Defend the Integrity of Physics

This week’s Nature features a call to arms from George Ellis and Joe Silk, entitled Scientific method: Defend the integrity of physics. I’m very glad to see well-known physicists highlighting the serious problem for the credibility of science raised by the string theory multiverse and the associated ongoing campaign to justify the failures of string theory by attacking the scientific method. Acknowledging evidence that an idea you cherished doesn’t work is at the core of what science is and physics now has a major problem with prominent theorists refusing to abide by this principle. Ellis and Silk do a great job of identifying and characterizing an important challenge the scientific community is facing.

The issue is however complicated, and while the Nature piece carefully and clearly addresses some of the complexities, there are places where things get over-simplified. In particular, the introduction frames the issue as whether a theory being “sufficiently elegant and explanatory” allows it to not need experimental testing. The problem with the string theory multiverse though is not this, since such a theory is the antithesis of “elegant and explanatory”. There’s just about nothing in science as inelegant as the various attempts (e.g. the KKLT mechanism) to make string theory fit with known physics, and “the multiverse did it” is no more an actual explanation of anything than “a big omnipotent turtle did it”.

Trying to cut through the complexities, Ellis and Silk write:

In our view, the issue boils down to clarifying one question: what potential observational or experimental evidence is there that would persuade you that the theory is wrong and lead you to abandoning it? If there is none, it is not a scientific theory.

This is at the heart of the matter, but there are subtleties. A common recent move among some prominent string theorists has been to argue that string theory is falsifiable: it is based on quantum mechanics, so if experiments falsify quantum mechanics, they falsify string theory. This just makes clear that the question of falsifiability can be slippery. Philosophers of science are experts at the intricacies of such questions and Ellis and Silk are right to call for help from them.

They also make the interesting call for the convening of a conference to address these issues. How such a thing would work and how it might be helpful seem well worth thinking about. As for one of their other recommendations though:

In the meantime, journal editors and publishers could assign speculative work to other research categories — such as mathematical rather than physical cosmology — according to its potential testability.

I’m leery of the impulse among physicists to solve their problem of how to deal with bad physics by calling it mathematics. Yes, there is good mathematics that has come out of untestable ideas about string theory, but no, this doesn’t include the string landscape/multiverse cop-out, which physicists need to face up to themselves.

For the specific arguments from Sean Carroll and Richard Dawid that Ellis and Silk address, I’ve written about them elsewhere, see for instance here, where I discussed in some detail Dawid’s arguments.

: Sabine Hossenfelder has commentary on this here.

Update: Taking the opposite side of the argument in January’s Smithsonian magazine is by colleague Brian Greene, with an article entitled Is String Theory About to Unravel?. As you might expect, Brian’s answer is “No”, and he gives a good account of the point of view Ellis and Silk are warning against. He mentions the possibility of encouraging news for string theory from the next LHC run, but says that “I now hold only modest hope that the theory will confront data during my lifetime.”

Update: Sean Carroll responds to the criticism from Ellis and Silk with a tweet characterizing them as belonging to the “falsifiability police”:

My real problem with the falsifiability police is: we don’t get to demand ahead of time what kind of theory correctly describes the world.

Update: Gordon Kane joins the fight in a comment at Nature, claiming that, before the LHC, string theory predicted a gluino mass of 1.5 TeV.

The literature contains clear and easily understood predictions published before LHC from compactified string theories that gluinos, for example, should have been too heavy to find in Run 1 but will be found in Run 2 (gluino mass of about 1.5 TeV).

As far as I can tell, this is utter nonsense, with Kane publicly claiming string theory predictions of a gluino mass of around 600 GeV (see page 22 of this) back in 2011, then moving the “prediction” up as Run 1 data falsified his earlier predictions. Kane at least makes falsifiable predictions, the problem with him only comes when they get falsified…

Update: Chad Orzel has his take here.

Update: Adam Frank has an essay on this here.

Posted in Multiverse Mania | 34 Comments

Weinberg on the Desert, Seiberg on QFT

Last week Steven Weinberg gave a Lee Historical Lecture at Harvard, entitled Glimpses of a World Within. There’s a report on the talk at the Harvard Gazette.

