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Timothy Gowers
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Timothy Gowers

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This is fun to read. I can't help being reminded of a recent post by +Richard Elwes about how we can learn from how babies learn. Conway, it seems to me, has benefited enormously from a conscious decision to adopt a childlike attitude to mathematics, following whatever he finds interesting without paying too much attention to what others will think of him.
The long read: John Horton Conway is a cross between Archimedes, Mick Jagger and Salvador Dalí. For many years, he worried that his obsession with playing silly games was ruining his career – until he realised that it could lead to extraordinary discoveries
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Here is a quote from Grothendieck (Récoltes et Semailles)
“Discovery is the privilege of the child, the child who has no fear of being once again wrong, of looking like an idiot, of not being serious, of not doing things like everyone else.”
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Why do tennis players serve differently when it's their first serve? Here are two arguments that go in opposite directions.

Argument 1. The first time round, they can afford to take a bigger risk on their serve, because they'll have a second chance if they miss.

Argument 2. If the first-serve probability is p, the probability of winning the point given that the first serve goes in is q, the second-serve probability is r, and the probability of winning the point given that the second serve goes in is s, then to maximize your chances of winning, you should do a "first serve" if pq>rs and a "second serve" if rs>pq.

The second argument, though it has a certain plausibility to it, is wrong, for the following reason: it ignores the fact that if it's your first serve, then you don't have to win the point, as long as you lose it by missing your serve. So it's wrong to say that you are aiming to maximize the probability of winning the point during that rally.

So what is the right strategy, for given p,q,r,s? If it's your second serve, then you've got just one attempt, so Argument 2 is correct in that situation. That is, you do a second serve if and only if rs>pq, which presumably it is for most tennis players (though I'd be very interested to see whether there are in fact some players who in some matches would have been better off doing first serves all the time). 

As for the first serve, let's assume that rs>pq. If you actually do a first serve and then follow up with a second serve if you miss it, then your chances of winning the point are pq + (1-p)rs. If you do second serves both times, then your chances are rs + (1-r)rs. So it's better to do a first serve on your first serve provided that p(q-rs)>rs(1-r), or equivalently rs-pq>(r-p)rs. I can't quite get my head round what the right-hand side means here, but let's take an example or two. Suppose that p=1/2, q=1, r=1, s=2/3. (That is, your first serve is devastating if it goes in, but does so with only a 50% chance, and your second serve always goes in but leads to only a 2/3 chance of winning the point.) Then rs-pq = 1/6, and (r-p)rs = 1/3. In that case it would be better to do a second serve on your first serve. 

Suppose now that p=1/2, q=1, r=1, s=1/2. That is, a first serve with a 50% chance of going in guarantees the point, whereas a second serve that's guaranteed to go in gives you a 50% chance of the point. Here it's rather easy to see why doing a first serve is better: you have a 50% chance of winning the point there and then, but if lose it you get a second chance, whereas for a second serve it's the same but without the second chance. Doing the arithmetic, we find that rs-pq = 0 and (r-p)rs = 1/4. Since there's a non-zero difference, we can perturb these numbers a little bit and get an example where pq<rs but it's still better to start with a first serve.

Now let's see whether Djokovic and Federer got their tactics right in the Wimbledon final this afternoon. (Before doing the calculation, I strongly expect the answer to be yes, since being good at judging the percentages must surely give you the edge as a professional tennis player.)

For Djokovic we had p = 0.66, q = 0.74, r = 1 (approximately) and s = 0.6. So pq<rs, which is a good start, as it shows that Djokovic was right not to do first serves for his second serves. But also, rs - pq was approximately 0.11 and (r-p)rs was approximately 0.204, which was indeed bigger.

For Federer the figures were p=0.67, q=0.74, r=1, s=0.49. Interestingly, pq = 0.4958, so it looks as though Federer would have done minutely better by doing first serves all the time. (Of course, there may well be other factors to take into account, but still I find this interesting.) Not surprisingly in the light of this, given that pq and rs are at least approximately equal whereas (r-p)rs is distinctly positive, he was definitely right to do first serves for his first serves. 

