Not Even Wrong

At the Hollywood-style awards ceremony last night for $3 million string theory and biomedical research prizes, it was announced that Yuri Milner and Mark Zuckerberg will now start funding something similar in mathematics, called the Breakthrough Prize in Mathematics. According to the New York Times:

Yuri Milner, the Russian entrepreneur, philanthropist and self-described “failed physicist” who made a splash two years ago when he began handing out lavish cash awards to scientists, announced Thursday that he was expanding the universe of his largess again: This time, he will begin handing out $3 million awards to mathematicians…

For the new math award, Mr. Milner and Mr. Zuckerberg, the co-sponsor of the math prize, will decide who gets the money, in consultation with experts. Mr. Milner declined to say how many mathematicians would be chosen, but there could be quite a number of windfalls in store: for the physics price, there were nine inaugural winners, and for the life sciences prize, there were 11.

I’ve written extensively about the “Fundamental Physics Prize” and what I see as the worst problem with it (heavily rewarding and propping up a failed research program). While many physicists are privately unhappy about this prize and its effects, few prominent ones are willing to speak publicly with their name attached, since this kind of mouthing-off could turn out to be personally extremely expensive. Ian Sample at the Guardian has a story today, which quotes a “prominent physicist who did not wish to be named”:

One prominent physicist who did not wish to be named said the huge sums of money could be used better: “The great philanthropists of the 19th and 20th centuries, like the Rockefellers and the Carnegies, did not create prizes – they created universities and research institutes that have enabled thousands of scientists to make great breakthroughs over the succeeding decades.

“By contrast, giving a prize has a negligible effect on the progress of science. A few already well-recognised people get enriched, but there is little value added in terms of the progress of science compared to the multiplier effect of creating new institutions for scientific research.”

The Guardian does quote one critic by name, but it’s just the usual one.

The physics prize has turned out to be extremely narrowly targeted at one particular subfield of physics, and from what little I know of the life sciences, the prizes in that area seem to be also narrowly targeted (US biomedical research aimed at curing diseases that most afflict those in the developed world). I’m highly ignorant about life sciences research, but it seems striking that the 6 $3 million winners in this field were all men.

I have no idea how Milner and Zuckerberg will go about choosing the $3 million winners in mathematics, and whether this new prize will end up being narrowly targeted to a certain sort of mathematics research. If so, it may have very significant effects on what kinds of mathematics get done. Based on the other prizes, it seems likely that the winners will be mostly prominent US academics, people already well-rewarded by the current academic star system. I don’t see any reason to believe that these kinds of financial awards will allow such mathematicians to do work they wouldn’t otherwise do, so the main argument for the prizes is that the money (and Academy Awards-style ceremonies) will help make them celebrities, and that this is a good thing. One can predict that public criticism from prominent US academics may be rather muted once the checks start coming.

Even if the Milner-Zuckerberg prize does end up focused on the best mathematics research, I still think the whole concept is problematic. The US today is increasingly dominated by a grotesque winner-take-all culture that values wealth and celebrity above all else. While mathematics research, like the rest of academia, has been affected as a star system has become increasingly part of the picture, this field has been somewhat immune to celebrity culture. While people typically think that what mathematicians do is perfectly respectable, they don’t understand much about it and aren’t especially interested. Milner and Zuckerberg want to change this by turning mathematicians into celebrities, but I don’t see any reason to believe this is going to lead to better mathematics.

Update: Here’s the statement from Milner about the planned mathematics prize:

Yuri Milner said: “Einstein said, Pure mathematics is the poetry of logical ideas. It is in this spirit that Mark and myself are announcing a new Breakthrough Prize in Mathematics. The work that the Prize recognizes could be the foundation for genetic engineering, quantum computing or Artificial Intelligence; but above all, for human knowledge itself.”

Last March an Oscar-style ceremony hosted by Morgan Freeman was held in Geneva (see here) to award the 2013 \$3 million Milner Prize to Princeton string theorist Alexander Polyakov. Tomorrow an even more lavish ceremony designed to turn “Oscars of Science” into instant multi-millionaires will be held in Mountain View, California (see here). It will feature Kevin Spacey, Conan O’Brien and Glenn Close, one of whom will presumably award the 2014 $3 million Milner string theory Prize to either Polchinski, Green/Schwarz, or Strominger/Vafa.

If I had to bet I’d go for Polchinski, purely because if they don’t give it to him, that will be two years in a row he walks away with a \$300,000 consolation prize, and having to have him a third time up next year before getting his $3 million would be a bit silly. On the other hand, John Preskill is predicting Green/Schwarz, and he may be right. If you’re going to have a prize devoted to the idea that string theory = fundamental physics since it’s our hope for a TOE, then one really has to give it to Green/Schwarz for originating the whole superstring = TOE business.