In essence, Weinberg argues in the talk for an idea that first started to dominate thinking among HEP theorists nearly forty years ago, one that is sometimes called the “Desert Hypothesis”. The idea is that by looking at what we know of the SM and gravity, you can find indications that the next level of unification takes place around the Planck scale, with no new physics over the many orders of magnitude between the scales we can observe and that scale, at least no new physics that will affect running of coupling constants for instance. The evidence Weinberg gives for this is three-fold (and very old by now):

  • He describes listening to Politzer’s first talk on asymptotic freedom in 1973, and quickly realizing that if the strong coupling decreases at short distances, at some scale it would become similar to the coupling for the other fundamental forces. In a 1974 paper with Georgi and Quinn this was made explicit, and he argues this is evidence for a GUT scale a bit below or around the Planck scale.
  • He explains about the Planck scale, where gravity should be of similar strength to the other interactions. This idea is even older, well-known in the fifties I would guess.
  • He refers to arguments (which he attributes to himself, Wilczek and Zee in 1977) for a Majorana neutrino mass that invoke a non-renormalizable term in the Lagrangian that would come from the GUT scale.

Weinberg sees these three hints as “strongly suggesting” that there is a fundamental GUT/Planck scale, and that’s what will explain unification. Personally though, I don’t see how three weak arguments add up to anything other than a weak argument. GUTs are now a forty-year old idea that never explained very much to start with, with their best feature that they were testable since they generally predicted observable proton decay (which we haven’t seen). We know nothing at all about the source of particle masses and mixing angles, or the reason for their very different scales, and there seems to be zero evidence for the mechanism Weinberg likes for getting small neutrino masses (including zero evidence that the masses are even Majorana). As for quantum gravity and the Planck scale, again, we really have no evidence at all. I just don’t think he has any significant evidence for a desert up to a Planck unification scale, and this is now a very old idea, one that has been unfruitful in the extreme.

Weinberg ended his talk with another very old idea, that cosmology will somehow give us evidence about unification and GUT-scale physics. That also hasn’t worked out, but Weinberg quotes the BICEP2 value of r as providing yet more evidence for the GUT scale (he gives it a 50/50 chance of being correct). Again though, one more weak piece of evidence, even if it holds up (which I’d give less than 50/50 odds for at this point…), is still weak evidence.

For a much more encouraging vision talk, I recommend listening to Nati Seiberg at the recent Breakthrough Prize symposium. Seiberg’s talk was entitled What is QFT?, and to the claim that QFT is something understood, he responds “I really, really disagree”. His point of view is that we are missing some fundamental insights into the subject, that QFT likely needs to be reformulated, that there exists some better and more insightful way of thinking about it than our current conventional wisdom. In particular, there seems to be more to QFT than just picking a Lagrangian and applying standard techniques (for one thing, there are QFTs with no known Lagrangian). Seiberg takes the fact that mathematicians (who he describes a “much smarter than most quantum field theorists”…) have not been able to come up with a satisfactory rigorous version of QFT to indicate not that this is a boring technical problem, but that we don’t have the right definition to work with.

To make things more specific, he describes joint recent work (for another version of this see here) on “Generalized Global Symmetries” that works with global symmetries associated to higher co-dimension spaces than the usual codimension one case of Noether symmetries and Lagrangian field theory. Evidently there’s a forthcoming paper with more details. I’m in complete agreement with him that there must be better ways of thinking about QFT, and I think these will involve some deeper insights into the role of symmetries in the subject.

Update: The paper Seiberg mentions is now available here.

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Very Short Items

  • Long-awaited results from the Planck experiment were unveiled last week, with a new model for how to do this: hold a conference with no videos, no slides released, no wifi in the lecture hall, and put out a press release in French. They did release an amazing image that looks like a Van Gogh, but if you want numbers, you have to search Twitter. Stories at Nature and the New York Times indicate not much new, data relevant to primordial gravitational waves still to come (Dec. 22?, next year?).
  • News from MIT is that, after an investigation of charges of sexual harassment of one or more students online, the university has revoked physics professor Walter Lewin’s emeritus status and is removing his lecture videos and course material from their online course sites.
  • Today’s Wall Street Journal has a sensible piece by Ira Rothstein on The Perils of Romanticizing Physics.
  • I took a look at Kip Thorne’s The Science of Interstellar in a local bookstore. It gives a detailed explanation of the “science” behind the film, explaining what a lot of the highly confusing later plot of the film was supposedly about. It seems it’s all based on the “large extra dimension” business of 15 years ago, the dimensions that were supposed to show up at the LHC. If you want to see all the equations, go here and look for the pictures of the blackboards.
  • The LHC magnets are now getting trained for 6.5 TeV operation, as well as inspiring fashion designers.
  • I mentioned last year’s Gelfand Centennial conference at MIT here, thought that there were no videos. Luckily I was wrong, quite a few talks well worth watching are now available here.
  • Videos from the Breakthrough Prize symposia recently held at Stanford are now available. For the physics talks, see here. For the math talks, see here, here, here, here, here and here.
  • If you need a change of pace, and can’t get enough of the string theory/LQG debate, this is for you.
  • For talks about the implications of not seeing new physics at the LHC, there’s Naturalness 2014. Nima Arkani-Hamed kicked it off with “Hopefully My Last Ever Talk On This!” (seems unlikely…). He argues for the idea that it’s the Multiverse that did it, and we should keep looking for Split SUSY, disses “conformality” approaches. Matt Strassler on the other hand points out that Arkani-Hamed’s use of the multiverse explanation doesn’t make sense (there’s no anthropic reason for the highly non-generic SM).
  • There’s a workshop this week at Caltech on scattering amplitudes and the Grassmanian.
  • Finally, a HEPAP meeting this week. Budget news for HEP theory doesn’t look good, but on the other hand the US now seems to be functioning without a budget, so it’s kind of hard to be sure…