Based on this little experiment, I'd be willing to bet that many tennis players play suboptimally in many matches in this simple respect. Of course, I've oversimplified things quite a bit since there are different levels of risk one can take even with a first serve. So let's do the very slightly more complicated analysis. Suppose that if your serve goes in with probability p, then your probability of winning the point is f(p). Here f(p) decreases as p increases: given that it goes in, a safer serve is less likely to lead to your winning the point.

Then when it's your second serve, you should choose p to maximize the product pf(p). That's straightforward. Suppose that that maximum value is t. Then if your first serve goes in with probability p and you do the right thing for your second serve, then your probability of winning the point is pf(p) + (1-p)t, so you want to maximize p(f(p)-t). That is equivalent to maximizing log(p) + log(f(p)-t), so you want 1/p + f'(p)/(f(p)-t) to be zero. (Note that f'(p) is negative.) Equivalently, you want p to equal (f(p)-t)/(-f'(p)). Or -pf'(p) = f(p) - t. Here the right-hand side measures the advantage you get, if your first serve goes in, over your winning probability if it doesn't go in. The left-hand side seems harder to interpret: certainly I don't see an intuitive explanation for why the maximum should occur at a p for which this equation is satisfied, or an intuitive explanation of how you should choose the risk level of your first serve.

Can we at least show that a first serve should be riskier than a second serve? Suppose we take p = r+delta, which results in q = s - eta, with delta and eta small. Then to first order rs-pq = eta p - delta q, while (r-p)rs = delta rs. It's possible for eta p - delta q to be pretty small but positive, so it looks possible that for some players it's best to do second serves all the time. I think I may be such a player -- my second serve is risibly bad but its chances of going in drop off very quickly if I try to make it harder to return.
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Wow, I'd never watched that. Back in 2001 I was so disappointed by Ivanisevic just edging out Tim Henman in the semifinals that I wasn't very interested in the final. I took a small relief in the fact that Henman lost to the eventual champion (and would probably have lost to Rafter). Had I known about Ivanisevic's unconventional approach, my pleasure at the result would have been much greater. 
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An approach to climate-change campaigning that hadn't occurred to me: a group of 866 Dutch citizens have successfully sued their government for failing to protect them against it. The court has ordered the Dutch government to reduce its emissions by 25% in five years. Of course, it isn't at all clear what will actually happen as a result of this ruling. The article suggests that it will provoke people to try similar lawsuits in other European countries. Apparently US law is such that this approach would be unlikely to work there.
Dutch ruling could trigger similar cases worldwide with citizens taking their governments to courts to make them act on climate promises
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I wish there are laws around the world which can hold government responsible for their negligence and I think Africa won't be in a huge mess as it is today. I am jealous of Europeans! It is a confession.
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Here's a fine example of open peer review in mathematics. It is written as a blog post, and the authors have commented on the post, saying that they have made changes to their paper in response to it. The review is polite and positive, but not fawning or afraid to make minor criticisms here and there. And we, the readers, now have a far better idea of how interesting/important the paper is than we would be able to deduce from the mere fact that it has been accepted by such and such a journal.
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Lots of people are publishing their reviews, including me.  Check out Publons: https://publons.com/
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This is an extremely entertaining (and somewhat frightening) article by the same person who had a nonsense paper accepted by multiple open access journals. Worth reading in full for the details of how he did it.
 
The Dark Chocolate Science Heist

...or how a small group of scientists and journalists fooled millions into believing that chocolate helps weight loss. This is their story. One of the journalists reveals the process and why they did it.

This is an excellent article that really puts parts of science journalism (and science) into perspective. And it's the sort of bad journalism that the chocolate heisters (dibs on the band name) are bringing attention to that inspired me to start blogging about physics.

Thanks to +Jeanne Clelland for the link.
“Slim by Chocolate!” the headlines blared. A team of German researchers had found that people on a low-carb diet lost weight 10 percent faster if they ate a chocolate bar every day. It made the front page of Bild, Europe’s largest daily newspaper, just beneath their update about the Germanwings crash. From there, it ricocheted around the internet and beyond, making news in more than 20 countries and half a dozen languages. It was discussed on tel...
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"Attempt to shame journalists with chocolate study is shameful" https://goo.gl/qAhBZP
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I've been meaning to post for a long time to give an update on my 4-year-old daughter's reading and my 7-year-old son's mathematics. The result of the delay is that I'm a bit hazier about some of the details that I found fascinating at the time, and some of what I say is more like a reconstruction based on this hazy memory than a 100% accurate reporting of what happened.

