CircleCount helps you better understand Google+

2013-05-21 10:52:12 (14 comments, 0 reshares, 11 +1s)

Is there some epic battle going on in the spam wars that I don't know about? In recent months, the volume of spam comments coming to my blog has increased dramatically, to the point where it is no longer possible to sift through it in case there is a genuine comment lurking there. That's annoying, but not strange in any way. But in the last week or two someone somewhere has worked out a way of getting past the usually excellent Akismet filter, and also past my own defences (that is, identifying a string that occurs in almost all the messages and blocking it). A typical message consists of jumbles of letters that don't even make words, and not enough links to fail to be published. But even that is not what I find odd, though it is very irritating to come back to my blog and find that all visible comments (which are usually replies to comments on old posts -- I could close the comments on those... more »

2013-05-17 20:08:57 (34 comments, 10 reshares, 33 +1s)

If you think that academics should be judged on the quality of what they produce rather than on dubious measures, such as impact factors, associated with where they publish, then there is a declaration that you can sign. It won't be easy to change the culture, but the benefits of doing so would be considerable, and one way to hasten the demise of the current system is to keep reminding people of its defects.

2013-05-17 07:13:54 (1 comments, 10 reshares, 34 +1s)

If you enjoy literary games, then here's one for you. How many independent reasons can you count for Scott Aaronson to explode with anger when reading the following article? I've got to three, but I think there are probably more. (If you don't read Scott's blog then (i) you won't have any idea what I'm talking about and (ii) you should.)

2013-05-14 08:11:22 (0 comments, 3 reshares, 7 +1s)

Busy day in analytic number theory; Harald Helfgott has complemented his previous paper http://arxiv.org/abs/1205.5252 (obtaining minor arc estimates for the odd Goldbach problem) with major arc estimates, thus finally obtaining an unconditional proof of the odd Goldbach conjecture that every odd number greater than five is the sum of three primes.  (This improves upon a result of mine from last year http://terrytao.wordpress.com/2012/02/01/every-odd-integer-larger-than-1-is-the-sum-of-at-most-five-primes/ showing that such numbers are the sum of five or fewer primes, though at the cost of a significantly lengthier argument.) As with virtually all successful partial results on the Goldbach problem, the argument proceeds by the Hardy-Littlewood-Vinogradov circle method; the challenge is to make all the estimates completely effective and to optimise all parameters (which, among other things, requires ac... more »

2013-05-14 08:10:00 (1 comments, 8 reshares, 25 +1s)

Recall that the Twin Prime Conjecture states that there are infinitely many primes p and q such that | p - q | = 2.

http://en.wikipedia.org/wiki/Twin_prime

This has been, to put it mildly, EXTREMELY HARD to prove. An equivalent statement is that there are infinitely many primes p and q such that | p - q | < 3, and so one could try to arrive at a weaker statement, where 3 is replaced by some number N.

Conjecture(N): There are infinitely many primes p and q such that | p - q | < N.

Note that this is very non-obvious, because it may be that the prime numbers get more and more spaced out as they get larger, in the sense that the minimum distance between primes in [M,∞) grows as M grows. We do know that this spacing grows at most linearly, by Bertrand's posulate:

http://en.wikipedia.org/wiki/Bertrand's_postulate

whichs... more »

2013-05-12 21:47:51 (0 comments, 16 reshares, 35 +1s)

This is one of the best newspaper articles I've read on climate change. It's not too long, and it discusses in a measured way what we know and don't know about the effect of increasing the proportion of CO2 in the atmosphere.    The short version is that if there were no complicating factors, then the greenhouse effect would mean that a doubling of CO2 will result in about a 1.2 degrees Centigrade increase in global temperatures before a new equilibrium is reached (between heat coming in and heat going out). But there are complicating factors, namely various feedbacks. For example, an increase in global temperatures causes the atmosphere to hold more water vapour, and water vapour is another greenhouse gas, so that's a positive feedback. Unfortunately, it seems to be easier to think of positive feedbacks than negative ones, though there are at least some of the latter as well. Allt... more »

2013-05-11 09:23:10 (3 comments, 2 reshares, 9 +1s)

