Not Even Wrong

The last posting here was about an unusually collaborative effort among mathematicians, whereas this one is about the opposite, an unusually contentious situation surrounding important recent mathematical progress.

What’s at issue is the proof of what has become known as the “Yau-Tian-Donaldson” conjecture, which describes when compact Kähler manifolds with positive first Chern class have a Kähler-Einstein metric. This is analogous to the Calabi conjecture, which deals with the case of vanishing first Chern class. Progress by Donaldson on this was first mentioned on this blog here (based on his talk at Atiyah’s 80th birthday conference in 2009). Last fall a proof of the conjecture was announced by Chen-Donaldson-Sun, with an independent claim for a proof by Gang Tian, see here. I wrote a bit about this last winter here, after the details appeared of the Chen-Donaldson-Sun proof, and that posting gives some links to expository articles about the subject.

I had heard that there were complaints about Tian’s behavior in this story, including claims that he did not have a complete proof of the conjecture and was not acknowledging his use of ideas from Chen-Donaldson-Sun. Recently this controversy has become public, with Chen-Donaldson-Sun deciding to put out a document (linked to from Donaldson’s website) that challenges Tian’s claims to have an independent proof. The introduction includes:

Gang Tian has made claims to credit for these results. The purpose of this document is to rebut these claims on the grounds of originality, priority and correctness of the mathematical arguments. We acknowledge Tian’s many contributions to this field in the past and, partly for this reason, we have avoided raising our objections publicly over the last 15 months, but it seems now that this is the course we have to take in order to document the facts. In addition, this seems to us the responsible action to take and one we owe to our colleagues, especially those affected by these developments.

I should make it clear I’m no expert on this mathematics, so ill-equipped to judge many of the technical claims being made. The Chen-Donaldson-Sun document is giving one side of a complicated story, so it would be useful to have Tian’s side for comparison, but I have no idea if he intends to respond.

On a more positive note, perhaps this controversy will not interfere much with future progress in this area, as Donaldson and Tian are jointly organizing a Spring 2016 workshop on this topic at MSRI.

Update: I hear from Tian that he has recently written a response to the Chen-Donaldson-Sun document, which is available here, and he may at some point write some more about this. Anyone who has read the CDS side of this should also take a look at what Tian has to say in response.

There’s a new paper out on the arXiv last night, Small gaps between primes, by James Maynard, which brings the bound on the size of gaps between primes down to 600. This uses some new methods, beating out the Polymath8 project, which has been improving Zhang’s original bound of 70,000,000, getting it down to 4680.

To follow the Polymath8 project, the place to look is Terence Tao’s blog, here. They’re working on a paper, with the current draft version available here. This is a remarkable collaborative project bringing together a sizable group of mathematicians in an unusual way.

For more about this, see this expository article by Andrew Granville, which is pre-Maynard. At Quanta magazine, Erica Klarreich has an excellent long popular article telling the story to date, including that of Maynard’s new result.

Philip Anderson’s 90th birthday is coming up next month, and Princeton will host a workshop commemorating the event. Witten and Wilczek will give talks on the Anderson-Higgs mechanism, for which Anderson recently was not awarded a Nobel Prize (for the history of this, more here).

Princeton condensed matter theorist Shivaji Sondhi has an article here about the role of Anderson in the Higgs story, rightly emphasizing “the remarkable intellectual unity of modern physics.”

Many have speculated that a reason for Anderson not getting a piece of this year’s Nobel Prize was his public opposition to the SSC project back in the 1980s. He was far from the only physicist opposing the project, since there was widespread concern that in the Reagan-era environment of budget-cutting, devoting large sums to an HEP project would mean reduced funding for the rest of physics. Anderson has a letter in the latest APS News about this. For a summary of his concerns about the SSC, see this opinion piece from 1987.

One thing that exacerbated conflict between HEP physicists and others at the time were claims about “spin-offs” from building large accelerators, with some people claiming that HEP physics was responsible for MRI machines. Anderson recalls:

As I was leaving the committee room behind Steve Weinberg, the particle physicist who had testified for the SSC, one of the senators accosted him and effusively thanked him for his role in the development of MRI, which had been instrumental in treatment of a relative. Since close friends and I had been responsible for most of the basic research underlying MRI’s superconductiing magnets, this was a bit of a bitter pill for me to swallow.

For Weinberg’s point of view on this, see here, where he writes:

The claim of elementary-particle physicists to be leading the exploration of the reductionist frontier has at times produced resentment among condensed-matter physicists. (This was not helped by a distinguished particle theorist, who was fond of referring to condensed-matter physics as “squalid state physics”.) This resentment surfaced during the debate over the funding of the Superconducting Super Collider (SSC). I remember that Phil Anderson and I testified in the same Senate committee hearing on the issue, he against the SSC and I for it. His testimony was so scrupulously honest that I think it helped the SSC more than it hurt it. What really did hurt was a statement opposing the SSC by a condensed-matter physicist who happened at the time to be the president of the American Physical Society.