I'll talk about my daughter in this post and save my son for another one. For a long time I had been working to get her to the point where she could reliably answer questions of the form "What does P - I - G make?" By the way, I pronounce the letters puh i guh and not pee eye jee, so there is a direct connection between the sounds of the letters and the simple words that they make, though even then there is a highly non-trivial rule for a young child's brain to induce from the data -- that you have to remove those "uh" sounds and then "concatenate" what's left. Anyhow, she had become very reliable at those, and the rule was firm enough in her mind that she could do more complicated examples like "stop" or "glad". So it seemed like a good moment (I think this might have been February or March) to make a start on two other important stages in learning to read: learning the sounds made by letter combinations such as ch, sh, th, ee, oo, etc., and learning to recognise familiar words such as "the", "here", "my", etc. 

Before I say what happened, I want to say a bit about where I stand in the debate about the respective merits of what in this country have been called the phonics method of teaching reading and the look-say method. Roughly, the phonics method is to teach children what sounds the letters make, so that they can work out what words say, whereas the look-say method teaches recognition of whole words, from which, I suppose, the child is supposed to pick up regularities and begin to be able to make predictions about further words that come her/his way. 

I used to be very firmly in the phonics camp and contemptuous of the look-say method. But my position is a little different now, and if I had to use one word to describe it, it would be "Bayesian", which turns out to include both phonics and look-say aspects, but with a qualification that I'll come to. (By the way, I don't for a moment imagine that these ideas are original to me, even if I did come up with them independently. As usual when I make this remark, which I do frequently, if anyone knows where essentially these ideas can be found in the literature, then I welcome being told about it.)

The basic idea behind a Bayesian approach is that the effort needed to learn a new piece of information (such as how to read a particular word) should be thought of not as the number of bits needed to encode that piece of information in isolation, but the number of bits needed to encode it given what you know already. I don't want to get too mathematical here, so I won't say how this idea of conditional information can be made precise -- suffice it to say that it can. Instead, let me give a couple of examples. Suppose you have "got" the rule that when your doting father asks "What does cuh a tuh make?" you have to remove those "uh"s and run the remaining sounds together. Then when that same doting father asks, "What does buh e duh make?" you will not need any effort of memorization to be able to answer "bed". By contrast, with a purely look-say approach, the fact that the visual stimulus BED is associated with the sound "bed" is a completely different fact from the relationship between CAT and "cat", so memorization is needed. 

But I've ignored some subtleties there. For instance, as I've discussed in previous posts, my daughter didn't go from zero to understanding the rule in one gigantic step. Rather, I had to reduce the burden on her by doing things like asking her to read the word "dog" when there was a picture of a dog right next to it, or asking her to read "rat" when she had just read "cat". Note that in both these examples, one could argue that the conditional probability (in advance) that the correct answer is what it in fact is is higher than if the questions were asked without the accompanying clues: if there is a picture of a dog, then it is much more likely that "dog" is the right answer, and if CAT makes "cat" then it is much more likely that RAT makes "rat".

A second subtlety is that English pronunciation is full of regularities that are usually not formulated explicitly as rules. One that I noticed two or three years ago -- and here I should make clear that I am talking about the pronunciation of the particular kind of English that I myself speak, which is far from universal -- is the strange effect of the letter W on the letter A. Roughly speaking, it turns an A into an O. A few examples: "war" rhymes with "or", "wart" rhymes with "fort", "wattle" rhymes with "bottle", "want" rhymes with the first syllable of "ontological", "wally" rhymes with "dolly", "wad" rhymes with "cod", and so on.

But as with many rules of this kind, no sooner have you noticed it than you start to notice a whole lot of exceptions: "wag" rhymes with "bag", "wacky", as in the Wacky Races, rhymes with "tacky", "wall" ... well, that's an interesting one, because another rule seems to take priority, which is that words ending "all" such as "hall", "tall", "ball", all rhyme with each other and with the word "maul", and again I could go on. Part of that going on would be to detect not just exceptions but regularities within those exceptions and exceptions to those regularities, and so on.

