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[*This guest post is authored by Ingrid Daubechies, who is the current president of the International Mathematical Union, and (as she describes below) is heavily involved in planning for a next-generation digital mathematical library that can go beyond the current network of preprint servers (such as the arXiv), journal web pages, article databases (such as MathSciNet), individual author web pages, and general web search engines to create a more integrated and useful mathematical resource. I have lightly edited the post for this blog, mostly by adding additional hyperlinks. - T.*]

This guest blog entry concerns the many roles a World Digital Mathematical Library (WDML) could play for the mathematical community worldwide. We seek input to help sketch how a WDML could be so much more than just a huge collection of digitally available mathematical documents. If this is of interest to you, please read on!

The “we” seeking input are the Committee on Electronic Information and Communication (CEIC) of the International Mathematical Union (IMU), and a special committee of the US National Research Council (NRC), charged by the Sloan Foundation to look into this matter. In the US, mathematicians may know the Sloan Foundation best for the prestigious early-career fellowships it awards annually, but the foundation plays a prominent role in other disciplines as well. For instance, the Sloan Digital Sky Survey (SDSS) has had a profound impact on astronomy, serving researchers in many more ways than even its ambitious original setup foresaw. The report being commissioned by the Sloan Foundation from the NRC study group could possibly be the basis for an equally ambitious program funded by the Sloan Foundation for a WDML with the potential to change the practice of mathematical research as profoundly as the SDSS did in astronomy. But to get there, we must formulate a vision that, like the original SDSS proposal, imagines at least some of those impacts. The members of the NRC committee are extremely knowledgeable, and have been picked judiciously so as to span collectively a wide range of expertise and connections. As president of the IMU, I was asked to co-chair this committee, together with Clifford Lynch, of the Coalition for Networked Information; Peter Olver, chair of the IMU’s CEIC, is also a member of the committee. But each of us is at least a quarter century older than the originators of MathOverflow or the ArXiv when they started. We need you, internet-savvy, imaginative, social-networking, young mathematicians to help us formulate the vision that may inspire the creation of a truly revolutionary WDML!

Some history first. Several years ago, an international initiative was started to create a World Digital Mathematical Library. The website for this library, hosted by the IMU, is now mostly a “ghost” website — nothing has been posted there for the last seven years. [It does provide useful links, however, to many sites that continue to be updated, such as the European Mathematical Information Service, which in turn links to many interesting journals, books and other websites featuring electronically available mathematical publications. So it is still worth exploring ...] Many of the efforts towards building (parts of) the WDML as originally envisaged have had to grapple with business interests, copyright agreements, search obstructions, metadata secrecy, … and many an enterprising, idealistic effort has been slowly ground down by this. We are still dealing with these frustrations — as witnessed by, e.g., the CostofKnowledge initiative. They are real, important issues, and will need to be addressed.

The charge of the NRC committee, however, is to NOT focus on issues of copyright or open-access or who bears the cost of publishing, but instead on what could/can be done with documents that are (or once they are) freely electronically accessible, apart from simply finding and downloading them. Earlier this year, I posted a question about one possible use on MathOverflow and then on MathForge, about the possibility to “enrich” a paper by annotations from readers, which other readers could wish to consult (or not). These posts elicited some very useful comments. But this was but one way in which a WDML could be more than just an opportunity to find and download papers. Surely there are many more, that you, bloggers and blog-readers, can imagine, suggest, sketch. This is an opportunity: can we — no, YOU! — formulate an ambitious setup that would capture the imagination of sufficiently many of us, that would be workable and that would really make a difference?

For the past few months, Cambridge University Press (in consultation with a number of mathematicians, including Tim Gowers and myself) has been preparing to launch a new open access journal (or more precisely, a complex of journals – see below) in mathematics, under the title “Forum of Mathematics“, as an experiment in moving away from the traditional library subscription based model of mathematical academic publishing. (The initial planning for this journal happened to precede the Cost of Knowledge boycott, but the philosophy behind the journal is certainly aligned with that of the boycott, which I believe is further evidence that the time has come for mathematical journal reform.) The journal will formally begin accepting submissions on October 1st, but it has already been officially announced by Cambridge University Press, with an editorial board (with Rob Kirby as managing editor, thirteen other editors including Tim and myself, and a board of associate editors that is still in the process of being assembled) and FAQ already in place.