Update: Slides from the Planck conference are now available.

It seems the US does have a budget now, some info here. DOE HEP and Cosmic Frontier $766 Million, down very slightly from last year’s $775 million, higher than the White House requeset of $744 million.

Update: Scott Aaronson on Walter Lewin here.

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The Multiverse in a Nutshell

The Guardian has a podcast up today featuring Robert Trotta and David Wallace called The Multiverse in a Nutshell. It’s largely more of the usual uncritical multiverse hype that has been flooding the public expositions of fundamental physics for years now. Trotta gives the usual promotion of the cosmological multiverse, with no indication there is any problem with it. He assures us that this is being tested (by looking for “bruises” in CMB collisions). As far as I can tell, the Planck results released today, like all CMB data, show no evidence for anything like this. It appears that the Planck people don’t even think this is worth mentioning. The public channels used for this hype will never report the fact that there’s nothing there, instead they will just endlessly talk about this as something “scientists are looking for.”

Wallace talks about something completely different, many-worlds, with nobody telling listeners that this has nothing at all to do with the cosmological material. Instead we’re told that it’s all related, because “most theories” “tell us there must be a multiverse”. When challenged about the splitting universe business in QM, Wallace admits that at the fundamental level there is no splitting, there’s just one theory and one universe, that “many worlds” is just a way of talking about the emergent behavior of the classical approximation. His book about this, The Emergent Multiverse, is quite good and makes clear what the “Multiverse” there really is. It’s a real shame that he chooses to involve himself in this kind of attempt to muddy the waters and promote pseudo-science to the public.

Thankfully at least the physics community has one physicist trying to do something about this nonsense: Paul Steinhardt. In an interview with John Horgan, here’s his “Multiverse in a Nutshell”:

Unfortunately, what has happened since is that all attempts to resolve the multiverse problem have failed and, in the process, it has become clear that the problem is much stickier than originally imagined. In fact, at this point, some proponents of inflation have suggested that there can be no solution. We should cease bothering to look for one. Instead, we should simply take inflation and the multiverse as fact and accept the notion that the features of the observable universe are accidental: consequences of living in this particular region of the multiverse rather than another.

To me, the accidental universe idea is scientifically meaningless because it explains nothing and predicts nothing. Also, it misses the most salient fact we have learned about large-scale structure of the universe: its extraordinary simplicity when averaged over large scales. In order to explain the one simple universe we can see, the inflationary multiverse and accidental universe hypotheses posit an infinite variety of universes with arbitrary amounts of complexity that we cannot see. Variations on the accidental universe, such as those employing the anthropic principle, do nothing to help the situation.

Scientific ideas should be simple, explanatory, predictive. The inflationary multiverse as currently understood appears to have none of those properties.

Posted in Multiverse Mania | 29 Comments

For Your Viewing Pleasure

If you’ve already seen the various new math/physics films coming out of Hollywood, this week you might be interested in watching some of the real thing, including the following:

  • The hot ticket this week will be Monday’s Planck session at the conference in Ferrara. They’ve now edited their website to remove references to a promised webcast and slides. So, the only way to get images suitable for scraping may be to get yourself into the lecture hall at Ferrara and bring a camera. Press release here, conference program here.
  • Also on Monday, if you’re in Cambridge (MA), there’s Steven Weinberg’s Lee Historical Lecture in Physics, topic Glimpses of a World Within. The only blurb is

    “Since the 1970s the evidence has accumulated that the structures appearing in the laws of nature at a really fundamental level are vastly smaller than anything we encounter in our high energy laboratories.”

    which I don’t think I’d personally agree with, quite curious to see what case he makes. These lectures often are later made available here.

