Not Even Wrong

John Baez’s latest This Week’s Finds is out. As in other recent issues, he starts with some of the most fantastic astronomical pictures around. He also links to his recent non-technical talk Fundamental Physics: Where We Stand Today, which also has fantastic pictures. In the talk he describes how, since the 80s, “many physicists feel stuck”, and “continue to make predictions but they are usually wrong or not yet testable. This has led to a feeling of malaise. Why are they failing?” He partially answers this question with

But when their theories made incorrect or untestable predictions, many theorists failed to rethink their position. It is difficult to publicly retract bold claims. Instead, they focus more and more attention on the mathematical elegance of their theories… some becoming mathematicians in disguise. (There are worse fates).

Someone who was at the talk reports that afterwards Carlo Rovelli asked Baez “whether what he had just presented didn’t imply that the theoretical physics of the last 25 years was ‘junk'”, and that Baez “replied after some hesitation ‘You said it'”.

A physicist who has been concerned for quite a while about the sociological changes in how particle theory is done and the ever more critical situation that the field finds itself in is theorist Bert Schroer. His specialty is in the area of algebraic approaches to QFT, especially conformally invariant ones. More than a decade ago he was writing review articles on QFT well-worth reading that included warnings about what has been going on. For some examples, see his Reminiscences about Many Pitfalls and Some Successes of QFT Within the Last Three Decades and Motivations and Physical Aims of Algebraic QFT.

Schroer has just posted three new articles on the arXiv. One of these is entitled String theory and the crisis in particle physics and is well worth reading if you have any interest in the ongoing controversy over string theory. Schroer has many interesting points to make on the subject, and one of his main concerns is that a great deal of knowledge developed about QFT during the last century may be effectively lost as the training of young theorists focuses on string theory. This article has already drawn Lubos Motl’s trademark rant accusing anyone skeptical about string theory of being an incompetent crackpot.

The second of his new articles is called Physicists in times of war and begins with comments on the Iraq war and Schroer’s profound disappointment at the refusal of Witten and others to join him in a public campaign against the war before it began. The second part of the article tells the story of Pascual Jordan, one of the founders of quantum mechanics who joined the Nazi party. Schroer’s politics are diametrically opposite to those of Jordan, but he is highly sympathetic to Jordan’s scientific point of view, from the earliest years of quantum mechanics, that it is necessary to think about quantum systems in a way which doesn’t depend on starting with a classical Lagrangian and “quantizing”.

The last of Schroer’s new articles should appear on hep-th tonight and is entitled Positivity and Integrability. It tells some of the history of the QFT group at the Free University in Berlin and has a lot of interesting things to say about reflection positivity and the Euclidean approach to quantum field theory.

Update: I haven’t heard anything at all back from the arXiv about the trackback issue, but just noticed that trackbacks to the two recent Schroer articles mentioned here have appeared. The ways of the arXiv are highly mysterious….

Update: Baez has a clarification here of his response to Rovelli.

This week is the second anniversary of this weblog, so perhaps a good moment for some reflections on what has been happening over the past two years.

In many ways, the weblog has been successful far beyond my wildest dreams. My original expectation was that there would be a handful of people with similar interests who would regularly read it, and it would be quite a success if I ended up with a couple hundred readers. I don’t have completely accurate recent statistics, but recently each day at least several thousand people are checking up to see what is going on here. This is quite gratifying, and makes the significant amount of effort and time I’ve been putting into this seem worthwhile. It has been interesting to note from looking at some other blogger’s publication records that starting an active weblog seems to correspond to starting to write many fewer papers. My one regret is that the time spent on this has definitely taken away from time that could be devoted to finishing and writing up various research projects. In the future I hope to find a better balance on this issue.

One of the main topics covered on this blog, and by far the most controversial, is the ongoing story about string theory and its dominance of theoretical high energy physics. The public perception of string theory seems to me to have changed significantly recently, as more and more science journalists have started to realize that things are not going well. Many of them have moved from a stance of uncritical acceptance of the claims of string theorists to a more skeptical and balanced view of the subject. The kind of overhyped popular string theory article that was a staple for 20 years is increasingly unlikely to be written by professional science journalists. Such things now occur most often in places like university press releases, authored by people with no experience in the subject.