What explains the fact that an adult reader of English who reads of a fictional place called Wapplesford, will instinctively pronounce the first syllable to rhyme with "shop" and not with "clap"? We are not told about a rule to this effect. Rather, we become familiar with a number of words and make a guess based on those words. So there is clearly something to the look-say method after all. 

As an aside, I would like to say that if somebody makes the mistake of thinking that (x+y)^2 = x^2+y^2, then you should not think of that person as stupid. They are using a very important mechanism of thought -- saving mental effort by guessing that unfamiliar situations will be similar to familiar ones -- that happens to give the wrong answer in this case. I'm not sure what the best way is to convey the point that the rule "Mathematical operations tend to distribute over addition" is nearly always false, but it's not an unreasonable thing to think when almost all the instances of f(x+y) you have come across are when f is multiplication by a constant.

The problem with the look-say method if that is all you use is that the process of induction (in the scientific sense) of the rules is very hard. If you learn the words "not", "come", "go", "home", "above", and "move" as single entities, what are you going to make of the role of the letter O? A much better method, in my view, is to learn the phonic alphabet (that is, a, buh, cuh, duh, e, fuh, etc.) and how to use it to make simple three-letter words, and only then to move to recognising whole words. The point then is that after you have done that, you no longer have to learn how to read entire words in isolation from any system, but rather how the way words are pronounced differs from what you might otherwise have expected. And a few more rules make that process easier still. Suppose, for instance, that you have been told that the reason "home" is pronounced the way it is is that the final E (which some people call a magic E) makes the O (as in "hot") say Oh. Now let's look at the list of words given earlier. The word "not" is straightforward. "Home" follows from the magic-E rule. "Go" doesn't follow from any rule the child has been taught, but at least the idea that an O can be pronounced Oh is familiar, and there is an additional rule that is extremely helpful, namely that words you see in books are actually words. Furthermore, the correct pronunciation of a word often resembles the pronunciation you get from blindly following the rules, even if it isn't quite the same: we have something like an error-correcting code here, where we pass from what we see to the word that is closest to it. So it isn't hard to learn to read the word "go". And once that's been done, it is even easier to read "so" and "no" and "ho ho". 

In order to get my daughter started on recognising common short words, I dug out some books from a reading scheme that everyone in the UK of a certain age is familiar with: Peter and Jane. (The main drawback with these books is what to a twenty-first-century sensibility comes across as the most incredible sexual stereotyping -- Jane is always helping Mummy put out the tea while Daddy is showing Peter how to put oil in the car and things like that.) These books introduce words one or two at a time, so the first few books in the series have an extremely limited vocabulary, and are therefore full of sentences like "Peter likes the toy and Jane likes the toy." This has a marked effect on the conditional probabilities: for example, if the context is such that a main verb is expected, then that verb has a very good chance of being "likes". So my daughter will often look at a word like "is" and say "likes". And just as with (x+y)^2=x^2+y^2 this is actually an indication that her brain is working in the right way, though remaining patient when she does it for the tenth time is a challenge. 

Here are a few other interesting (to me at any rate) things I've noticed.

1. She had no difficulty with the words "some" and "come", guessing them without my having to say "These are strange words and the O is pronounced Uh". That illustrates very well the principles I discussed above: there just aren't very many words that fit the pattern S-vowel-M (maybe also she had picked up that final Es are not usually sounded) or C-vowel-M, especially when the sentence context is taken into account. 

2. By contrast, the word "the" is still a real problem. I've told her countless times what it says, but she still hasn't got to the point where she reliably recognises it. That said, she often does recognise it because often it is followed by "dog" and she knows the book well enough to know that the phrase "the dog" occurs frequently. I've also told her frequently what TH makes, but this still hasn't sunk in. 

3. It is possible for me to tell her what "the" says, and for her not to know what "the" says one line later (and there are very few words per line in the early books). However, if I make her spell it out, it increases the chances that she will be able to read it.

4. Sometimes she finds "the" fairly easy to read, but still can't read "The". This suggests that a certain degree of (phonetically informed) whole-word recognition is going on.