In many respects, Forum of Mathematics functions as a regular mathematics journal, in that papers are submitted by the authors, sent out to referees by the editors, and (if accepted) published by the Forum. There are however a couple of important features that distinguish the Forum from traditional mathematics journals. The first is the open access, publication-charge based publishing model (sometimes known as “gold open access”). Namely, all articles will be freely available without subscription charges, but authors, upon their paper being accepted, be asked to pay a publication charge to cover costs. The publication charges will be set at zero for the first three years, and then raised to somewhere around £500 GBP or $750 USD after the initial three-year period (with fee waivers available for authors from developing countries). (One reason that the publication charges are not entirely fixed at this point is that there is the possibility of obtaining additional funding sources for this journal, for instance from philanthropic organisations, which may allow for fee reductions or additional waivers.) This is of course a non-trivial sum of money, but it is significantly lower than the charges for most other gold open access journals. Also, editorial decisions will not be influenced by the author’s ability to pay for the charges, which only come into effect in the event that the paper is accepted for publication.

(One way in which Cambridge University Press is keeping costs low, by the way, is to keep the journal purely electronic, with physical issues available on a print-on-demand basis only. A side benefit of this choice is that there is no hard constraint on how many or how few pages will be published each year, so that acceptance decisions will not be influenced by artificial constraints such as the size of the journal backlog.)

Another distinctive feature of Forum of Mathematics lies in its scope and structure. It is not exactly a single journal, but is instead a complex consisting of a generalist flagship journal (officially known as Forum of Mathematics, Pi) and a specialist journal (Forum of Mathematics, Sigma) which is in turn loosely organised for editorial purposes into “clusters” for each of the major subfields of mathematics (analysis, topology, algebra, discrete mathematics, etc.). As a first approximation, Pi is intended as a top-tier journal (on the level of, say, the Journal of the American Mathematical Society, Inventiones, or Annals of Mathematics) that only accepts significant papers of interest to a wide audience of mathematicians, while Sigma resembles a collection of specialist journals, one for each major subfield of mathematics. However, the journals will be using the same editorial interface, and so it will be possible to easily transfer a submission between journals or clusters (while retaining all the referee reports and other editorial data). This is meant to help address a common issue in traditional mathematical journals, namely that if the editorial board decides that a submission falls too far outside the scope of the journal, or is not quite at the desired level of quality, then the authors have to start all over again with a new journal (and new referee reports). Of course, it is still possible (and perhaps even fairly common) that a submission to Forum of Mathematics will be deemed unsuitable for either Pi or Sigma, and thus rejected entirely; but the structure of the Forum should give some additional flexibility, to reduce the frequency that papers are rejected for artificial reasons such as being out of scope. (Of course, we would still expect authors to aim their submission at the most appropriate location to begin with, in order to reduce the time and effort expended on processing the paper by everyone involved.)

Further discussion of this journal can be found at Tim Gowers’ blog. It should be fully operational in a few months (barring last-minute hitches, we should be open for submissions on 1 October 2012). Of course, a single journal is not going to resolve all the extant concerns about the need for journal publishing reform, such as those raised in the Cost of Knowledge boycott; but I feel that it is important to have some experimentation with different publishing models, to see what alternatives to the *status quo* are possible.

As an experiment, I’ve recently started using Google Buzz as an outlet for various things I wanted to say or share, but which were too insubstantial to merit a mention on this blog. (In turn, one of the reasons of starting this blog was to share various bits of mathematics which were too insubstantial for a published paper. Presumably the process becomes degenerate if iterated any further…) I don’t know how frequently I will be updating, though.

The level and quality of discourse in this U.S. presidential campaign has not been particularly high, especially in recent weeks. So I found former Gen. Powell’s recent analysis of the current state of affairs, as part of his widely publicised endorsement of Sen. Obama, to be a welcome and refreshing improvement in this regard:

It’s a shame that much of the rhetoric and commentary surrounding this campaign – from all sides – was not more like this. [In keeping with this, I would like to remind commenters to keep the discussion constructive, polite, and on-topic.]

[*Update*, Oct 22: Unfortunately, some of the more recent comments have not been as constructive, polite, and on-topic as I would have hoped. I am therefore closing this post to further comments, though anyone who wishes to discuss these issues on their own blog is welcome to leave a pingback to this post here.]

Over a year ago, I had a brief post here pointing out Gene Weingarten‘s article in the Washington Post entitled “Pearls before breakfast“, in which the Post asked the question of what would happen if a world-class musician (in this case, Joshua Bell), were to perform incognito and out of context, in a Washington subway during the morning rush hour? If you haven’t yet read the article describing the experiment and the outcome, I recommend it to you.

Anyway, a few weeks ago, this article was awarded the 2008 Pulitzer Prize for Feature Writing. Congratulations to Gene, Joshua, and the other Washington Post staff!