If you're in Cambridge tomorrow afternoon (Sunday May 12th) and want to hear one of the great anthems being performed by one of the great choirs, in my totally unbiased opinion on both counts, then go to King's College Chapel for evensong at 3.30, where they will be singing this:

2013-04-26 19:48:24 (53 comments, 9 reshares, 42 +1s)

A couple of days ago I noticed that a recent paper of Green and Tao (http://arxiv.org/pdf/1205.1330v1.pdf) has an interesting style of bibliography: for each paper they give not just the journal where it appears but also an indication of how, if possible, to find it online. Usually this is an arXiv reference, but sometimes they say, "available from the author's homepage". Is this the way of the future? And will whoever publishes this paper allow them to keep all those arXiv references? I very much hope that the answer to the second question will be yes (and that Green and Tao will threaten to withdraw the paper if they are not allowed to keep the bibliography as it is). 

While I thoroughly approve of their bibliography and hope that others will follow this practice (of course, some may already be doing so), I also think that its importance is more symbolic than practical. By that I... more »

2013-04-25 06:50:37 (14 comments, 15 reshares, 32 +1s)

http://blog.stephenwolfram.com/2013/04/data-science-of-the-facebook-world/

2013-04-20 13:55:55 (33 comments, 8 reshares, 25 +1s)

Probably this story, of a student who discovered serious mistakes in a paper by two eminent Harvard economists, should be taken with a pinch of salt, though the BBC programme More or Less is excellent and I trust it more than I would trust most journalism. However, the paper surprises me for a different reason. The main result is that when a country's debt reaches 90% of GDP, its growth is typically significantly reduced. As they put it, 'Seldom do countries "grow" their way out of debts.' They establish this result by looking at lots of countries at lots of times and comparing their growth rates with their debt levels. A natural question that arises is this: is the reduction in growth a consequence of austerity measures that the countries take on? In other words, is it unusual for countries to grow their way out of debt because that strategy doesn't work, or is it unusual because... more »

2013-04-16 17:24:34 (1 comments, 0 reshares, 19 +1s)

Full marks to this man (from near Cambridge) who decided to throw in his day job and do what really mattered to him. I'm thankful not to be faced with that dilemma.

2013-04-15 09:10:44 (12 comments, 3 reshares, 9 +1s)

This grammar test is fun. For the most part the twelve questions are of a kind that mathematicians should do quite well on, as long as they are careful. Despite the title, none of them requires you to know about the subjunctive or about subordinate clauses. Thanks to Emily Gowers for drawing my attention to it.

Edit. Spoiler alert: do not read the first comment on this post if you don't want to be told the answer to one of the questions.

2013-04-14 18:07:39 (2 comments, 13 reshares, 40 +1s)

The results of the experiment to see whether people could detect computer-generated write-ups are now out. Mohan Ganesalingam and I were pleased by how the program did: although its write-ups were the ones most often chosen, they weren't the overwhelming "winners" that we had feared. More details can be found here. Many thanks to all who took part.

2013-04-13 08:56:11 (31 comments, 7 reshares, 22 +1s)

Hypothetical question of the day. Suppose that at some point in the future, while you were still alive, somebody (or more likely some large team of people) produced a computer program that could solve interesting and hard unsolved problems in mathematics. What factors would influence how much you (i) trusted and (ii) welcomed such a program? It would be very useful to Mohan Ganesalingam and me to have an idea of what the views of research mathematicians -- ideally from a broad range of different areas of maths -- are about this. So if you can spare a couple of minutes for a comment, that would be great. 

2013-04-02 19:28:50 (1 comments, 9 reshares, 34 +1s)

Can you tell the difference between computer-generated proofs and human-generated proofs? Here's a chance to find out.

2013-03-29 21:46:48 (11 comments, 3 reshares, 18 +1s)

A recent scientific study purports to show that Dickens is not such a great writer after all: apparently people's ability to tell his writing from that of the very much less well-regarded writer Edward Bulwer-Lytton is no better than chance. There's a quiz one can do online (the one on which the study was based). There are twelve excerpts, and you have to guess for each one whether it is by Dickens or Bulwer-Lytton. I'm glad to say that I did rather better than chance -- I got 10 out of 12 -- so I'm inclined to say that there is a discernible difference between the two writers. However, I had to think quite a bit about my answers, and that in itself was interesting.