  • For another historical lecture, there will be a webcast of this event at CERN on Tuesday. It features film of interviews with Roy Glauber, characterized as “the last living scientist from the Theory Division of the Manhattan Project”. Glauber taught the first quantum field theory course I ever took, at Harvard in 1976-77, almost forty years ago (I thought he was pretty ancient at the time). The year earlier I had taken quantum mechanics with Norman Ramsey, here shown signing Fat Man. At the time it seemed perfectly normal that all my instructors had gotten their start designing weapons.
  • If you’re in Berkeley this week, you could attend a Langlands-related conference at MSRI, which in addition is honoring Michael Harris. Program is here, videos to appear soon after the talks.
  • Recently concluded at MSRI was a workshop on geometric representation theory, with lots of interesting talks, videos available here.

Update: There is supposed to be video from Ferrara here, but not working. A press conference was held, but the only thing I see from Planck online is in French here. Nothing about primordial gravitational waves, just confirmation of the standard cosmological model and of 3 neutrinos.

Update: No public release of any numbers from Planck that I can see, although they are being discussed in Ferrara. People are pointing out that the authoritative source for the best values of cosmological parameters at the moment is Twitter.

Update: Peter Coles has this take on the Ferrara Planck results: “a bit of a farce.” Among the many oddities here, it seems that only the French component of Planck is putting out any news to the public.

Update: Adrian Cho at Science has a report about the latest Planck results here. Speculation is that Planck data alone and their joint analysis with BICEP2 will not see a gravitational wave signal, just set an upper limit. Planck is supposed to release papers Dec. 22, unclear if this will include the analysis with BICEP2.

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The Imitation Game

This season’s Hollywood math/physics extravaganza is starting to come to an end. For coverage of the Breakthrough Prize ceremony, I enthusiastically recommend Michael Harris’s new piece at Slate which just appeared.

The final high profile production, one promoted at the Silicon Valley ceremony, should be The Imitation Game, a film based on the life of Alan Turing, to be released on November 28th. I had the chance to attend a preview screening last night, featuring a Q and A with the film’s screenwriter. The short version of a review is: go to see this is you like watching Benedict Cumberbatch and Keira Knightley perform, but if you want to know anything about Turing, avoid the film and spend your money instead on a copy of the new edition of Alan Turing: The Enigma by Andrew Hodges.

Turing’s story was little known until 1983, when Hodges published his biography, which is just fantastically good. Hodges (see his web-site here) is a mathematical physicist who began working with Penrose back in the 1970s on twistor diagrams, work that has recently played a prominent role in the hot topic of new methods for computing scattering amplitudes. The Hodges book made Turing a famous figure, partly for his code-breaking role, partly as a martyr for gay rights given the horrific story of the way he was treated because of his sexual orientation. By 1986 the biography had inspired a play, Breaking the Code, that ran in London and New York, and then became a 1996 movie. There have been other film treatments of the story since, including the 2011 Codebreaker.

Other than a few general facts, the part of the film set at Bletchley Park has little relationship to reality, with almost none of what is portrayed actually having happened. As just one example of the sort of thing that was made up out of whole cloth, the film has Turing discovering a Soviet spy, who uses his homosexuality to blackmail him into silence. Cumberbatch plays a compelling character, but one much like his Sherlock Holmes on TV, not like the Turing of the Hodges book, or like any other mathematically talented person I’ve ever known.

It often mystifies me why people who make movies based on fascinating real stories sometimes just ignore what really happened and instead make up a much less interesting plot. In this case, hearing from the screenwriter after the film made the problem clear. He seems convinced that Turing is a little known figure, and that it is his job to reveal this unknown story to the public, unaware that this was done much better back when he was in pre-school. From his comments, he never bothered to understand anything about what Turing actually did during the war, in particular he is convinced that Turing’s big breakthrough was to realize that to break codes it was helpful to know some phrases that were likely to be in the message (e.g. “Heil Hitler”). He explained that he was sure that Turing saw himself as a figure in a thriller, and that informed how he wrote the film. All in all, he had a very simplistic agenda (to reveal the unknown fact that a gay man had won World War II) which completely overwhelmed any interest in the details of what actually happened.

