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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 
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 
[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.]
I’ve received quite a lot of inquiries regarding a recent article in the New York Times, so I am borrowing some space on this blog to respond to some of the more common of these, and also to initiate a discussion on maths education, which was briefly touched upon in the article.
Firstly, some links:
- The video for the talk “Structure and randomness in the prime numbers” mentioned in the article can be found here (requires RealPlayer). The slides can be found here. My other expository and research material on number theory can be found here.
- I don’t have any specific advice regarding gifted education, though some articles on my own experiences can be found here. I do however have some thoughts on career advice at the undergraduate level and beyond.
- I have some responses to several other common queries (e.g. regarding books, interviews, invitations, etc.) at my contact information page.
Most of the feedback I received, though, concerned the issue of maths education. I mentioned in the article that I feel that the skill of thinking in a mathematical and rigorous way is one which can be taught to virtually anyone, and I would in the future hope to be involved in some project aimed towards this goal. I received a surprising number of inquiries on this, particularly from parents of school-age children. Unfortunately, my maths teaching experience is almost completely restricted to the undergraduate and graduate levels – and my own school experience was perhaps somewhat unusual – so I currently have close to zero expertise in K-12 maths education. (This may change though as my son gets older…) Still, I think it is a worthy topic of discussion as to what the mathematical academic community can do to promote interest in mathematics, and to encourage mathematical ways of thinking and of looking at the world, so I am opening the discussion to others who may have something of interest to say on these matters.
(Update, March 13: A bad link has been repaired. Also, I can’t resist a somewhat political plug: for Californian readers, there is an open letter in support of California’s K-12 education standards, together with some background information.)
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