SPS Mathematics Blog

This talk took us through one of the most counterintuitive ideas: that not every polynomial can be factorised in terms of its solutions and that the barrier for that is so low as to be the cubic. Starting with the quadratic, a base of knowledge we all know, Toller's exceptional talk then brought us to the cubic, explaining its quirks and how to reduce it to a form we all know, with a neat trick to turn it into a depressed cubic. He then used a clever method to split x into u+v and then made everything a quadratic. After following through the algebra, we transitioned into the quartic, having solved a few examples with both real and complex roots. For the quartic, the method was more complicated but doable all the same. Yet he posed the idea that the quintic cannot be solved with a formula. This took us into a tour of group theory, starting with what a group is and its symmetries, then moving to the symmetric group of n things. Then he posed a clever game where, knowing the roots of ...

The start of the spring term is always a bittersweet moment in the Hans Woyda calendar. The excitement of moving through to the knockout rounds is tempered by the knowledge that I will soon have to pick the final team of 4 from the superb squad of 12 pupils who took part in last term’s group stage matches. As ever, the selection trials were fiercely contested, and any of the 81 different possible teams would have stood us in good stead for the remainder of the competition, but eventually Haoming (4 th ), Rafael (6 th ), Lucas (L8 th ) and Adavya (U8 th ) emerged victorious. I had provided each of the team members with a set of practice questions for the journey which they eagerly worked through, swapping sheets with each other and comparing methods for the hardest questions, and at one point Adavya started loudly listing all of the squares from  16 2 to  29 2 to ensure he had them to hand in case he needed them later. The west London traffic and soporific drizzle had dampene...

This talk took us on a tour through one of the most quietly powerful equations in mathematics: the heat equation. On the surface, it’s “just” a formula describing how temperature spreads through space over time. In reality, it turns out to be a kind of mathematical celebrity, popping up everywhere from physics to finance. The talk began by unpacking what the equation says. Temperature at a point changes depending on how curved the temperature is around it – in other words, heat flows from hotter regions to colder ones, smoothing things out. Partial derivatives made a cameo appearance here, framed intuitively as rates of change and curvature rather than scary symbols. Then came some history. Long before the equation became standard, heat was thought of as a weightless fluid (“caloric”). That changed thanks to Joseph Fourier, whose radical claim that any function – even jagged ones – could be written as a sum of sines and cosines initially got his work rejected. Awkward, given how fo...

To put a cap on a brilliant first term of MathsSoc, Yidong came up with a fantastic Christmas Quiz including a greatly enjoyed maths race. Adrenaline was flowing throughout this speed-based event, and while the difference was only made up of a few points, Team 1 (a name they accurately picked for themselves) took home a well-deserved win and a mountain of chocolates. A big thank you goes out to Yidong for entertaining us with this quiz, as well as all the people that have helped run and organise MathsSoc this term. It has been absolutely incredible, and I hope to see everyone there in 2026. -  Arié

It was another successful year for the students who qualified for the British Mathematical Olympiad Round 1 (BMO1). Of the 85 students who took part, 35 received merits, 25 received distinctions, and 7 students qualified for BMO2. Having 7 students qualify for BMO2 is a fantastic achievement, especially given that only around 100–120 students nationwide reach this stage each year. This is also the highest number of merits and distinctions the school has ever attained in BMO1. Well done to all the students who took part — your hard work is truly paying off! Here is a selection of questions from the six problems on the BMO1 2025 paper, courtesy of UKMT. The full paper and mark scheme are available here :

SPS held a maths partnership event with a variety of the partnership schools in the local area. The event included a series of UKMT Team Challenge problems where groups were composed of one student from each school. The event kicked off with a 10 question quick fire quiz, followed up by a maths crossword, called the crossnumber. The event finished with a unique maths relay, in which each group was split in half and the teams competed in finishing a 20 question quiz, where the questions had to be completed sequentially with one half doing odd numbered questions and the other half doing the even ones.  There were two competitions those with 3 team members and those with 4. The scores were very tight and so huge congratulations to the winning team in both category. The top team was outstanding, almost scoring almost full marks. Overall, it was a great day where everyone enjoyed themselves and had their fill of maths. - Shorta