In recent years the hot topic in the string theory end of HEP theory has become “AdS/CMT”, the attempt to apply AdS/CFT ideas to condensed matter theory models. Anderson at nearly 90 is still dealing with HEP hype, see this from the April issue of Physics Today.

• Mathematician Sasha Beilinson has a letter to the editor in this month’s AMS Notices calling on the AMS to sever all ties with the NSA (right now it manages NSA grants, and runs ads from the NSA in the Notices). Beilinson compares the NSA to the KGB of the former Soviet Union. For discussion of the Beilinson letter, see here.
• Beijing now has a Center for Future High Energy Physics, with Director the ubiquitous Nima Arkani-Hamed. The inaugural conference of the Center will be next month, on Future High Energy Circular Colliders. Nature has an article on the topic this week, Physicists plan to build a bigger LHC, about proposals to build a 100 TeV pp collider, with a possible electron-positron collider Higgs factory using the same tunnel. For the latest on TLEP, the proposal for such a Higgs factory at CERN, see here.
• I was in London a few days too early for this, but this week the Science Museum there celebrated the opening of its exhibition about the LHC with an event featuring Stephen Hawking. The Guardian has a report here. Hawking seems to think the LHC may see evidence for M-theory:
  

  “There is still hope that we see the first evidence for M-theory at the LHC particle accelerator in Geneva,” said Hawking. “From an M-theory perspective, the collider only probes low energies, but we might be lucky and see a weaker signal of fundamental theory, such as supersymmetry.

  “I think the discovery of supersymmetric partners for the known particles would revolutionise our understanding of the universe.”

  As is often the case in stories like this, the wording about evidence for string/M-theory is rather odd. We’re told:

  As yet there has been no incontrovertible experimental evidence to show that M-theory is correct.

  but “no incontrovertible experimental evidence” is a peculiar way of phrasing “absolutely zero experimental evidence of any kind whatsoever.”

• For an interview with Shiraz Minwalla, one of the winners of this year’s Milner prizes for young researchers, see here.
• Edward Frenkel’s new book, Love and Math, has been getting quite a few good reviews, with the latest from Jim Holt in the New York Review of Books.
• Finally, your best source of fascinating mathematically-related graphics is surely going to be John Baez’s new Visual Insight blog.

Update: One more. The Perimeter Institute announced yesterday the funding (half provided by the Krembil Foundation) of two new chairs in theoretical physics. These will be held by two young mathematical physicists: Kevin Costello and Davide Gaiotto. As far as I know, the hiring of Costello away from Northwestern is the first time Perimeter has hired someone with a pure mathematics background. It’s good to see them moving in this direction.

Update: More about the new Perimeter chairs here. The article discusses the fact that this is a change of direction towards mathematics:

The choice is a strategic shift and a gamble for the 12-year-old institute, which is in a global tug-of-war for talent and looking to grow its profile as a centre for high-level thinking on some of the deepest questions in the universe.

Although math is the working language of physics and equations cram every available blackboard at Perimeter, Dr. Costello’s hiring, to be announced Saturday, will mark the first time the institute has sought a pure mathematician for its faculty….

“There’s something about the situation in physics today which makes it especially important to bring in high-powered mathematics,” said Neil Turok, the institute’s director.

I’m now back to regular internet access, in London for a few days after a trip to East Africa, where I managed to see the November 3 total solar eclipse through light clouds from a location in Northern Uganda. From checking various news sources, it looks like the main pieces of HEP-related news that I missed weren’t very surprising:

• The LUX experiment reported stronger limits on WIMP dark matter, ruling out various claims for evidence of such dark matter particles at relatively low mass. For more about this, good sources are Resonaances, Matt Strassler, and Tommaso Dorigo.
• The $3 million Fundamental Physics Prize as usual identifies “Fundamental Physics” with string theory, with the announcement that the nominees for the 2014 prize are 5 string theorists (Polchinski, Green/Schwarz, and Strominger/Vafa). I confess that I can’t figure out exactly how this prize process is supposed to work. The announcement says that the nominees get a “Physics Frontiers Prize”, a shot at the $3 million, and
  

  Those who do not win it will each receive $300,000 and will automatically be re-nominated for the next 5 years.

  What I don’t understand is that Polchinski already got such a nomination and prize last year (and the $300,000 consolation prize for not getting the $3 million). It seems that he is getting another identical prize this year, with another $300,000 or $3 million. On the other hand, the only non-string theorists ever to win this prize (last year’s condensed matter group Kane/Molenkamp/Zhang) didn’t get a second one this year, and it’s unclear if they still have a possible $3 million payday in 2014. Perhaps the rules are different for string theorists, the idea being that you just can’t give too many prizes for string theory.

