SPS Mathematics Blog

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...