2013-03-29 18:28:35 (4 comments, 5 reshares, 22 +1s)

Now all we need is to work out how to get similar emergence from a large group of mathematicians.

2013-03-25 22:21:57 (12 comments, 2 reshares, 14 +1s)

Mathematics hits the headlines yet again.

2013-03-25 09:48:31 (0 comments, 9 reshares, 21 +1s)

If you know the basic theory of metric spaces and would like to be a subject in a small experiment, then you would be doing me a big favour. Participating will take a few minutes. Many thanks in advance.

For reasons connected with the experiment, I have disabled comments on this Google plus post.

2013-03-20 12:20:12 (5 comments, 28 reshares, 47 +1s)

And the winner is ...

2013-03-19 18:25:06 (2 comments, 12 reshares, 27 +1s)

For those who like that kind of thing, the winner of the 2013 Abel Prize will be announced tomorrow and the announcement will be streamed live from the Norwegian Academy of Science and Letters. The ceremony starts at 12:00 Norwegian time. I am writing this from Oslo, because, as I was for the last two years, I am the person whose job it is to give a short presentation of the winner's work for a general audience. More about that when the announcement has taken place.

2013-03-11 15:13:52 (11 comments, 4 reshares, 17 +1s)

How about this for a novel technique for demonstrating that global warming is not a serious problem? You just plot temperatures on a graph with the scale of the y-axis chosen so that the range of temperatures occupies only a small fraction of it. (Oh, and start in 1997 just for good measure, but that trick is well known.) It would be funny if it weren't for the fact that there are people in power who take this kind of thing seriously.

2013-03-07 21:03:14 (11 comments, 24 reshares, 34 +1s)

I have sometimes said that the main use of journals is as a stamp of quality, and the main use of that stamp of quality is enabling people to come to quick judgments when they haven't got time to look in detail at papers -- as is the case, for example, if they have to come up with a shortlist from hundreds of job applicants. Once the shortlist is drawn up, other factors come in such as ... er ... what's actually in the papers and whether it is interesting and important. Anyhow, it seems that even using journals as a crude measure is a highly suspect practice in science. It's hard to believe that the conclusions of this article apply to mathematics -- surely an article published in the Annals is, on average, genuinely better than an article published in, for example, the Journal of the LMS. But probably a corresponding statement would seem obviously true to people in the medical sciences. It... more »

2013-03-06 19:57:08 (1 comments, 3 reshares, 6 +1s)

The new chairman of EPSRC has commissioned a review into EPSRC's decision-making process. After talking to academics, “He found that the strongest concerns were that EPSRC is putting short-term impact ahead of academic excellence, that it is micromanaging the grant portfolio to achieve this, and not taking sufficient advice from active researchers.”

One of the people on the panel is Dr Suzanne Fortier, outgoing President of NSERC, the Canadian counterpart of EPSRC. Nassif Ghoussoub says, "Weren’t these exactly the same concerns that the Canadian scientific community had expressed about Madame Fortier’s dirigisme at NSERC during the past six years?" It will be interesting (to UK scientists at any rate) to see what the review has to say.

2013-02-25 23:06:50 (18 comments, 6 reshares, 61 +1s)

One of the things I like about being both a father and a mathematician is watching how children's understanding of mathematics develops in tiny steps. In this connection, I was delighted by something that happened a few days ago. I asked my five-year-old son what 7+4 was. He answered 11. I then asked him how he knew. He said, "Well, 6+4=10, so 7+4 must be 11," or words to that effect. I liked his answer for two reasons. The first is that I am very keen on the idea that the facts that we remember are not isolated but linked together in a complex web that greatly reduces what would otherwise be the excessive demands all those facts would place on our memories. It was great to see that happening with something as simple as 7+4. The other reason occurred to me only today, which was that my son was showing an intuitive grasp of the definition of addition in Peano arithmetic: that s(m)+n=s(m+n),... more »

2013-02-23 09:41:22 (6 comments, 9 reshares, 30 +1s)

White House response to the open access petition.  The Whitehouse has:

issued a memorandum today (.pdf) to Federal agencies that directs those with more than $100 million in research and development expenditures to develop plans to make the results of federally-funded research publically available free of charge within 12 months after original publication.... while this new policy call does not insist that every agency copy the NIH approach exactly, it does ensure that similar policies will appear across government.