  I’ll bet that Green/Schwarz will be the 2014 winners, on the grounds that if you’re going to hand out lots of prizes for working on the superstring, its co-discoverers should be among the first in line. While this means that Polchinski will only get a second $300,000, it’s in his interest to lose as many times as possible before winning.

  As for the $100,000 prizes for young researchers, this year was different than last year. The winners (Cachazo/Minwalla/Rychkov) were two Princeton Ph.Ds and one ex-Princeton post-doc, whereas last year is was one Princeton Ph.D and all three were ex-Princeton post-docs.

• In other news, Max Tegmark, known for his work on the multiverse, is running a “Project Einstein”, which has found 400 theoretical physicists and mathematicians who have agreed to have their genes sequenced. The idea is that they are “math geniuses”, but no one seems to know what will be done with the genetic data for these geniuses. It’s unclear who these “geniuses” are, but we do know that one person who was asked and declined was Curt McMullen. His reaction to this project was what I suspect was a common one:
  

  “I thought it was strange that it was called ‘Project Einstein’, which seemed designed to appeal to the participants’ egos,” he says. He asked the project’s staff and the New England Institutional Review Board, which approved the study, to explain how results would be used. “The uniform answer to my questions was that ‘we are not responsible for how the information is used after the study is completed’,” he says.

  If Project Einstein identifies a common gene among its participants, and uses the knowledge to breed a race of übermenschen, they may find they have selected not for unusual mathematical genius, but for unusual ego.

Update: I realized there’s one other remarkable thing about the six winners of the “New Horizons in Physics Prize”. Besides all having a close Princeton connection, none of them has a job in the US. It seems US physics departments are not buying what Princeton is selling right now…

Well, maybe one more before I leave…

Tom Siegfried, last heard from telling us that Belief in multiverse requires exceptional vision, now has two new pieces at Science News (here and here) arguing that the failure of the LHC to see SUSY is not really a big problem for SUSY proponents. You see, it’s only a problem if you believe physics theories should be simple and if you believe in naturalness. According to Siegfried, what the LHC is telling us is that you just have to give up on one of these, with your choices now:

1. Give up on simplicity. Just announce that SUSY is fine and solves the naturalness problem, but we’re not seeing it because it’s not the MSSM (which adds more than a hundred parameters), but something really, really complicated, so complicated that it manages to show up in such a way that the LHC experiments can’t see any evidence of it. Believe this, and you can still believe in SUSY, no need to face the tragedy of an idea you’ve done so much to promote getting killed by heartless experimentalists.
2. Give up on naturalness and have the exceptional vision to believe in the multiverse. Then you can fine-tune your SUSY particles up to very high energies and make them unobservable. Again, you’re free to keep believing in SUSY, writing articles and books about it, etc., despite the negative experimental results. The advantage of this option is that you don’t need to make your SUSY complicated, it can just be the MSSM, so you keep simplicity. Of course, once you accept fine-tuning, you could get a whole lot more simplicity really easily: just throw out SUSY and stick to the SM….

In a few days I’m heading to East Africa for a couple-week long trip, planning to be in Uganda on November 3 for the (short) total solar eclipse that day. This will be followed by a few days in London, then back here with regular programming resuming around November 11. While away I’ll shut off the commenting system, since I’m hoping to not have internet access during most of the trip.

Here’s some short items that might be of interest:

• For the latest from CERN about SUSY, see this overview from ATLAS. The bottom line is quite simple: zilch, in every channel examined. Limits on a gluino mass are about 1.2 TeV, and there seems little prospect of much change until 2015, when results at 13 TeV start to come in. A naive extrapolation says that ultimately the LHC should be able to set limits on gluino masses of up to 2 TeV. Pre-LHC, the limits were about 300 GeV (from the Tevatron). I don’t know anyone who is optimistic that it will turn out that the 62.5% energy jump in 2015 will find something when the 400% energy jump didn’t (and the theoretical arguments for SUSY implied that it should have already been seen at the Tevatron).
• Steven Weinberg has an article about the current state of cosmology and particle physics, entitled Physics: What We Do and Don’t Know. About string theory he has this to say:
  

  String theory is attractive because it incorporates gravitation, it contains no infinities, and its structure is tightly constrained by conditions of mathematical consistency, so apparently there is just one string theory. Unfortunately, although we do not yet know the exact underlying equations of string theory, there are reasons to believe that whatever these equations are, they have a vast number of solutions. I have been a fan of string theory, but it is disappointing that no one so far has succeeded in finding a solution that corresponds to the world we observe.