The contrast with the recent Stephen Hawking biopic is striking. That film took some dramatic license, and simplified some complex people and situations, but it didn’t just completely make things up, and the star’s portrayal of Hawking was convincingly true to life. The memory of Alan Turing would have been much better served by a similar degree of respect for reality.

Update: The Guardian has a review, which explains some of what the film gets wrong. For something with more detail, see this.

Posted in Book Reviews | 24 Comments

Planck News?

The timing for release of long-awaited Planck polarization data keeps getting pushed back. At one point it was supposed to be earlier this year, most recently it was supposed to be this month, with that timing forced by a conference devoted to discussion of the results planned for December 1-5. The website for that conference now says:

The 2014 Planck public release of data products and papers will actually take place a few weeks after this conference. This conference is therefore the first occasion to preview the Planck 2014 data products and discuss their scientific impact. The presentations will be videocast online. After the conference, the presentation slides will be made available.

Another conference scheduled assuming the data will have been released is this one in Paris December 15-19.

The Planck website now reports:

- The data products and scientific results will be presented at a public conference in Ferrara. The presentations will be videocast during the conference and slides will be made available after the end of the conference.

– It is planned to release all major data products and scientific papers to the public before the end of 2014. A few of the derived products (e.g. the Likelihood code) will need a little more time to be readied for release, but will be made public within the month of January 2015.

David Spergel on Twitter reports December 22 as the date for release of papers and data.

It will be interesting to see how the cosmology community deals with the situation of no papers or data, just videocast and slides, from December 1 on. From similar situations in the past, some people have highly developed technology for scraping data off slides, presumably that will be in high demand.

Posted in Uncategorized | 7 Comments

Advertisements for the Multiverse

After watching the Breakthrough Prize awards tonight, tomorrow night on the Science Channel you can watch a program that actually features physicists rather than Hollywood/Silicon Valley celebrities. There’s an hour long infomercial for the Multiverse, entitled “Which Universe Are We In?”. You get to hear from

  • Max Tegmark starting and ending the show with a generic promotional spiel about how wonderful the multiverse is.
  • Seth Lloyd about how weird QM is, and that it and cosmology provide strong experimental support for the multiverse.
  • Anthony Aguirre explaining about seeing collisions of other universes in the sky, and about how evidence for the multiverse has now been seen (BICEP2), providing a huge leap forward for the multiverse.
  • Laura Mersini-Houghton about the string landscape and how she has used it to make predictions, which are now becoming accepted.

The program ends kind of like a car commercial, with beautiful scenery and swelling music. A voice over mentions un-named fuddy-duddy critics, mainly to say that BICEP2’s “great support for the theory of the multiverse” has “given then something to think about”. It suggests that the answer to the question raised by all these different kinds of multiverse (“which one is true?”) can be answered by believing all multiverse models at once, no need to choose.

No mention of tedious things like dust. This multiverse is all new and shiny, slices, dices, provides every reality you could possibly want.

On a somewhat higher level, Quanta magazine followed up last week’s multiverse piece with a new one this past week, Multiverse Collisions May Dot the Sky from Jennifer Ouellette. Aguirre appears here too, working with collaborators on analyzing possibly observable consequences of bubble collisions. One of them is Hiranya Peiris, who explains that multiverse theory is like the theory of evolution:

Peiris acknowledges that this argument has its critics. “It can predict anything, and therefore it’s not valid,” Peiris said of the reasoning typically used to dismiss the notion of a multiverse as a tautology, rather than a true scientific theory. “But I think that’s the wrong way to think about it.” The theory of evolution, Peiris argues, also resembles a tautology in certain respects — “an organism exists because it survived” — yet it holds tremendous explanatory power. It is a simple model that requires little initial input to produce the vast diversity of species we see today.

A multiverse model tied to eternal inflation could have the same kind of explanatory power. In this case, the bubble universes function much like speciation. Those universes that happen to have the right laws of physics will eventually “succeed” — that is, they will become home to conscious observers like ourselves. If our universe is one of many in a much larger multiverse, our existence seems less unlikely.

The problem of course with bubble collision “predictions” are that they’re not falsifiable. As far as they’re concerned, you can only win: seeing nothing doesn’t disprove the multiverse. The most recent attempt to look for evidence in the CMB that I’m aware of is this, which found nothing in the WMAP-7 data. I haven’t seen anything using Planck data released so far. Presumably when new data is released later this month some kind of search for bubble collision evidence will be done, and Quanta magazine isn’t likely to report the likely outcome.