[Actually, this article was highly atypical for Gene; he usually sticks to writing a weekly low-brow humour column entitled "Below the Beltway". By a random coincidence, I, together with Curt McMullen, even have a very minor bit part in one of these columns (on page 2), thanks to a brief phone conversation we each had with Gene.]

I usually try to keep political issues out of this blog, and I certainly try to avoid asking friends and readers of this blog for favours, but there is an urgent situation developing in mathematics (and related disciplines) in my home country of Australia, and I need to ask all of you for assistance to prevent an impending disaster.

When I was an undergraduate at Flinders University in South Australia from 1989 to 1992, the level of mathematics education in Australia was comparable to that of world-class institutions overseas. Even in a small and little-known university such as Flinders, I received a first-rate honours undergraduate education in mathematics, computer science, and physics which I continue to use daily in my career. (Examples of topics I learned as an undergraduate include wavelets; information theory; Lie algebras; differential geometry; nonlinear PDE; quantum mechanics; statistical mechanics; and harmonic analysis. I rely on my knowledge of all of these topics today, for instance many of them are are helpful for me in teaching my current class on the Poincaré conjecture.) In addition, several of the faculty (including the chair and my undergraduate advisor, Garth Gaudry) had the time to spare an hour a week with me to discuss mathematics, as they were not overloaded with large teaching loads and other duties. I honestly think that I would not be where I am today without the high-quality undergraduate education that I received (in particular, I would definitely have floundered in graduate school at Princeton, if I were admitted at all).

The situation for mathematics education in Australia began however to deteriorate in later years, due to a combination of factors including government neglect (the federal government is the most significant source of funding for most universities in Australia) and the low priority of basic education in mathematics and sciences among university administrators. In particular, at Flinders University, the School of Mathematics suffered severe attrition due to lack of support and was eventually folded into the School of Informatics and Engineering. In fact the number of mathematicians on the faculty at Flinders has dwindled down to just three (in my day it was close to 20).

The decline of mathematics departments across the country, particularly in a time in which mathematics skills are desperately needed in the workforce, has been documented thoroughly in the 2006 national strategic review of the mathematical sciences. In response to that report, the federal government in 2007 announced an increase in the funding allocation to universities based on their student enrollments in key majors including mathematics and the sciences. The newly elected federal government is also likely to continue and extend this support in its upcoming budget in May of this year.

Unfortunately, it appears that at many universities, the additional funding was diverted away from the schools that it was intended to support, for the administrator’s own priorities. (See also the letter by the international authors of the above mentioned review, Jean-Pierre Bourguignon, Brenda Dietrich, and Iain Johnstone, condemning this diversion.) As a consequence, many mathematics departments are in fact in worse shape than before.

There is a particular crisis unfolding at the University of Southern Queensland. On March 17, the university announced a rationalisation and restructuring proposal that would cut the number of mathematics faculty from 14 to 6, eliminate the majors in mathematics, chemistry, physics, and statistics, and phase out all non-service courses (for instance, any of the types of courses I mentioned above at Flinders would be lost). Similar cuts were also proposed in statistics, computer science, and physics, although other schools retained their funding and some even obtained increases. This is despite the increases in funding from the federal government for mathematics and statistics students (enrollments in these areas at USQ has held steady so far, though of course with the proposed cuts this is unlikely to last). Already as a consequence of these proposals, initiatives of the department such as an education program for high school mathematics teachers have had to be scrapped. Somewhat ironically, the Dean of Sciences at USQ, Janet Verbyla, who has been heavily involved in proposing the cuts, had also presided over similar reductions in the school of mathematics at Flinders.

If the proposed cuts at USQ go ahead, it is likely that other small universities in Australia will be tempted to similarly ignore concerns about mathematics and science education and perform similar cuts, even while receiving government support for these disciplines. (The University of New England, which currently shares some statistics courses at USQ, would for instance be particularly vulnerable.) So the crisis here is not purely localised to USQ, but could be very damaging for mathematics and sciences in Australia as a whole.

The consultation period for these cuts ends very soon, on April 14, and the vice-chancellor of USQ, Bill Lovegrove, plans to announce the specific cuts on April 18 at an unspecified future date. While there has been some media attention in Australia given to this issue, it has not yet had much effect in reversing the decisions of these administrators. Because of this, I am reluctantly turning to my friends and readers of this blog to ask for your urgent assistance in saving the school of mathematics and computing at USQ. In collaboration with several good friends and colleagues in Australia, I have begun a web page on this blog,

http://terrytao.wordpress.com/support-usq-maths/

that is documenting the situation and outlining ways to help, including an online petition

http://terrytao.wordpress.com/about/petition-to-support-maths-statistics-and-computing-at-usq/

that you can sign to show support, and people to contact in the university administration and in the Australian government to express your concerns, or to express support for mathematics and its role in the sciences. Please also inform others, especially those in Australia and who may have influence in media, political, or administrative circles, of the current crisis. There is still time, especially in view of the expected increase in support for mathematics and sciences in the upcoming federal budget, to reverse the situation before the damage becomes permanent, and to show that the political support for mathematics education is not so negligible as to be easily ignored.