2013-02-19 20:41:57 (19 comments, 3 reshares, 26 +1s)

I have just had my first experience of benefiting from Elsevier's move last year to open up their back catalogue. I needed to look up a paper of Ajtai, Komlós and Szemerédi that was published in The Journal of Combinatorial Theory A in 1980 (proving a sharp upper bound for the Ramsey number R(3,k)). It was difficult to find online, but Googling was eventually enough to get the exact title, and when I Googled that I got a link to the paper on ScienceDirect. There, instead of being asked to pay, I found a link that said "pdf", and when I clicked on it, up came the paper. Nice and simple. I mention this in the interests of balance ...

2013-02-13 20:35:06 (9 comments, 4 reshares, 11 +1s)

A hybrid journal is a subscription journal that offers its authors the option of paying an article processing charge in return for the article being made freely available online. I am not at all in favour of this model, since it doesn't do anything to solve the problem of excessive journal costs. If anything it does the reverse. Societies like the LMS have open-access options, and they tell us that the take-up is extremely low.

In an interesting twist, the AMS has defined a variant of the hybrid model where instead of having an open-access option, you have a companion open-access journal, which you call <name of journal> series B, which has an article processing charge. The companion journal shares an editorial board with the original journal, and you don't decide which you are submitting to until your article is accepted. As far as I can tell, there are two differences between this... more »

2013-02-11 10:57:09 (20 comments, 10 reshares, 30 +1s)

Benoît Kloeckner has drawn my attention to this, an initiative where the peer review process is separated from the publication process. The idea is that papers get submitted anonymously to a peer review site and reviewed anonymously. After that, editors can bid for papers they like the look of, or authors can submit papers that have already been peer reviewed, thus saving everyone a lot of time. One can see possible objections of course -- but that's true of everything. For example, most editors want their references from people whose judgment they know they can trust. But even if there is a significant fraction of papers for which this is not so important, the initiative could be interesting. According to Benoît, it is actually being put into practice in the life sciences.

2013-02-02 17:54:50 (14 comments, 7 reshares, 37 +1s)

In broad terms, open science is the principle that as much of human knowledge as possible should be freely available to everybody. What would the exact opposite of this principle be? It would be that some knowledge that could in principle be shared should in fact be available to nobody. A good example of this principle was to be found in Timbuktu a few days ago. Rightly or wrongly, I feel more emotional reading about this than I do reading about people meeting violent deaths: I am inured to the latter but not to the wilful destruction of knowledge.

2013-01-28 17:25:14 (4 comments, 10 reshares, 37 +1s)

The Invariant Subspace Problem asks whether for every bounded linear operator T from a Hilbert space to itself there must be a non-trivial subspace X such that T(X) maps into X. In many situations, the answer is known to be yes. For example, if you can do something like diagonalization -- that is, express your Hilbert space as a function space with respect to which the operator becomes a multiplication operator -- then the answer is clearly yes. A counterexample would be an operator T such that for every point x the sequence x, Tx, T^2x, ...  generates a dense subspace.

The problem is one of the most famous in mathematics. My money was on a counterexample, but now Eva Gallardo and Carl Cowen have announced a positive solution. I am treating this news cautiously, since as far as I can tell they have not released a preprint. But as a piece of gossip that might turn out to be much more than that, I... more »

2013-01-16 18:48:41 (13 comments, 68 reshares, 76 +1s)

I have just put up a short post about a new initiative -- a platform that is due to come online in April -- that will, if successful, make it easy to set up arXiv overlay journals. I think it stands out from other, similar-sounding initiatives because it seems to have serious institutional back-up and funding and is intended specifically for mathematicians (in the first instance at least). I'm keen for its existence to be as widely known as possible, so as to maximize its chances of becoming part of the publishing landscape for mathematicians. It may even double up as a post-publication review site, but many details are yet to be worked out. It is called the Episciences project.

The title of the post is a reference to my previous post, which is called "Why I've joined the bad guys."