I’d like to think I had something to do with this, but there are much larger forces at work. The field of string theory has suffered a remarkable intellectual collapse, one that is not just a matter of opinion, but can be quantified in various ways. For many years Michael Peskin has written up a discussion of the yearly list of top cited HEP articles. I wrote up postings discussing the 2003 and 2004 lists. By 2004 there were only two post-1999 string theory papers among the list of 50 most heavily cited (the early 2002 Berenstein et. al. PP waves paper, and the early 2003 KKLT paper), and Peskin seems to have stopped writing up a discussion of the list, possibly because there was virtually nothing new to discuss. SPIRES has not yet produced a 2005 list and I don’t know if they ever intend to, but from some data gathered at physicsforums.com it would appear that the only two string theory papers likely to have accumulated the 150 or so citations needed to make the top 50 in 2005 are exactly the same two as in 2004. The subject has come to nearly a dead stop, and that rather than the complaints of its critics is behind the sense of crisis felt by many of its practitioners.

The panel discussion at Strings 2005 in Toronto was rather remarkable. For the first time, members of the audience started to raise real questions about what was going on in the subject and the panel members had difficulty in putting a positive face on the situation. It will be interesting to see if a similar discussion occurs at Strings 2006 this summer in Beijing.

The two post 2000 papers that are widely cited reflect the two main topics that string theorists are still working on. One is AdS/CFT, which many, many people work on since it is the best thing to have come out of the string theory project. There doesn’t however seem to be much significant progress in this area. The second paper, by KKLT, is the one that really launched the whole landscape business. The fact that it is the most recent hot area of activity in string theory is something that even most string theorists find very disturbing. Over the last couple years, the original implausible hopes that something could be gotten out of the Landscape have been pretty convincingly crushed. Leading figures in the field have abandoned the Landscape and moved out into the swampland of theories that have nothing to do with the real world and may or may not be low energy limits of a string theory. It remains very unclear what the point of this is.

The most active string theory blogs are becoming ever more bizarre, with increasingly strange behavior of all sorts from Lubos Motl, and Jacques Distler following the lead of others into the swampland while firmly sticking to the idea that my criticisms of string theory are some sort of illegitimate crackpotism. While most string theorists are well aware of what bad shape the field is in and casting about for something new to do, the true believers are exhibiting something more and more approaching religious fanaticism.

Unfortunately, leading figures in particle theory show no signs of being willing to publicly address the increasingly disturbing state of the subject. Part of my problem with the arXiv is the feeling of many that I do not have the stature in the community necessary to justify being allowed to make the kind of critical comments I have been making publicly. I’m willing to agree with this point, but it remains unfortunately true that those whose responsibility it is are doing little to address the situation. The whole field of particle theory is becoming increasingly damaged by these problems, and only one aspect of this is the problem of public perceptions, which is going to get a lot worse before it gets better.

I have no idea where this story is going next. The general attitude seems to be to hunker down for the next few years, try and wait out the crisis and hope that LHC results will save everything. This doesn’t seem to me to be the right way to address the serious problems that are all too obvious right now.

Update: Some anonymous person really has too much time on their hands. But I’m honored.

Update: One or more people definitely have too much time on their hands. Besides the Not Even Wrong parody mentioned above, there’s another one, and also Cosmic Variance and Lubos Motley’s Stringy Climate Theories. This last one informs us that

Recent fake blogs have brought shame to the Internet:

(1) http://motls.blogspot.com pokes fun at Dr Lubos Motl, by posting a mixture of insane climate drivel, interspersed with attacks on theoretical physicists. I can reveal it is fake.

Following up on the spectacular first year of data reported by the WMAP experiment in February 2003, results of analysis of the next year’s data were initially planned to be released a year later. The release of this data has been repeatedly delayed; for speculation about why, see here and here.

Over the last two years there have been a large number of scheduled colloquia by WMAP scientists that have been cancelled at the last moment. One relatively recent one was an astronomy colloquium at Caltech by Gary Hinshaw with the title “New Results from WMAP” that was initially scheduled for January 4, but was cancelled and now is scheduled for March 22.

From March 23-25 the new Center for Cosmology at UC Irvine will be hosting a workshop on Fundamental Physics With Cosmic Microwave Background Radiation. On the 23rd four WMAP team members are scheduled to speak with titles: “WMAP 0, WMAP I, WMAP II, and WMAP III.”

Over at CosmoCoffee (where I first noticed this), Alessandro Mechiorri is spreading the rumor that data will be released next week, on March 14. There’s also discussion of this at the Bad Astronomy and Universe Today Forum. So, looks to me like it’s maybe next week, and if not, almost certainly the week after.

Update: More news about the state of WMAP from Urbano Franca here.

