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标题:Gowers's Weblog | Mathematics related discussions
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Gowers's WeblogMathematics related discussionsUSS changes — don’t be fooledMarch 12, 2015This post is meant for anybody who will be affected by proposed changes to the Universities Superannuation Scheme, the body to which I and many other UK academics have paid our pension contributions and that now proposes to change the rules to deal with the fact that it has a large deficit as a result of the financial crisis. (Or rather, it says it has a large deficit, but there are arguments that the amount by which it is in deficit or surplus is highly volatile, so major changes are not necessarily justified.)Of course, any change will have to be in the direction of making the deal less generous for those with pensions. Indeed, changes have already been made. Until a few years ago, the amount you got at the end was based on your final salary. More precisely, you got one 80th of your final salary per year after retirement for each year that you contributed to the scheme, up to a maximum of 40 years of contributions (and thus a maximum of half your final salary when you retire). But a few years ago they closed this final-salary scheme to new entrants, because (they said) it had become too expensive. This was partly because now a much larger proportion of academics end up as professors, so their final salaries are higher, and also of course because people live for longer.Read the rest of this entry »Posted in General | 13 Comments »Sums of kth powersNovember 4, 2014Recently I was giving a talk at a school in London and had cause to think about sums of kth powers, because I wanted to show people the difference between unenlightening proofs and enlightening ones. (My brief was to try to give them some idea of what proofs are and why they are worth bothering about.) On the train down, I realized that there is a very simple general argument that can be used to work out formulae for sums of kth powers. After a brief look online, I haven’t found precisely this method, though I’ve found plenty of methods in the vicinity of it. It’s bound to be in the literature somewhere, so perhaps somebody can point me towards a reference. But even so, it’s worth a short post. I’ll start with the case . I want to phrase a familiar argument in a way that will make it easy to generalize in the way I want to generalize it. Let be the rectangle consisting of all integer points such that and . We can partition into those points for which and those points for which . The number of points of the first kind is , since for each we get possibilities for . The number of points of the second kind is , since for each we get possibilities for . Therefore, and we get the familiar formula. Read the rest of this entry »Posted in Straight maths | 18 Comments »ICM2014 — Bhargava, Gentry, SandersSeptember 7, 2014On my last day at the ICM I ended up going to fewer talks. As on the previous two days the first plena