5. Back when I first started with the Peter and Jane books, she had a problem recognising the letter Y, because in the font they used a lower-case Y was not made of two line segments but was more like a lower-case G with the top removed. She would read it as a G. It was as though her brain was a neural network that was not yet fully trained (which is presumably because that is exactly what it was), so it picked up on the way the tail of the letter curved round underneath a curvy shape above, without realizing that there were two letters that could be described that way that needed to be distinguished from one another. 

6. When we started, she was very enthusiastic, and pleased that she had managed to get through an entire book. We got through the first couple of levels in the series and made some headway with the third, but that was quite a bit tougher and in the end we both lost enthusiasm and didn't do much reading for a while. Then when we came back to it, she had improved as if by magic. Of course, during that time she had had plenty of opportunities to spot more patterns, with the help of the knowledge she already had.
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Reading is a strange thing, because once you have learned how to read, you never sound out words and when you have to sound out every word it is both slow and frustrating.  My wife learned how to read before going to school and without her parents teaching her.  Neither she nor they could explain how this happened.  I, on the other hand, struggled mightily to learn to read, and it took years.  I think I was put off with endless struggles to sound out words, and it discouraged me from trying to read on my own.  My point is that people are different and the best method for one may not be best for another.  And, finally, that the jump quickly from "sounding out" to "recognition" enough for getting the gist of reading simple books on your own can be both a motivator and a learning experience.
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Timothy Gowers

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Now an entire country is boycotting Elsevier. It is fitting that that country should be the country of origin of the company itself, though now Elsevier is much more international. The situation is a little bit complicated, because what the Dutch are asking for is not obviously what they should be asking for. They say that if they are paying very large subscription costs, then they should not have to pay any more to publish with open-access options. That is, their subscription costs should cover any APCs that Dutch academics might incur with Elsevier journals. The end game they would like is one where everyone has moved over to the Gold Open Access model. It is natural that Elsevier should resist this, since they are raking in a lot of money through APCs paid to "hybrid" journals without lowering their subscription costs to those journals. (They have a different interpretation of the data, needless to say -- they argue that the reason subscription costs haven't gone down is that they are offering more content. That argument would have more force if universities had the option of declining this extra content and paying less, but of course they don't.)

I don't object to the existence of Gold Open Access journals, especially in subjects like biology and medicine, but I do object to the idea that this should be a near-universal model. However, on balance I think that the Dutch boycott is a good thing, especially if they stand firm and come to realize that they can manage reasonably easily without Elsevier journals. The hope is that that will embolden other countries and help us all to reach the long-awaited tipping point that will surely come eventually.