Update: Looks like it definitely will be very soon now, possibly some time this week. The WMAP Mission Status page says:

Second Data Release

While the first-year results were based mainly on temperature measurements, the continued mission operations are now primarily focused on the much weaker polarized signals – an invaluable “stretch” goal of the extended mission. Analyses of these weaker signals are more difficult. The calibration and systematic error analyses have been completed, and the data files have been documented for use by researchers. For an overview see RESULTS.

This last link is to a New Three Year Results page which right now just says:

Stay tuned for the release of the most recent results from the Wilkinson Microwave Anisotropy Probe (WMAP). Very soon now….

Update: It’s official, the release will be on Thursday. Here’s the announcement:

Dear colleagues:

Sincerely,
Gary Hinshaw
NASA/GSFC
for the Legacy Archive for Microwave Background Data Analysis (LAMBDA)

Several blogs today have discussions of the arXiv trackback issue, mostly spawned by Sean Carroll’s posting on the topic.

Jacques Distler has a posting where he explains that the arXiv has instituted an ill-defined “active researcher” criterion for allowing trackbacks to blogs and that:
Peter Woit’s publication record doesn’t put him anywhere close to “active researcher status”
I’ve written an extensive comment over there about why I happen to think I am an active researcher and the evident absurdity of the idea the Jacques Distler is capable of making a rational evaluation of this question.

More discussion of this is at Chad Orzel’s Uncertain Principles, and Georg von Hippel’s Life on the Lattice.

Update: Yet more on trackbackgate from Lieven le Bruyn , Evan Goer and Capitalist Imperialist Pig. The first has the useful suggestion of using Technorati to automatically generate complete sets of links to discussions of arXiv papers on blogs. The second reminds me why it’s a bad idea to hit the “submit” button when you’re extremely pissed off.

Update: In discussion over at Jacques’s blog about what an “active researcher” is, the dicey issue has arisen that Jacques actually doesn’t seem to be one himself. One commenter has suggested that this whole issue could easily be resolved by just picking a definition of the term, noting that

Few will object to defining a minimallly active researcher as one who has posted an average of 2 papers per year to arXiv over the last 3 years.

Jacques comes no where near qualifying as “minimally active”, since he has only posted 3 papers to the arXiv during the last 3 years.

Personally I don’t think the 2 paper/year criterion is very good. It doesn’t account for length of papers, or that they may be the product of a collaboration, so the author in question is only responsible for a fraction of the paper. A more accurate measure would be based on counting pages of papers and dividing by number of authors. Under this measure, over the last four years Jacques’s research productivity looks like this:

2002: 9.3 pages
2003: 3 pages
2004: 0 pages
2005: 23.7 pages

for an average of 9 pages/year (this count is being a bit charitable, since 15 of the 2005 pages are from a “landscape” paper that may not even be science).

Jacques has made it clear that a certain author for whom this number is 14 pages/year is not “anywhere close to ‘active researcher’ status”, so I guess he is even farther away from qualifying as an “active researcher”.

Always seems surprising the way people living in glass houses like to throw stones…

Update: This particular food-fight has even been written up for the on-line component of Discover Magazine.

Update: A couple more people weigh in on this, Jim Hu and Alejandro Satz.

Update: I haven’t heard anything at all from anyone associated with the arXiv, but a couple trackbacks to one of my recent postings have appeared, so there seems to have been some sort of change of policy there.

Harvard mathematician Barry Mazur has many new things up on his web-site. These include an expository article on motives (this via David Corfield), and a foreword to a forthcoming popular book called Fearless Symmetry : Exposing the Hidden Patterns of Numbers. This book looks to be the first popular book to deal with the modern use of group representations in number theory, explaining what reciprocity laws are and a bit about the Langlands program.

The concept of a motive and that of using representations of Galois groups constructed using things like motives are two of the most important ideas in modern number theory. Some of the latest developments in this field concern extensions of the Langlands program involving p-adic modular forms. Mazur and Buzzard are teaching courses on this topic, and Mazur has put some lecture notes up on his course web-site. These courses are part of a special semester on Eigenvarieties at Harvard.

Mazur also has a revised version of his expository piece on category theory, a short piece about Serge Lang, and some very non-basic notes for a “Basic Notions” seminar.

Nature has a short article entitled Physicists told to confront those big questions about the Foundational Questions Institute call for proposals. There’s a very positive quote about this from Lee Smolin, who is on the advisory board, but also a much more skeptical one from Paul Steinhardt: “Metaphysics is running rampant through string theory and cosmology,” he says. “I would like to see things go a little bit in the other direction.”

