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Seven videotaped lectures from 1964 by Richard Feynman given in Cornell, on “The Character of Physical Law“, have recently been put online (by Microsoft Research, through the purchase of these lectures from the Feynman estate by Bill Gates, as described in this interview with Gates), with a number of multimedia enhancements (external links, subtitles, etc.). These lectures, intended for a general audience, broadly cover the same type of material that is in his famous lectures on physics.

I have just finished the first lecture, describing the history and impact of the law of gravitation as a model example of a physical law; I had of course known of Feynman’s reputation as an outstandingly clear, passionate, and entertaining lecturer, but it is quite something else to see that lecturing style directly. The lectures are each about an hour long, but I recommend setting aside the time to view at least one of them, both for the substance of the lecture and for the presentation. His introduction to the first lecture is surprisingly poetic:

The artists of the Renaissance said that man’s main concern should be for man.

And yet, there are some other things of interest in this world: even the artist appreciates sunsets, and ocean waves, and the march of the stars across the heavens.

And there is some reason, then, to talk of other things sometimes.

As we look into these things, we get an aesthetic pleasure directly on observation, but there’s also a rhythm and pattern between the phenomena of nature, which isn’t apparent to the eye, but only to the eye of analysis.

And it’s these rhythms and patterns that we call physical laws.

What I want to talk about in this series of lectures is the general characteristics of these physical laws. …

The talk then shifts to the very concrete and specific topic of gravitation, though, as can be seen in this portion of the video:

Coincidentally, I covered some of the material in Feynman’s first lecture in my own talk on the cosmic distance ladder, though I was approaching the topic from a rather different angle, and with a less elegant presentation.

[*Via the New York Times*. Note that some browsers may need a Silverlight extension in order to view the videos. Youtube versions of three of the seven lectures are available here. Another, much more recent, series of videotaped lectures of Feynman is available here.]

[*Update*, July 15: Of particular interest to mathematicians is his second lecture "The relation of mathematics and physics". He draws several important contrasts between the reasoning of physics and the axiomatic reasoning of formal, settled mathematics, of the type found in textbooks; but it is quite striking to me that the reasoning of *unsettled* mathematics - recent fields in which the precise axioms and theoretical framework has not yet been fully formalised and standardised - matches Feynman's description of physical reasoning in many ways. I suspect that Feynman's impressions of mathematics as performed by mathematicians in 1964 may differ a little from the way mathematics is performed today.]

As readers of this blog are no doubt aware, I (in conjunction with Tim Gowers and many others) have been working collaboratively on a mathematical project. To do this, we have been jury-rigging together a wide variety of online tools for this, including at least two blogs, a wiki, some online spreadsheets, and good old-fashioned email, together with offline tools such as Maple, LaTeX, C, and other programming languages and packages. (To a lesser extent, I also rely this sort of mish-mash of semi-compatible online and offline software packages in my more normal mathematical collaborations, though polymath1 has been particularly chaotic in this regard.)

While this has been working reasonably well so far, the mix of all the various tools has been somewhat clunky, to put it charitably, and it would be good to have a more integrated online framework to do all of these things seamlessly; currently there seem to be software that achieves various subsets of what one would need for this, but not all. (This point has also recently been made at the Secret Blogging Seminar.)

Yesterday, though, Google Australia unveiled a new collaborative software platform called “Google Wave” which incorporates many of these features already, and looks flexible enough to incorporate them all eventually. (Full disclosure: my brother is one of the software engineers for this project.) It’s nowhere near ready for release yet – it’s still in the development phase – but with the right type of support for things like LaTeX, this could be an extremely useful platform for mathematical collaboration (including the more traditional type of collaboration with just a handful of authors).

There is a demo for the product below. It’s 80 minutes long, and aimed more at software developers than at end users, but I found it quite interesting, and worth watching through to the end:

[*Update*, May 30: Apparently a LaTeX renderer is already being developed as an API extension to Google Wave; here is a very preliminary screenshot. Also, a shorter explanation of what Google Wave is and does can be found here. ]

[*Update*, Jun 7: Another review can be found here.]

This weekend I was in Washington, D.C., for the annual meeting of the National Academy of Sciences. Among the various events at this meeting was an address to the Academy by President Obama this morning on several major science and education policy initiatives, including some already announced in the economic stimulus package and draft federal budget, and some carried over from the previous administration. (I myself missed the address, though, as I had to return back to LA to teach.) Among the initiatives stated were the creation of an Advanced Research Projects Agency for Energy (ARPA-E), modeled on DARPA (and recommended by the NAS); a significant increase in funding to the NSF and related agencies (which was committed to by the Bush administration, but not yet implemented; this is distinct from the one-time funding from the stimulus package discussed in this previous post), leading in particular to a tripling in the number of NSF graduate research fellowships; and a “race to the top” fund administered by the Department of Education to provide incentives for states to improve their quality of maths and science education, among other goals. Some of these initiatives may not survive the budgetary process, of course, but it does seem that there is both symbolic and substantive support for science and education at the federal level.

Here are the video, audio, and transcript of the talk.

[*Update*, Apr 28: Another event at the meeting is the announcement of the new membership of the Academy for 2009. In mathematics, the new members include Alice Chang, Percy Deift, John Morgan, and Gilbert Strang; congratulations to all four, of course.]

Now that the project to upgrade my old multiple choice applet to a more modern and collaborative format is underway (see this server-side demo and this javascript/wiki demo, as well as the discussion here), I thought it would be a good time to collect my own personal opinions and thoughts regarding how multiple choice quizzes are currently used in teaching mathematics, and on the potential ways they could be used in the future. The short version of my opinions is that multiple choice quizzes have significant limitations when used in the traditional classroom setting, but have a lot of interesting and underexplored potential when used as a self-assessment tool.

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.]

Prodded by several comments, I have finally decided to write up some my thoughts on time management here. I actually have been drafting something about this subject for a while, but I soon realised that my own experience with time management is still very much a work in progress (you should see my backlog of papers that need writing up) and I don’t yet have a coherent or definitive philosophy on this topic (other than my advice on writing papers, for instance my page on rapid prototyping). Also, I can only talk about my own personal experiences, which probably do not generalise to all personality types or work situations, though perhaps readers may wish to contribute their own thoughts, experiences, or suggestions in the comments here. [I should also add that I don't always follow my own advice on these matters, often to my own regret.]

I can maybe make some unorganised comments, though. Firstly, I am very lucky to have some excellent collaborators who put a lot of effort into our joint papers; many of the papers appearing recently on this blog, for instance, were to a large extent handled by co-authors. Generally, I find that papers written in collaboration take longer than singly-authored papers, but the net effort expended per author is significantly less (and the quality of writing higher). Also, I find that I can work on many joint papers in parallel (since the ball is often in another co-author’s court, or is pending some other development), but only on one single-authored paper at a time.

[For reasons having to do with the academic calendar, many more of these papers get finished during the summer than any other time of year, but many of these projects have actually been gestating for quite some time. (There should be a joint paper appearing shortly which we have been working on for about three or four years, for instance; and I have been thinking about the global regularity problem for wave maps problem on and off (mostly off) since about 2000.) So a paper being released every week does not actually correspond to a week being the time needed to conceive and then write up a paper; there is in fact quite a long pipeline of development which mostly happens out of public view.]

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.]

The newly elected Australian Prime Minister, Kevin Rudd, apologises to the “Stolen Generation” of indigenous Australians for past government policies.

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.]

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.]

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