In the mean time, if you were wondering whether to publish in an Elsevier journal, bear in mind that your Dutch colleagues will have difficulty reading it -- unless, that is, you have made it freely available online. So far, the Dutch boycott consists in their refusing to pay for the Elsevier Big Deal -- i.e., to subscribe to Elsevier journals on their outrageous terms -- but if Elsevier still won't budge then they will consider asking Dutch academics not to referee for, or submit to, or do editorial work for, Elsevier journals. That would constitute a dramatic increase in the number of people boycotting Elsevier (from the current 15,140 who have signed up to the Cost of Knowledge boycott).
A long running dispute between Dutch universities and Elsevier has taken an interesting turn. Yesterday Koen Becking, chairman of the Executive Board of Tilburg University who has been negotiating with scientific publishers about an open access policy on behalf of Dutch universities with his ...
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+Timothy Gowers There are some more developments in the Netherlands. A recent law enforces that academics affiliated with a Dutch university have the right to publish their  articles openly. However, few (mathematical) articles are published under Dutch copyright law.
http://www.uu.nl/en/news/right-to-open-access-laid-down-in-copyright-act
Apparently, a similar law exists in Germany. What is keeping the UK?
https://blogs.ucl.ac.uk/copyright/
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If you aren't already making sure your papers are freely available online in preprint form, then here's a good reason to start now: it means your colleagues in Greece will be able to benefit from your insights.
The country's economic crisis is hitting researchers hard.
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Some people have started something called biorXiv, but I don't think it has caught on yet, and I think biology journals are much less likely to tolerate people putting their preprints there than maths journals are to tolerate the arXiv. Of course, I hope this will change.
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One of my favourite jazz musicians, Ornette Coleman, died today. In the 1960s he was a pioneer of so-called free jazz, the freedom being from the constraints of sticking rigidly to a given harmonic sequence that repeats itself over and over again. But that didn't mean that anything went, especially in his early period, which is the period I like most. What I like about his music is the quirky tunes, the pianoless sound (annoyingly for me, given that the piano is my instrument, I particularly like pianoless jazz, where your brain has to fill in the harmony rather than having it spelt out), the tone of his plastic saxophone, which often feels very like a human voice, and his melodic sense. He sometimes plays out of tune, which would normally bother me a lot, but with him I find it an essential part of his sound and something I wouldn't want to change. The video below is of the first record of his that I got to know. My father introduced me to it when I was a teenager. He didn't really like it and played it to me in order to explain why not. (At one time he used to be jazz critic for the Financial Times, and it may well have been a record he got given in order to review it.) But I ended up developing a taste for it. 
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Here's a more recent rebroadcast from +BBC Radio 3. The streaming service is available (27 days and counting) which may be of interest to those of us outside the UK, since for some reason streaming is not region restricted.  As with the earlier programme, however, the mp3 file is available only for those who pay the license fee.
Geoffrey Smith salutes the legendary free-jazz maverick and saxophonist Ornette Coleman, who died this week, in a tribute first broadcast in January to celebrate his 85th birthday. http://goo.gl/v5q2xv
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GCSE (General Certificate of Secondary Education) is a school exam taken in the UK (minus Scotland where they have something else) when you are about 16 and have two years of school left. For a long time, there have been accusations of grade inflation, which have some plausibility given that (i) the exams do seem easier now and (ii) exam boards compete to get schools to take their versions of the exams. The government has made attempts to make the maths exam more "rigorous" and this is the first year of the new-look papers. One question has caused outrage on Twitter because many people thought it was much too hard. The question is as follows. (I haven't actually managed to find the exact wording, so this is a reconstruction from what I have read about it.)

Hannah has a bag of n sweets, of which six are red. She takes two sweets at random from the bag. The probability that they are both red is 1/3. Prove that n^2-n-90=0.

I think that the question rather coolly doesn't go on to ask for the value of n, but I may be wrong about that. 

Here is what I imagine was the intended solution. (I'm assuming that a typical person who reads my posts will find the question easy, but I suppose this should be a spoiler alert for anyone who feels like trying it for themselves.)

The probability that the first sweet is red is 6/n. If the first one is red, then the probability that the second is also red is 5/(n-1) (since there are five red sweets left and n-1 sweets left). Therefore the information we are given tells us that  (6/n) x (5/(n-1)) = 1/3. Multiplying both sides by 3n(n-1) we deduce that 90 = n(n-1), which rearranges to n^2-n-90=0.

It is interesting to speculate about why this question was found so hard. My guess is that the people taking the exam had done many "direct" questions, such as, "There is a bag of 12 sweets of which five are red. Graham chooses three sweets at random. What is the probability that none of them is red?" But this question is an "inverse" question: that is, we are given the answer and have to work out what some of the data must have been (or at least to obtain information about it) in order to yield that answer. This requires people to be comfortable with a certain level of abstraction: solving a direct problem about n sweets for arbitrary n in order to obtain a condition on n. Of course, it also needs a bit of algebraic fluency so that you don't mess up the rearranging of the equation you get.

Possibly a more fundamental reason that the question was found hard is that it requires more than one idea. (To an expert mathematician that is not true, but I'm talking about an average 16-year-old.) You first have to solve a probability problem with an arbitrary n, and you then have to follow that up with the solution of an algebraic-manipulation problem. This is of course precisely the kind of thing that mathematicians (in the broadest sense of people who use mathematics) have to do the whole time, but over the years our education system has broken questions up into smaller and smaller pieces so that questions that test more than one skill at a time are now very unfamiliar and perceived as extremely hard. 