Kimball Martin’s web-site of Exceptional MathReviews includes one by Robert Oeckl about a paper of the Bogdanovs. For more about them see here, here, here, and here. Remarkably, they seem to have some support from at least one string theorist.

Via Bitch Ph.D., perhaps the strangest math-related web-site I’ve ever seen.

The High Energy Physics Advisory Panel (HEPAP) is meeting today and tomorrow in Washington. Presentations there will include one from Bush’s science advisor, John Marburger, and should be available on-line soon.

This weekend, the Mathematical Sciences Research Institute (MSRI) will be dedicating its new building, named after Shiing-Shen Chern. As part of the festivities, Roger Penrose will be giving talks, including a public lecture Sunday on Fashion, Faith and Fantasy in modern theoretical physics.

The second LHC Olympics were recently held at CERN and the talks are available on-line. This is a rather unusual exercise designed to get string theorists and other not-so-hardcore phenomenologists involved in analyzing simulated LHC data. There seem to me to be two big problems with this. First of all, there are no backgrounds in this simulated data, and understanding these backgrounds is going to be the main problem with the LHC data for quite a while. It will be the experimenters who will have to do this, and they may need help from theorists, but help of a very different nature than what this exercise is aiming at. Secondly, once backgrounds are understood and potential signals are extracted, I doubt that the LHC experimenters will be releasing the kind of data simulated here for use by theorists. I suspect they’ll be doing the kind of analysis going on at the LHC Olympics themselves and releasing the results as papers under their own names. For more about this, see postings by Lubos here and here. The first of these drew the following comment from a European phenomenologist:

Phenomenology has been always been strong in Europe, hundreds of ppl work in this field since decades, and most consider this contest as child’s play. Guess why no European team took part in this activity, right within a truly European institution which has scores of local phenomenologists? It is a bit like if a few phenomenologists decide to learn string theory and organize a contest in Princeton about who can build the best string model….

While this exercise is unrealistic, it may at least clarify various issues about how testable certain specific scenarios really will be at the LHC.

The latest Seed Magazine has some interesting articles. One about mathematical proof discusses problems with proofs in mathematics that may be too complicated to be properly refereed, especially the recent work by Thomas Hales on the Kepler conjecture. It ends with a depressingly silly comment by Keith Devlin:

I see a parallel between the uncertainty of these proofs and developments in physics like string theory, where we’re developing mathematical theories of matter that may forever remain elusive to experimental verification.

This is the same kind of foolishness as the comment that “physicists may have to rethink what it means for a theory to explain experimental data” because of string theory (see here).

Another Seed article that has gotten a lot of attention because of it’s topic is one called Getting Physical about physicists and sex. See commentary here, here and here. This last link is to Jennifer Ouellette’s new blog Cocktail Party Physics, which is of independent interest.

Michael Douglas has written up his talk at the recent Solvay conference, with the title Understanding the Landscape. For previous postings about this conference, see here, here, and here.

Douglas’s article is mainly a series of excuses for why string theory can’t predict anything. He begins with an historical analogy, comparing the present state of string theory to that of quantum mechanics in the period 1913-1926, and the Bohr model of the hydrogen atom to N=4 supersymmetric YM and AdS/CFT. This kind of analogy has some rather obvious problems: it took 13 years to get from the Bohr model to the complete theory of QM, whereas the idea of string unification has been around for about 30 years, with not the slightest sign of success. More importantly, the Bohr model of the hydrogen atom gave a fairly accurate prediction of the spectrum of the hydrogen atom, so it was clear that there was something very right about it. On the other hand, N=4 supersymmetry YM doesn’t predict anything that corresponds to the real world. In a footnote, Douglas writes:

A similar analogy was made by David Gross in talks given around 2000. However, to judge from his talk here, he now has serious reservations about it.

but I’m not sure what reservations of Gross this refers to.

Douglas’s second analogy is a “chemical” analogy, basically pointing to the fact that deriving bulk properties of solids from the underlying many-particle Schrodinger equation is difficult if not impossible. Again, this isn’t a very good analogy. The problem isn’t that you have a simple theory whose ground state is hard to identify because of the numbers of degrees of freedom, like in condensed matter physics. The problem instead is that the ground state of the superstring doesn’t look like the real world. Douglas describes the current situation as:

Perhaps all this is a nightmare from which we will awake, the history of Kekule’s dream being repeated as farce.

