number of faces, originally rendered in Metafont, which are available as Postscript type faces. They are quite pleasant to the eye, and are very readable. Another source of potential type faces is the X Consortium, although I would check the license regarding typeface use outside of the X environment. A Google search showed there are a number of people who have contributed type faces to the public domain, as well as providing faces in a shareware distribution format.

There's no excuse for copyright infringement.

Stridar writes "A paper presented in a recent article quotes Donald Knuth as saying the computer science has 500 deep algorithms. He mentions that Euclid's algorithm is one of the most important, and he seems to agree with the idea that CS will be mature when it has 1000 deep algorithms. What I would like to ask Slashdot is the following. What are the most important algorithms in CS? What is your favorite algorithm? And finally, what are the outstanding problems for which algorithms would be immediately placed in the "Top 1000" category." We had an older story where two scientists picked their top ten algorithms .

The guy is smart, but his choice of format is more suitable for old, soon to be obsolette printable media not for the Internet.

Well, presumably it was the AMS who chose to put it in PDF, not Knuth himself. Although yeah, it does seem kinda silly that they made that choice. Especially given their interest in TeX (I use the amsmath LaTeX package all the time).

OK, I may be biased (I work for one of them) but they can be quite helpful. Most if not all have reduced rates for students. I know that SIAM has activity groups focusing on different areas of Mathematics. (Anyone care to guess who I work for?).

I am a 2nd year undergrad at a local university studying Computer Science, and I work tech support here. I can't form a real accurate opinion of what we do for our members, as I'm not all that interested in it, or do I work with members much. But I know we have conferences all over the country and have Job listing and such. Plus it's a good way to network with other geeks... Umm... I mean Mathematicians.

I suggest you check out some websites, see what you like, and perhaps pose the question towards some of them.

Society for Industrial and Applied Mathematics
American Mathematical Society
Association for Women in Mathematics
Mathematical Association of America

Also, here is a direct link to the AMS's link page

Good Luck, and feel free to email me with questions.

OK, I may be biased (I work for one of them) but they can be quite helpful. Most if not all have reduced rates for students. I know that SIAM has activity groups focusing on different areas of Mathematics. (Anyone care to guess who I work for?).

I am a 2nd year undergrad at a local university studying Computer Science, and I work tech support here. I can't form a real accurate opinion of what we do for our members, as I'm not all that interested in it, or do I work with members much. But I know we have conferences all over the country and have Job listing and such. Plus it's a good way to network with other geeks... Umm... I mean Mathematicians.

I suggest you check out some websites, see what you like, and perhaps pose the question towards some of them.

Society for Industrial and Applied Mathematics
American Mathematical Society
Association for Women in Mathematics
Mathematical Association of America

Also, here is a direct link to the AMS's link page

Good Luck, and feel free to email me with questions.

Well I am a junior math major at a not so pristegious university and I would say that I am in the same boat. I posted a topic similar to this on the alt.math newsgroup and I got about 50/50 = "go for it" / "Stick w/ computers and keep math as a hobby"

If I were you I would take a few more classes until I make a lifelong commitment. Math is one of those subjects where the upper division work differs greatly from most of what you see in ugrad/hs.If that hasn't scared you enough then try the AMS Job Search just to see what type of positions seem to be open in your state.

True :-).

But it is on the web. Try here. I think that it should be generally accessible (i.e., I hope I'm not getting to it based solely on an institutional subscription).

Here are even more links...

I don't see an eternal flame in the Turing Memorial. Of course, it should have have an infinite tape

Since these journals are being reviewed by peers, publishing by such non-profit groups can work. Both the submitter and review wants the highest quality publication since it helps their respective reputations, the reviewer does not need a hugh amount of cash, just enough to cover expensives or pay for the costs of their next paper.

Smaller topics in mathematics, computer science, and physics already have free pre-print services (arXiv.org www.acm.org/dl), and more than a few online peer reviewed publications. These areas have quickly adapted because they already use electronic submissions of "camera-ready" papers in TeX format.

I think the important point is that these speciality publications are for a small community not for a general audience. The numbers are small, and most participates main income comes from elsewhere.

I didn't even say peer2peer once.

LaTeX is a wonderful way of expressing mathematical notions and is the defacto standard amoung mathematicians. Once you know TeX, using something else is a real downer, from the elegance, portability and functionality standpoints.

Unfortunately for the more mathematical amoung us, LaTeX will never/has not caught on as a competitor to HTML, largely because so little of the web needs precise mathematical notation.

A few years ago, in the Notices of the American Mathematical Society, an article appeared about the promise of MathML. All the research mathematicians I know had the same reaction to the article, which was: "It took 40 lines of code to express x^2+4x=0? Is this some kind of joke?" (see the article in PDF, which was rosy about MathML and seemed to think that 40 lines of code was reasonable for that...) Mozilla supports MathML but MathML has not caught on with mathematicians and will not budge anyone away from TeX. People post their preprints in TeX, journals and conferences want articles in TeX, and it is the most reasonable way of exchanging mathematical papers.