2013-01-12 23:16:59 (4 comments, 15 reshares, 47 +1s)

Aaron Swartz committed suicide yesterday. He was being pursued for downloading large numbers of JSTOR articles, which he believed should be freely available but had not got as far as distributing. (JSTOR were not the ones pursuing him.) More details can be found in this article, or just by looking for them on the internet.

2012-12-23 16:04:19 (1 comments, 12 reshares, 33 +1s)

MathJax in Google+!

Let's make this happen! Vote!!

2012-12-15 15:06:57 (12 comments, 9 reshares, 59 +1s)

A few days ago I was asked whether I would be prepared to add my name to a letter to the Daily Telegraph calling on the Government to issue a formal pardon to Alan Turing for his conviction for homosexuality, or, as it was called, gross indecency, a conviction that led to his suicide a couple of years later. I normally think carefully before signing anything, but this felt like a pretty easy decision, so I agreed immediately.

But nothing is ever simple. The first surprise was that the letter attracted a great deal of attention, which in retrospect I realize I should have expected, since Stephen Hawking was another signatory. The next surprise was that I was invited to appear on about four TV news programmes and one on the radio. I was quite reluctant, because I hadn't thought about the issues enough to feel confident that I could defend the pardon against a determined attack, but eventually I... more »

2012-12-10 10:10:33 (1 comments, 14 reshares, 25 +1s)

Factor Dance

2012-12-09 08:37:43 (26 comments, 3 reshares, 7 +1s)

I've just chanced on a puzzling blog comment picked up by my blog's spam filter. It says the following: "When teaching the integration method of u-substitution, I like to emphasize its connection with the chain rule of integration. Likewise, the intimate connection between the product rule of derivatives and the method of integration by parts comes up in discussion." What's puzzling about it is that it is interesting enough, and relevant enough to the post, to count as a legitimate comment, but it comes from a website that advertises investing in gold bullion: in particular, if I were to accept it, then anyone who clicked on the username (gold account) would reach that website. The latter means that I won't accept the comment, but I'm still curious to know whether it is genuine spam of a new and seemingly highly sophisticated kind, or whether it's a comment that has got... more »

2012-12-05 21:23:00 (1 comments, 9 reshares, 23 +1s)

It's been a long time coming, but the Cost of Knowledge petition has recently passed 13,000 signatures. 

Meanwhile, just to remind you what it's all about, here's most of an email that Martin Huxley wrote to an Elsevier sympathizer and shared with me. I'm reproducing it with his permission.

"On the matter of pricing of mathematical journals, you appear to be talking through your hat. I have been the library liaison for the Mathematics Department in Cardiff, so I have had to look at the prices charged to universities for the various journals. Elsevier is far and away the most skilful user of Gresham's Law. There are two main classes of Mathematics journal: the learned journal, published by a local scientific society, and the commercial journal, produced by a big European publisher; there are probably American publishers in it too, but no example springs to... more »

2012-11-21 20:21:23 (1 comments, 6 reshares, 16 +1s)

Here is my suggestion on how to deal with traditional scholarly publishers: innovate over the top of them.

This should interest +Timothy Gowers , +Terence Tao and +Michael Nielsen 

2012-11-11 18:23:01 (43 comments, 9 reshares, 43 +1s)

Here's a parenting dilemma. A son of mine has just turned five. A couple of days ago he was shown a film at school about the life of Jesus. He was full of it that evening, and told us that Jesus had been killed and had come to life again. I am pretty sure that this was presented to him as fact (we are now going to see a film about a remarkable man who lived 2000 years ago, or something along those lines). What is the right thing to do? I see two main arguments.

1. Relax about the whole thing. It doesn't bother you that he believes in Father Christmas. Similarly, he will have an entire growing-up process during which he will learn that the physical resuscitation of Jesus is, to say the least, disputed. Better not to undermine the school where he has just gone.

2. Don't relax about the whole thing. Implanting religious memes in five-year-olds is taking advantage of their... more »

2012-11-05 18:39:34 (13 comments, 4 reshares, 16 +1s)

In which I try to convince myself that a 1/1000 risk of death is not worth getting unduly worried about.

2012-11-04 21:10:34 (13 comments, 7 reshares, 35 +1s)

Here's the difference between what it's like to look up journal articles and what it should be like.