He goes on to give the standard argument for the landscape, referring to it by the novel name of the Weinberg-Banks-Abbott-Brown-Teitelboim-Bousso-Polchinski et. al. solution to the cosmological constant problem, but notes that:

On further developing these analogies, one realizes that we do not know even the most basic organizing principles of the stringy landscape.

and proceeds to discuss a little bit two topics that he hopes might be related to this problem, but I don’t see any evidence for this. One topic is an abstract proposal for a metric on the “space of all CFTs”, the other is the classification of D-branes on a Calabi-Yau in terms of a derived category.

He goes on to discuss his recent work with Denef on computational complexity, which indicates that even if our universe corresponds to some local minimum in the landscape, there is no hope of ever identifying which one it is and actually computing anything about the real world. In his concluding section, he admits that there is no evidence of any simple structure in the landscape, and argues that maybe this is just the way the world is:

Still, our role as physicists is not to hope that one or the other picture turns out to be more correct, but to find the evidence from experiment and theory which will show us which if any of our present ideas are correct.

The problem with his invocation of the role of experimental evidence is that he has just finished making an excellent case that there is no hope at all of ever getting any such evidence for string theory. He seems to have completely abandoned without comment his project of the last few years of counting vacua in hopes of making statistical predictions, and is left with not a single idea about how one can ever hope to get a prediction of any kind out of this framework. In this kind of circumstance, standard scientific practice is to acknowledge that this is a failed project and go on to something else. Douglas not only refuses to acknowledge the failure of string theory, he doesn’t anywhere even mention the possibililty that the underlying idea might be wrong.

Yesterday’s hep-th preprints included another landscape one, Probabilities in the Landscape by Alexander Vilenkin. Vilenkin shows no more evidence of having a viable way of ever making a physical prediction than does Douglas, but like Douglas invokes experimental confirmation at the end of his paper, then closes with one prediction that is sure to be accurate:

It seems safe to predict that we will hear more on this subject in the future.

For some more entertaining reading, take a look at A Comment on Emergent Gravity by Waldyr A. Rodrigues Jr. Rodrigues says that he gave as an exercise to his students to find the errors in Jack Sarfatti’s recent arXiv posting Emergent Gravity. Sarfatti had been blocked for many years from posting on the arXiv, but the arXiv moderators recently relented, perhaps because this paper includes a section at the end about the landscape. Susskind’s recent book is one of only two references in the paper. Sarfatti’s paper has gone through six drafts, three of which are on the arXiv, and the latest of which incorporates some of the objections from Rodrigues. Rodrigues however concludes his paper thus:

Sarfatti’s paper we regret to say, is unfortunately a potpourri of nonsense Mathematics. The fact that he found endorsers which permitted him to put his article in the arXiv is a preoccupying fact. Indeed, the incident shows that endorsers did not pay attention to what they read, or worse, that there are a lot of people with almost null mathematical knowledge publishing Physics papers replete of nonsense Mathematics…

A careful reading of [Sarfatti’s paper] shows that his hypotheses are completely ad hoc assumptions, since in our view no arguments from Physics or Mathematics are given for them. Summing up, we must say that Sarfatti’s claim to have deduced Einstein’s equations as an emergent phenomena is a typical example of self delusion and wishful thinking.

Sarfatti will be giving the closing talk at the 22nd Pacific Coast Gravity Meeting, to be held this coming weekend at the KITP in Santa Barbara.

Mathematical Reviews is a publication of the American Mathematics Society that provides capsule reviews of essentially every mathematics research paper that is published. It has been in operation since 1940, and in recent years the entire database has been on-line, with the name MathSciNet. Some of the reviews are rather entertaining in one way or another, and the availability of this database has led to a new form of diversion among mathematicians: searching on promising words (e.g. “plagiarism”) to see what turns up. My colleague Kimball Martin has put together a new web-page entitled Exceptional MathReviews with links to the best reviews he has heard about.

One of the most famous such reviews turns out to be apocryphal. In the days before the searchable database, I had heard it claimed that one Math Review contained the following devastating evaluation: “This paper fills a much-needed gap in the literature.” It turns out that this isn’t actually true. For the real story and more about Math Reviews, see an article from the 1997 Notices of the AMS.

After more than three months of effort to try and get an answer about this, I’ve finally heard officially from the arXiv that trackbacks to my weblog are currently not being allowed by the moderators. I’m sending the following message protesting this to members of the arXiv advisory board.

To the arXiv advisory board:

Peter Woit
Department of Mathematics
Columbia University
212-854-2642

Update: Sean Carroll’s posting about this has finally shaken loose some indication of what argument was used to disallow links to my blog at the arXiv. For details, see the comment section of his posting.