It would be nice if TeX were more widely used, but its role is different than HTML. TeX is optimized for typesetting documents that have significant mathematical structure and though it can take a while to render something complicated in TeX, the page layout will be gorgeous. HTML or its replacements need to be quickly rendered by the browser and only very rarely have the need to use mathematical expressions.

Going back to who owns the copyright of the individual entries, a lot of entries on the properties of sequences of integers were submitted by Steven Finch of MathSoft. Steven still maintains a website with this material on, so I wonder if CRC will start chasing him? (Maybe he has a separate agreement with CRC, though - I don't know.)

Incidentally, some academic journals in mathematics allow for authors to have an electronic version of their papers on their homepages. The AMS is one example, where you will often see in the copyright notice on a paper `copyright retained by author'. A lot of other journals turn a blind eye. (As you might expect, the copyright notice in the CRC Encyclopedia is the standard `it's ours so hands off' one: no reproducing or transmitting in any form or by any means, electronic or mechanical, etc etc.)

My own feelings are that the best place for the encyclopedia is on the web. Some of the entries are mathematically wrong, and many are misleading. This is not a criticism of Eric, who obviously put a lot of work into the project, it's just a fact that a book containing so much material will contain many many errors. (See the (often extrmely rude) posts from about 5 years ago on sci.math.research complaining about the lack of mathematical precision in the treasure trove!) Having the treasure trove on the web would and should have allowed the project to grow, both in terms of the accuracy and the number of the entries. Sadly, the only way that such errors could be corrected in the printed version would be for CRC to issue a second edition - something I would imagine Eric is now unlikely to want to get involved in...

Go have a look at the SETI@Home Downloads page. Tell me there are no processors in there that might have vector-optimised maths units.

Go have a look at the Crusoe Technology page, or the VMWare site. Tell me that it's impossible to use hardware or software to emulate or translate from one instruction set to another. Besides, what's stopping the KrosnoConv "surplus military" stock being military-spec MIPS or SPARC clones? I didn't read the "about the company" bit, so I expected this was just an American company picking up after the excesses of the United States war machine.

Heck, check any Pentium III and tell me that it's impossible to execute another device's instruction set (8088) natively.

The only points that concerned me about the KrosnoConv boards were the Linux-in-Flash claim, and 32Mb of RAM per processor for less than $US200 (either very slow memory, or only 32Mbit perhaps, co-packaged RAM from the old 8086 days). There are projects out there to put Linux in a PC BIOS, or even an LS120. You can get CompactFlash cards, which behave like very small hard drives (either Flash memory pretending to be an IDE drives, or IBM microdrives really being IDE drives). But they're not cheap.

x86 is not the only architecture that SETI@Home supports. Why shouldn't someone produce an add-in card that uses your existing infrastructure? I would still be interested in getting a (cheap!) board full of heavy-maths processors to do hardware encryption for Virtual Private Networks, or even just a heavy duty key server.

I've already got the expensive bits like hard drives, network cards, monitors, cases and memory. I'd actually love to have a "parasitic" processor running its own OS, where I can download software to it, and have it process data that I store for it in my real RAM. Kinda like a multi-processor machine, where one or more processors are especially suited to encryption math.

Don't just spout "that's not how things work". Because with the introduction of technology like that used in the Crusoe, or even older technology like that used in VMWare, or any C64 emulator, you know this is how things work now.

Having said all that, the other poster was right; if this were easy someone would have done it already. At the very least you will need enough mathematical background to write with the correct terminology and symbols. Really you shouldn't seriously attempt this sort of research without first becoming familliar with what other people have tried and why it didn't work. Please don't annoy the journal editors with bogus submissions (not that I think you were planning to, but it bears repeating nonetheless).

-rpl

I'm heading up a technical group evaluating proposals for a new, hopefully complete, set of scientific/mathematical fonts that we plan to make freely available - obviously Knuth's well-reasoned opinions are highly relevant. What he suggests, that somebody should be out there sponsoring font designers, is exactly what we're trying to do! But it sometimes seems hard to persuade publishers to part with their money for something they won't fully control. Even those who make tens of millions in profits seem reluctant to spend more than a few tens of thousands on something that will be freely distributed - despite the fact that it will likely save a lot in licensing and other proprietary-based costs. Is this a strange psychological problem here?

Anyway, we're trying to work with both the Microsoft side of things and the Mozilla/MathML people, plus support TeX of course. As an advertising plug - if you would like to contribute your thoughts or experience (or cash) towards the effort, send me a note at apsmith@aps.org.

And many thanks to /. for highlighting this wonderful interview with Knuth.

Like the article says, Wiles solved a special case of STW to knock off Fermat's Last Theorem. I guess this is a proof of the general version (but the article is a little vague--any number theorists around who are in the loop?)

• on Eric's Treasure Trove of Mathematics
• H ow it relates to FLT
• Several link on FLT and STW
• If you're at a University or otherwise have access to the American Mathematical Society's MathSciNet, there are a couple of papers

If you have a casual interest in this area of mathematics, good places to start might be Ireland/Rosen, A classical introduction to modern number theory, or Silverman, The arithmetic of elliptic curves (both Springer GTM). See also my bibliography of math textbooks.

You should also check out the AMS's website explaining turing machines

-Dave