Thank you all in advance for any help you can give – and I promise that I will keep the remainder of my blog on topic and focus primarily on mathematics. :-)

[*Update*, April 9: See my editorial at the Funneled Web, "Mathematics in Today's world", for a more detailed discussion of the USQ crisis, and also the broader context of the importance of higher mathematics education, and the pivotal role universities have to play in providing it.]

[*Update*, April 12: The Toowoomba Chronicle has a two-page article by Merryl Miller focusing on the crisis, and in particular focusing on its impact on a 10-year old child prodigy, Adam Walsh, currently taking maths classes at USQ. (Reprinted with permission.)]

[*Update*, April 14: The petition has been formally sent to the USQ administration. Apparently, the previously planned announcement of the cuts on April

18 has been delayed to some unspecified later date, but no further details are currently available.]

[*Update*, April 17: In response to the concerns of constituents, Hon. Mike Horan MP, the state member for Toowoomba South, spoke in the Queensland parliament urging the University of Southern Queensland to reconsider its cutbacks to mathematics and statistics. (The full and official transcript of the day's session in Parliament can be found here; the speech above is on page 1198.)]

[*Update*, April 29: The USQ administration released a revised draft proposal on April 22, but the details are largely unchanged (e.g. 11 staff cuts to the department of mathematics and computing instead of 12, and a "review" of the maths major and its courses rather than automatic elimination). The revised plan has already attracted criticism from the National Tertiary Education Union, and we are continuing to organise further opposition to the proposals. (For instance, László Lovász, President of the International Mathematical Union, wrote a letter of support on April 25.]

[*Update*, May 1. A second revised draft proposal has been released, which uses some new (but possibly non-permanent) sources of funding to add some specialised positions to partially offset the cuts (e.g. there will be 2-3 such positions in mathematics and statistics, although the 11 staff cuts are still in effect). The USQ administration has apparently also agreed to recheck the student load and financial data that is being used to underlie these proposals, as there appears to be some irregularities with this data in previous rationales.]

This post will have only the most tangential connection to mathematics.

I am an Australian citizen (and permanent resident in the US), but I nevertheless take an interest in the upcoming US presidential election in 2008. I’ve recently learned of a grassroots campaign to have one of the presidential debates focused on policy issues in science, technology, health, and the environment. (See also this LA Times op-ed and Wall Street Journal op-ed.) Personally, I think this is an excellent idea, and hope that it succeeds; it seems that they are currently petitioning signatures towards this goal.

While on this topic, it is also interesting to see what the political prediction markets are currently forecasting as the outcome of the election…

[Via Bad Astronomy.]

[*Update*, Dec 20: Here is a table listing the major candidates and their positions on mostly science-related issues.]

I’ve joined the inaugural editorial board for a new mathematical journal, Analysis & PDE. This journal is owned by Mathematical Sciences Publishers, a non-profit organisation dedicated to high-quality, low-cost, and broad-availability mathematical publishing, and run primarily by professional mathematicians. The scope of the journal is, of course, self-explanatory; MSP’s other journals have titles such as Geometry & Topology, Algebra & Number Theory, and Algebraic & Geometric Topology.

We’re just starting out (and haven’t even filled up our first issue yet), so we are looking for strong and significant submissions in all areas of analysis and PDE (broadly defined). If you have a good paper in these areas and are deciding on which journal to submit to, you might want to take a look at the submission guidelines for our journal. Of course, the papers are subject to the usual peer review process and will be held to high standards in order to be accepted.

[*Update*, Nov 11: Link fixed.]

As you may already know, Danica McKellar, the actress and UCLA mathematics alumnus, has recently launched her book “Math Doesn’t Suck“, which is aimed at pre-teenage girls and is a friendly introduction to middle-school mathematics, such as the arithmetic of fractions. The book has received quite a bit of publicity, most of it rather favourable, and is selling quite well; at one point, it even made the Amazon top 20 bestseller list, which is a remarkable achievement for a mathematics book. (The current Amazon rank can be viewed in the product details of the Amazon page for this book.)