The Quanta piece isn’t an infomercial like the TV program, it does explain some of the problems with this whole endeavor, including this from Erick Weinberg:

“My own feeling is you need to adjust the numbers rather finely to get it to work,” Weinberg said. The rate of formation of the bubble universes is key. If they had formed slowly, collisions would not have been possible because space would have expanded and driven the bubbles apart long before any collision could take place. Alternatively, if the bubbles had formed too quickly, they would have merged before space could expand sufficiently to form disconnected pockets. Somewhere in between is the Goldilocks rate, the “just right” rate at which the bubbles would have had to form for a collision to be possible.

Researchers also worry about finding a false positive. Even if such a collision did happen and evidence was imprinted on the CMB, spotting the telltale pattern would not necessarily constitute evidence of a multiverse. “You can get an effect and say it will be consistent with the calculated predictions for these [bubble] collisions,” Weinberg said. “But it might well be consistent with lots of other things.” For instance, a distorted CMB might be evidence of theoretical entities called cosmic strings. These are like the cracks that form in the ice when a lake freezes over, except here the ice is the fabric of space-time. Magnetic monopoles are another hypothetical defect that could affect the CMB, as could knots or twists in space-time called textures.

Weinberg isn’t sure it would even be possible to tell the difference between these different possibilities, especially because many models of eternal inflation exist. Without knowing the precise details of the theory, trying to make a positive identification of the multiverse would be like trying to distinguish between the composition of two meteorites that hit the roof of a house solely by the sound of the impacts, without knowing how the house is constructed and with what materials.

There’s also the problem that even if you did see something, it really would tell you pretty much nothing about the supposed other universe:

Should a signature for a bubble collision be confirmed, Peiris doesn’t see a way to study another bubble universe any further because by now it would be entirely out of causal contact with ours. But it would be a stunning validation that the notion of a multiverse deserves a seat at the testable physics table.

Update: One problem with arguing that the multiverse is like the theory of evolution that physicists should keep in mind: creationists love it.

Posted in Multiverse Mania, Uncategorized | 43 Comments

Breakthrough Prize on TV

You can watch the recent Breakthrough Prize awards ceremony on TV tonight, 6 pm on the Science and Discovery channels. The Science Channel has a site with videos of highlights of the evening, the complete list of which is:

  • Christina Aguilera singing “Beautiful”.
  • Larry Page of Google talking about himself and Google.
  • Mark Zuckerberg talking about the universe and the “masters of string theory”, which is “our best hope for one explanation of reality”.
  • Michael C. Hall talking about his own cancer, then bringing on Jimmy Wales to talk about a cancer researcher.
  • Sergey Brin of Google talking about himself.
  • Sergey Brin’s wife Anne Wojicki talking about herself, and about her husband’s DNA (which supposedly indicates an increased risk for Parkinson’s, so research on curing that is important).
  • Lana Del Rey singing “Video Games”.

I’ve heard a rumor that one mathematician was actually allowed to say something, for 30 seconds. Will have to wait for the show tonight to see if that was true…

Update: Just saw the show. There was a nice video shown of the mathematicians saying some things about math in general. Unlike the rest of the scientists, they weren’t given their award by a star or starlet, but were brought on stage together already holding their awards, and Richard Taylor said something for 20-25 seconds on everyone’s behalf. I also hadn’t realized that a sizable part of the show was two promotional segments for Hollywood movies (the ones about Hawking and Turing).

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Alexander Grothendieck 1928-2014

I just heard that Alexander Grothendieck passed away today, at the age of 86, in Saint-Girons. For a French news story, see here.

Grothendieck’s story was one of the great romantic stories of modern mathematics, and many would consider him the greatest mathematician of the twentieth century. For some blog entries about him here, see for example this and this. I’ll add other links as I see them or think of them.

Update: For some blog entries about Grothendieck’s recent life, you could start here.

One of the best places to learn about Grothendieck is from his friend Pierre Cartier, in an article that can be found here, among other places.

Le Monde now has an obituary.

Steve Landsburg has a blog post.

Update: The news about Grothendieck came out in the French press a day ago, but at this point the only things I’ve seen in the English-language press are an AP wire story, and this at the Independent. Come on science journalists, if any story about mathematics and mathematicians is worth writing about, this one is.

Update: There are now obituaries at the New York Times and the Telegraph. The IHES has a page at their website.

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