It reminds me a little of an experiment we did at school when I was about 11 or so, which was supposed to measure the width of a molecule. The idea was that we started with an oil droplet and used a micrometer to measure its width. We then dropped it on to some water that was covered with a thin film of some dusty substance. The drop spread out rapidly and we quickly measured the diameter of the resulting circle. We were also told that the film was one molecule thick. I'm not sure how plausible that last part was, but if we accept it, then we end up with just enough information: the width of the drop gives its volume (approximately anyway, if we assume that it is spherical) and the film is a cylinder with a radius we know and a height we are trying to solve for, so that gives us a formula for the volume in terms of the height, and then we are done. One boy in my class (it was a boys' school) managed to solve the problem. For some reason the episode stuck in my mind, so I still remember his name: Aidan Hollick. No doubt this question too would cause an outcry if it was asked on a GCSE paper.
School kids who sat their GCSEs before Twitter was created only had their friends and family to vent to if they were convinced they had failed.
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I helped a girl with some of her GCSE maths work in the autumn, and from what I saw this looks like a very typical GCSE question.  Specifically, the "indirectness" of the question is something that occurred time and time again throughout the example questions we looked at.  For example, I remember a question where you were given a pyramid, a few of its side lengths and its volume and asked to compute another side length.  As I remember, she had some trouble learning the general strategy for such problems, which, roughly speaking, is to replace

Here is some incomplete information, together with the value of a thing that you would be able to compute if the information were complete.  Find the missing bit of information.

with

Here is some incomplete information.  Introduce a variable 'x' that completes the information, and find an expression for the thing in terms of x.  Using the value for the thing given in the question, obtain an equation in x.  Solve the equation.
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Timothy Gowers

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Elsevier news

Hard to believe I know, but a lot of people are getting cross with Elsevier again. Elsevier have recently revised their policy about sharing of articles, which can be examined in a web page written by Alicia Wise that goes by the superbly ironic title, "Unleashing the power of academic sharing." (I think the right word for a title like that has to be "wisecrack".) It's here:

  http://www.elsevier.com/connect/elsevier-updates-its-policies-perspectives-and-services-on-article-sharing

One of the highlights is that after publication a subscription article can be shared "As a link anywhere at any time." This policy is explained on another Elsevier page as follows: "If you are an author, please share a link to your article rather than the full-text. Millions of researchers have access to the formal publications on ScienceDirect, and so links will help your users to find, access, cite, and use the best available version." (The relevant page is this one: https://www.elsevier.com/about/policies/article-posting-policy#published-journal-article.)

I actually don't find Elsevier's policies all that unreasonable. For one thing, they are pretty liberal about preprints in mathematics, allowing you to post to the arXiv the version that takes into account comments by the referees. However, it is notable that they don't allow just any old repository, so they are clearly making special cases for certain subjects, while making sure that freely available preprints don't become the norm in the big-money subjects like biology and medicine. But even that is reasonable if you look at things from Elsevier's point of view: they have a business model that would be seriously threatened if you could get the information you wanted without subscribing to their journals. But their critics are also reasonable from their point of view: it is not good to have large amounts of the scientific literature behind paywalls. Also, Elsevier's defence of its policy -- that Science Direct is a wonderful resource that helps you find the best version of the article -- is ludicrous.

Basically, as everyone knows, we are seeing a clash between the future and the past. The future is surely destined to win eventually, and the main question is how much money the past can rake in before it does.

On another topic, I missed this when it happened, but on the 12th of May the Cost of Knowledge boycott passed the 15,000 mark. It now stands at 15039.
Statement against Elsevier's sharing policy. Organizations around the world denounce Elsevier's new policy that impedes open access and sharing. On April 30, 2015, Elsevier announced a new sharing and hosting policy for Elsevier journal articles. This policy represents a significant obstacle to ...
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From the direction of the discussion, you may be interested in this comparison between arXiv and the "megajournals" (their names, means PLOS etc) and also about this extremely curious trick they do when they don't count arXiv as green OA. https://plus.google.com/+MariusBuliga/posts/RY8wSk3wA3c
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Timothy Gowers

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Oh dear. What a terrible piece of news.
Mathematician John Nash, subject of film A Beautiful Mind, dies in a New Jersey taxi crash with his wife, US media reports say
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Sorry, so sad to the event and news of the killing of Nash, 
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