I’m very happy that the book is successful for a number of reasons. Firstly, I got to know Danica for a few months (she took my Introduction to Topology class way back in 1997, and in fact was the second-best student there; the class web page has long since disappeared, but you can at least see the midterm and final), and it is always very heartening to see a former student put her or his mathematical knowledge to good use :-) . Secondly, Danica is a wonderful role model and it seems that this book will encourage many school-age kids to give maths a chance. But the final reason is that the book is, in fact, rather good; the mathematical content is organised in a logical manner (for instance, it begins with prime factorisation, then covers least common multiples, then addition of fractions), well motivated, and interleaved with some entertaining, insightful, and slightly goofy digressions, anecdotes, and analogies. (To give one example: to motivate why dividing 6 by 1/2 should yield 12, she first discussed why 6 divided by 2 should give 3, by telling a story about having to serve lattes to a whole bunch of actors, where each actor demands two lattes each, but one could only carry the weight of six lattes at a time, so that only actors could be served in one go; she then asked what would happen instead of each actor only wanted half a latte instead of two. Danica also gives a very clear explanation of the concept of a variable (such as ), by using the familiar concept of a nickname given to someone with a complicated real name as an analogy.)

While I am not exactly in the target audience for this book, I can relate to its pedagogical approach. When I was a kid myself, one of my favourite maths books was a very obscure (and now completely out of print) book called “Creating Calculus“, which introduced the basics of single-variable calculus via concocting a number of slightly silly and rather contrived stories which always involved one or more ants. For instance, to illustrate the concept of a derivative, in one of these stories one of the ants kept walking up a mathematician’s shin while he was relaxing against a tree, but started slipping down at a point where the slope of the shin reached a certain threshold; this got the mathematician interested enough to compute that slope from first principles. The humour in the book was rather corny, involving for instance some truly awful puns, but it was perfect for me when I was 11: it inspired me to *play* with calculus, which is an important step towards improving one’s understanding of the subject beyond a superficial level. (Two other books in a similarly playful spirit, yet still full of genuine scientific substance, are “Darwin for beginners” and “Mr. Tompkins in paperback“, both of which I also enjoyed very much as a kid. They are of course no substitute for a serious textbook on these subjects, but they *complement *such treatments excellently.)

Anyway, Danica’s book has already been reviewed in several places, and there’s not much more I can add to what has been said elsewhere. I thought however that I could talk about another of Danica’s contributions to mathematics, namely her paper “Percolation and Gibbs states multiplicity for ferromagnetic Ashkin-Teller models on ” (PDF available here), joint with Brandy Winn and my colleague Lincoln Chayes. (Brandy, incidentally, was the only student in my topology class who did better than Danica; she has recently obtained a PhD in mathematics from U. Chicago, with a thesis in PDE.) This paper is noted from time to time in the above-mentioned publicity, and its main result is sometimes referred to there as the “Chayes-McKellar-Winn theorem”, but as far as I know, no serious effort has been made to explain exactly what this theorem is, or the wider context the result is placed in :-) . So I’ll give it a shot; this allows me an opportunity to talk about some beautiful topics in mathematical physics, namely statistical mechanics, spontaneous magnetisation, and percolation.

[*Update*, Aug 23: I added a non-technical "executive summary" of what the Chayes-McKellar-Winn theorem is at the very end of this post.]

The main topic of this post has absolutely nothing to do with mathematics, except insofar as the well-known analogies between mathematics and music are concerned, but the recent article “Pearls before breakfast” in the Washington Post makes for fascinating reading. They conduct a very interesting experiment regarding the relationship between quality and context: what would happen if one took one of the finest and most renowned violinists in the world, and made him give a concert-quality performance, while busking incognito at a busy subway station? The results… well, I won’t spoil them, but suffice to say that the article is well worth the read.

One wonders whether one could conduct a similar experiment in mathematics. The main new difficulty, of course, is that good music can (in principle) be appreciated by any attentive and interested listener, but the same is much less true of good mathematics. But perhaps there is a substitute experiment which would also be revealing. For instance, in Feynman’s well-known book (in the chapter “Alfred Nobel’s other mistake”), one reads that, to avoid crowds of curiosity-seekers, the Nobel prize-winning physicist would sometimes give public lectures unannounced, as a last minute substitute for the announced (and fictional) lecturer; but the published title and abstract (e.g. “On the structure of the proton”) would be absolutely accurate, and thus only draw in people who were interested in the subject matter and not in the lecturer himself. Indeed, the crowds were much reduced as a consequence.

[Update, April 25, 2008: The above article won the 2008 Pulitzer Prize for Feature Writing.]

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