What it's like: Just now I wanted to read an article related to certain medical treatments relevant to me. The article is published in the Lancet, a top medical journal published by Elsevier. Fortunately, Cambridge University subscribes (at vast expense) to Science Direct, the site where you can get access to all of Elsevier's journals. So I try to log in to Science Direct and am told I can't. The error message tells me there is a system error and to get in touch with the Help Desk (no link given) if the problem persists.

What it should be like: I Google the title of the article, click on one of the first few entries, and read the article.

Actually, let me say in more detail what happens when I try to log in. I first log in, and that appears to be... more »

2012-11-03 16:05:22 (8 comments, 8 reshares, 20 +1s)

I recently passed the air traffic control tower at Edinburgh airport (http://www.geograph.org.uk/photo/1846635), and immediately sensed that it was not a mathematically natural shape. That sense was easy to justify: for a non-zero section of the tower the slope was vertical, and yet the tower wasn't a cylinder (but it had rotational symmetry). I was with another mathematician and we started speculating about how acute this sense that mathematicians have is. For example, would we instantly notice that something was wrong with a curve if there was a jump in its second derivative? By pure coincidence, I stumbled on a closely related discussion today. It's worth reading not just the post but also the discussion that follows it.

2012-10-30 14:39:15 (33 comments, 132 reshares, 209 +1s)

I've just been told about a calculator that refuses to give you the answer unless you first give it a reasonable estimate. Apparently, it has had remarkable and positive effects on the willingness of young people to engage with mathematics. Designing it was difficult, because what constitutes a "reasonable estimate" is much subtler than just a tolerance for being out by a certain percentage. For example, the calculator does not consider 102 to be a reasonable estimate for 10 times 10, but it would consider 2.2 to be a reasonable estimate for the square root of 5. 

I don't know whether it lives up to its hype, but it's an ingenious idea and I wouldn't mind getting my hands on one.

2012-10-29 11:39:47 (1 comments, 7 reshares, 8 +1s)

If you haven't seen Japanese speed addition - the world's fastest numbers game - then it's worth a look.

2012-10-25 10:00:45 (2 comments, 0 reshares, 4 +1s)

Starting with the recent cabinet reshuffle, there has been a steady trickle of news items showing an anti-science drift to the British government. I think David Cameron has sensible views but would rather pander to rightwingers than act on those views. (Maybe one could level a similar accusation at Obama -- I read that climate change was not mentioned during any of the debates.) Anyhow, the latest annoying piece of British news is that Peter Lilley, a climate change sceptic, has been appointed to the House of Commons energy and climate change select committee. In a debate in 2009 he said, "The simple fact is that the science is not resolved." His views are of course entirely unrelated to the fact that he is a director of the oil company Tethys Petroleum, the mission statement of which is this. "Tethys Petroleum's mission is to create shareholder value by building an oil and gas... more »

2012-10-22 17:12:02 (9 comments, 4 reshares, 9 +1s)

Does anyone know any details about this case? In particular, have scientists been sentenced to prison merely for failing to predict something that is inherently unpredictable, or was there genuine negligence involved? Either way, it's a pretty extraordinary story.

2012-10-20 14:43:08 (7 comments, 3 reshares, 19 +1s)

At last, a thorough discussion of the issues facing America. (With thanks to someone I got this from but can't relocate.)

2012-10-15 22:24:28 (14 comments, 8 reshares, 44 +1s)

Something I've advocated a few times is using the internet to collect and organize mathematical knowledge of a kind that is not conventionally publishable but nevertheless potentially very useful. One of many examples might be a promising-looking strategy for solving an open problem together with a convincing argument for why the strategy is unlikely to work. You can't publish that, but you could save time for other people by making it known on, say, some central database that had a section on that problem.

Obviously I'm not the only person to have had this kind of thought. But I was quite surprised to learn recently that my great great grandfather William Gowers, who was a neurologist active in the late 19th century, expressed an almost identical wish over a century ago. (I learned it from an aunt of mine who has recently written a biography of him.) Here are his words from an... more »

2012-10-13 15:21:13 (7 comments, 3 reshares, 16 +1s)

Apologies if you've ben told this 100 times already, but if you type the phrase "completely wrong" into Google images, you get an interesting result. For an explanation of why you get that result, stick with Google itself.