On Friday, there will be a day-long symposium at Stanford sponsored by the Milner prize people (see here), with the $3 million man (or men) speaking at 5:30pm, introduced by Lenny Susskind.

Physics will actually be a relatively small part of this awards ceremony, since it will also include the award of six $3 million awards in the Life Sciences. These are being jointly funded by Milner and a group of other prominent internet entrepreneurs.

Update: News is that the awards ceremony will be broadcast by the Science Channel:

Hosted by actor Kevin Spacey, the awards will be presented by the Prize sponsors and by celebrities including Conan O’Brien, Glenn Close, Rob Lowe and Michael C. Hall. The event was produced and directed by Don Mischer, the producer and director of The Academy Awards among other television and live events. The world premiere special 2014 BREAKTHOUGH PRIZES will premiere on Science Channel on Monday, January 27 at 9 PM ET/PT.

According to the press release, Polchinski, Green/Schwarz or Strominger/Vafa will get $3 million for being “psychics”:

The 2014 Breakthrough Prizes are awarded to those who make major breakthroughs and contributions that represent significant advances in our fundamental knowledge of the world. At the ceremony, seven prizes (six for life sciences and one for psychics) of $3 million each will be awarded for a total of $21 million.

Update: As John Preskill predicted, the \$3 million string theory prize went to Green and Schwarz. Polchinski gets a second $300,000 consolation prize and another chance next year.

Update: Vanity Fair covers the event as Hollywood Stars Gather in Silicon Valley for 2014 Breakthrough Prizes in Physics and Life Sciences.

This week the Simons Center is hosting a workshop on “The Geometry and Physics of Scattering Amplitudes”, talks are available here. Last week they (and the YITP) held a one-day symposium on Trees, loops and precision QCD, based around the work of Zvi Bern, Lance Dixon and David Kosower that was recently awarded the 2014 Sakurai Prize. For more about this, see Dixon’s guest post here, or his talk at the symposium.

Bern, Dixon and Kosower started working on amplitudes more than twenty years ago, at a time that it was becoming clear that string theory was not working out as a theory of everything. Calculations in string theory did though lead to interesting new ideas about how to evaluate scattering amplitudes in gauge theory (I see from Dixon’s list of publications that in 1994 he wrote something for the SLAC Beam Line on “Whatever happened to the theory of everything?”, presumably about this, but now too deep in the past to be available on-line). The three Sakurai Prize winners have been steadily working at the problems of amplitudes in gauge theory and quantum gravity, for many years without getting much attention for their work. About ten years ago, things changed when Witten wrote a paper about getting amplitudes from the “twistor string”, a topological string theory in twistor space (the use of twistor space was originated by Penrose back in the late 1960s, and was applied by V.P. Nair to gauge theory amplitudes back in 1988 while he was here at Columbia).

About six years ago Nima Arkani-Hamed entered the subject, where he has had a dramatic effect as an impresario, arguing that this is a route to revolutionary ideas about physics, overthrowing conventional notions of space and time, locality and unitarity, and doing away with the notion that gauge invariance is important. This was partly responsible for his $3 million Milner prize.

For the latest along these lines, a paper with Trnka about “The Amplituhedron” has just appeared, a topic which got wide play in the press earlier this year as Physicists Discover Geometry Underlying Particle Physics, drawing a parody from Scott Aaronson about his own work on the “Unitarihedron” and “Diaperhedron”. Arkani-Hamed’s talk at the Symposium covers both the ideas of Bern, Dixon and Kosower and his recent work with Trnka. It includes many appreciative remarks about their work, including some interesting commentary on how theoretical physics is done. For instance, on the likely reason for people ignoring their early work:

It’s a natural reaction among theoretical physicists, right? At any given time there’s all sorts of interesting things going on, things that other people are doing and things that you are doing and especially if someone else is coming along with something that looks really exciting, in order to justify not dropping everything you have and working on it you have to sort of start inventing these reasons why what they are doing is irrelevant or crap, right? It’s a very human thing, a very human thing, a very natural thing. I think everyone does it to some extent, and really good people eventually will realize that they are fooling themselves and start changing their tune if it’s appropriate. Really bad people, well, we won’t talk about them. It was not at all obvious that this was the tip of a huge iceberg…

There’s also:

Often fields, other fields, have what you might call prophets and there’s I think usually an excessive amount of reverence for these prophets, because the prophets tend to have the property that they say some sort of vague things, I won’t name any names but you can probably figure out the sort of collection of people I’m talking about. They say some sort of vague things about what might happen with physics in the future, and then twenty years later when other people have done all the hard work and really figured out what is going on and how it works in detail and why it works that way and not another way, if it vaguely looks like something they did, they say “see, I said so all along!” They have a fair amount of attraction, I think it’s because a lot of physicists have father-figure issues. But anyway, Zvi and Lance and David were very much not like that, they weren’t just vague prophets saying something was going on, they were extremely specific: there was something going on in this area with these kind of computations in this arena and they knew it. And it took a decade or more for many other people in the field to catch up.