  The main reason for disappointment about string theory is not that a solution corresponding to the SM hasn’t been found, but that the theory predicts nothing at all. All indications are that the dead end that string theory has hit is not that (if one could actually figure out what the theory is…) of no SM solution, but that of so many solutions that you can get anything you want. Unfortunately Weinberg seems to be of the “if a fundamental theory predicts nothing, that’s too bad, but maybe how the world works” camp, rather than the more standard “if a fundamental theory predicts nothing, it’s a bad fundamental theory” camp. He goes on to argue that we may have to just give up on fundamental physics and be content with this theory that predicts nothing:

  Such crude anthropic explanations are not what we have hoped for in physics, but they may have to content us. Physical science has historically progressed not only by finding precise explanations of natural phenomena, but also by discovering what sorts of things can be precisely explained. These may be fewer than we had thought.

  Back in 1977, in the wake of the great advances of the Standard Model, Weinberg famously made the statement that:

  The more the universe seems comprehensible, the more it also seems pointless.

  Presumably the universe is still pointless, but now the argument seems to be that it’s also incomprehensible.

• Unlike Weinberg, Frank Wilczek hasn’t been a fan of string theory. From a recent interview:
  

  3. Is String Theory a dead end? Is there news coming, regarding scientific advances, or experimental confirmations?

  Many very smart people continue to work on string theory, and I expect that they’ll continue to do interesting work, in mathematics if nothing else. Whether they’d be more productive doing something else, is another question. It is unfortunate that in the early days people got carried away, and promised much more than the theory
  could reasonably be expected to deliver.

  and about anthropics:

  It is the scope of anthropic reasoning that’s debatable. I hope we can avoid appealing to it very much in fundamental physics, but time will tell.

• According to the Stony Brook newspaper though, based on information from Michael Douglas, all is well with string theory:
  

  String theory has done quite well so far in explaining all of the forces of the universe. The theory has matured, and so have the mathematical equations it has produced. An equation describing the universe is considered successful if it is symmetrical. What that means is if the equation is taken apart and its components rearranged, it should still produce the same conclusion. If the rearrangement of an equation does not yield the same result, it is deemed unstable and not a good descriptor of the universe or its forces.

  The equations that have stood up to the test of symmetry have predicted the existence of particles that help bridge the gap between general relativity and quantum field theory. For example, string theory predicts a particle called the graviton, thought to be a closed loop string that is responsible for the gravitational force…

  Gravity is weak.

  String theory not only predicts the particle that constitutes gravity, it also helps describe why it is so weak…

  Currently, the ability to test the predictions from string theory is very limited and some have said that this roadblock is impossible to overcome.

  Douglas thinks otherwise.

  The next phase of this theory will likely take a lot of hard work and fresh ideas. String theory has made enormous strides in the relatively short amount of time that it has been around, and it is thought by many to be the most promising of the so-called “theories of everything.”

  In a few more years, who knows what exciting advances could be in store?

  The article doesn’t mention Douglas’s decision to stop working on string theory and go to work for a hedge fund.

• The Financial Times has its own take on the current state of fundamental physics research, with an article on The new physics.
• Also at the Financial Times is a good survey of Physicists and the financial markets, describing various current activities of physicists now working in the financial industry.
• Harvard University Press has just released a new book by Steve Nadis and S.-T. Yau, a history of the Harvard math department entitled A History in Sum: 150 Years of Mathematics at Harvard. It concentrates on the period 1825-1975, and I enjoyed it quite a bit. It ends right about the time I arrived there as a student, so covered history that I never had known much about.

  Harvard’s role as a mathematics research institution began with Benjamin Peirce, who taught there from 1831-1880. It only started to become a world-class institution around 1900, with young faculty who had gone to Germany for their training. The book covers a fairly long list of great 20th-century Harvard mathematicians (including George David Birkhoff, Morse, Whitney, MacLane, Ahlfors, Gleason, Mackey, Zariski, Brauer and Bott), and makes a serious attempt to explain some of the mathematical ideas they developed. As a result, a large part of the book is not just history, but actual exposition at a popular level of a wide range of mathematics, together with quotes from many other prominent mathematicians about the significance of the ideas.

  If you’re interested at all in the history of mathematics, this book is well-worth finding a copy of.

• David Appell has an article about the SSC, the major disaster for US HEP research. Next year should see a book on the topic by Michael Riordan, Tunnel Visions: The Rise and Fall of the Superconducting Super Collider.
• The Simons Foundation Quanta magazine continues to put out many high quality stories about science, with one of the latest an article by Natalie Wolchover about experiments searching for neutrinoless double beta decay, which would indicate a Majorana neutrino mass term.
• The SETI institute has a series of SETI Talks, available on YouTube, with the latest featuring Joe Polchinski on Black Holes and Firewalls.
• The Boston area Joint Math Colloquium this week with have Edward Frenkel speaking on The Langlands Program and Quantum Physics. Afterwards you can go up to Harvard Square and get him to sign a copy of his new book.