Update: Lubos Motl has really outdone himself with his latest lunatic ranting about this blog. Note that, besides the blogs run by arXiv moderator Jacques Distler, Lubos’s is one of only a couple particle theory related blogs that the arXiv moderators allow trackbacks to. That trackbacks to this blog are censored, but allowed to Lubos’s (and almost no others not belonging to an arXiv moderator) should be more evidence than anyone needs that there is a serious problem with the arXiv moderation system, and it is due to the string fanaticism of the moderators.

The new Center for the Topology and Quantization of Moduli Spaces (CTQM) at Aarhus University wins my award for the most specialized pure mathematics institute. It will be hosting an opening symposium in a couple weeks featuring several talks that look interesting. If one is going to choose a specialized subject, this is an excellent one. Over the last couple decades the study of the moduli space of curves and of the moduli space of flat connections on a bundle over a surface has led to the discovery of many previously unsuspected relations between different parts of mathematics and between mathematics and physics. The fact that this subject is so fruitful remains somewhat of a mystery, and there is undoubtedly much more to be learned.

The National Academy of Sciences EPP 2010 committee should soon be producing a report with a 15 year plan for the future of high energy physics in the U.S. At the last meeting of the group last month Fermilab director Pier Oddone gave a presentation, focusing on opportunities in neutrino physics, strategy concerning the ILC, and the future of Fermilab.

Last week there was a conference on Particle Physics at the Verge of Discovery at Aspen. Lot of interesting talks on experimental particle physics. For an overview, see the summary talk by Paul Grannis.

The Templeton funded Foundational Questions Institute (FQXi) has announced that it will be publishing its inaugural request for proposals on Monday. This organization is led by Max Tegmark, who will be here at Columbia that day giving a physics department colloquium on From Derision Cosmology to Precision Cosmology. Unfortunately I have to be away that day and will miss the talk although I would have liked to attend it.

Steve Hsu, a physicist with a serious interest in economics, writes:

You might think science is a weighing machine, with experiments determining which theories survive and which ones perish. Healthy sciences certainly are weighing machines, and the imminence of weighing forces honesty in the voting. However, in particle physics the timescale over which voting is superseded by weighing has become decades — the length of a person’s entire scientific career. We will very likely (barring something amazing at the LHC, like the discovery of mini-black holes) have the first generation of string theorists retiring soon with absolutely no experimental tests of their *lifetime* of work. Nevertheless, some have been lavishly rewarded by the academic market for their contributions.

Scott Aaronson describes his field of computational complexity theory as “quantitative theology”, and goes on to note:

Incidentally, it’s ironic that some people derisively refer to string theory as “recreational mathematical theology.” String theory has to earn the status of mathematical theology — right now it’s merely physics! A good place for string theorists to start their theological training is this recent paper by Denef and Douglas.

Lee Smolin is giving a course on background independent quantum theories of gravity at the Perimeter Institute, with the lectures available online.

David Corfield has an interesting posting on research programs in mathematics. It includes links to various things from Ronald Brown including a new paper on Ehresmann’s work on groupoids, and his web-page on “Higher Dimensional Group Theory”. Among other things worth reading at Brown’s site is his account of the origins of Grothendieck’s “Pursuing Stacks”.

Corfield also points to an excellent list of problems in homotopy theory from Mark Hovey. Hovey starts off with the comment

The biggest problem, in my opinion, is to come up with a specific vision of where homotopy theory should go, analogous to the Weil conjectures in algebraic geometry or the Ravenel conjectures in our field in the late 70s. You can’t win the Fields Medal without a Fields Medal-winning problem; Deligne would not be DELIGNE without the Weil conjectures and Mike Hopkins would not be MIKE HOPKINS without the Ravenel conjectures.

I first met Mike Hopkins at a conference in Guanajuato around 1990, and he made a big impression on me. One thing that most impressed me (besides his joking comment that he went into topology because it was a field full of hard-drinking and living guys who got into gun-fights (this last part was a reference to Dennis Sullivan)), was the mathematical ambition he demonstrated. He said that he had up till then made his reputation proving other people’s conjectures, but now wanted to start making his own. Mike definitely followed through on this, since a sizable number of Hovey’s problems are inspired by him. His talk on elliptic cohomology in Guanajuato was a revelation, and he has over the years continued to work in that area, coming up with dramatic new ways of thinking about the subject.

Update: There is an extensive discussion of the Smolin lectures at Christine Dantas’s website.