(Personally, I have no idea which “prophets” he’s thinking of.)

Finally, there were some personal comments contrasting Bern, Dixon and Kosower’s low-key style and use of a variety of techniques with his own high-powered hype-driven sales-job of specific ideas to himself and others. Probably a good idea to read this in conjunction with the “Outlook” section of the new paper….

I must say, and I’m really not just saying this to say it, I’m VERY envious of this, because I AM an ideologue. In my defense at least I can say that I’m a serial ideologue, in the sense that I’ll take totally different ideologies and drop the last one without thinking about it, but it’s very important for me personally to be an ideologue when I’m working on something and I think, and I’m saying this in all honesty, the difference is talent. If you’re really good, you don’t have to be an ideologue. You take this, you take that, you’re solving for things left and right, you don’t care where things come from. If you’re not as good, there are 15 million things going on, you’re holding on for dear life in the stiff wind of all the crazy stuff going on in the subject. So you have to have a strong point of view about something, you have to have a strong point of view to sort of pursue a particular direction, otherwise you’ll get beaten around all the time and get nowhere.

So, usually I’ll get up when I talk about scattering amplitudes and give a long introduction about how spacetime is doomed, we have to find some way of thinking about quantum field theory without local evolution in space time and maybe even without a Hilbert space and blah-blah-blah. This is all very high-falutin stuff, this is stuff that Lance wouldn’t be get caught dead saying. I think none of these guys would ever say something that sounds so pretentious, but I have to say it, you know I have to say it, because this is the only way I can get up in the morning, and like “I suck again, OK, here we go, I’m doing it because spacetime is doomed, I swear to God, right”. But, quite seriously, the best people in the subject have this feature, they don’t need to be ideologues, they take the most interesting ideas from every direction they can to make progress, so I really am quite envious.

The Guardian has an interesting piece about Peter Higgs, evidently their reporter talked to him on his way to the Nobel Prize ceremonies this week in Stockholm. Higgs will be speaking tomorrow (Sunday), and I’m curious to hear what he will have to say. His talk will be available live at the Nobel Prize website.

Higgs points out that the kind of work he was awarded the prize for was done in an environment that no longer exists:

He doubts a similar breakthrough could be achieved in today’s academic culture, because of the expectations on academics to collaborate and keep churning out papers. He said: “It’s difficult to imagine how I would ever have enough peace and quiet in the present sort of climate to do what I did in 1964.”

By the time he retired in 1996, he was glad to be out of academia:

After I retired it was quite a long time before I went back to my department. I thought I was well out of it. It wasn’t my way of doing things any more. Today I wouldn’t get an academic job. It’s as simple as that. I don’t think I would be regarded as productive enough.

Higgs has definitely not been a careerist sort, turning down a knighthood in 1999:

I’m rather cynical about the way the honours system is used, frankly. A whole lot of the honours system is used for political purposes by the government in power.

He thinks he likely would have been fired by his university back in the 1980s if there hadn’t been a prospect of him getting a Nobel.

The work Higgs did in 1964 was on a rather unpopular topic. At the time the reigning ideology was “S-matrix theory”, which argued that local quantum field theory was a hopeless subject, so one should be working on formulating basic physics just in terms of S-matrix amplitudes, using their holomorphicity properties (this idea has had somewhat of a comeback in recent years). The 1960s however was a time of a great expansion in the number of university positions, so people like Higgs could make a career despite working on unpopular topics.

Progress in particle theory slowed dramatically after the early 1970s. One reason for this of course has been the huge success of the Standard Model, as well as the inherent difficulties involved in getting experimental access to higher energy scales. One wonders though whether the post-1970 collapse of the HEP theory job market and very different environment that ensued might have had something to do with this. As Higgs himself is well-aware, if he had come along 10 years later, he would not have found a job in the field.

In the UK today, things seem to be getting even worse, with strong pressures from the government to only fund work likely to have an immediate economic payoff. For more about this, see this commentary at Physicsfocus by Philip Moriarty on The Spirit-Crushing Impact of Impact. The UK has just announced the founding of a new Higgs Centre for Innovation, to be built in Edinburgh and opened in 2016. It will be devoted though not to the kind of research Higgs had success with, but to “big data” and “space”, considered by the government to be among the most promising technologies for the future. It’s rather ironic that Higgs is the sort of scientist who would not be employable by the Higgs Centre.

Update: For the acceptance speech by Higgs, see here, and see here for an official interview. For a different point of view, from one of the experimenters who made the award to Higgs possible, see here.

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.