SPS Mathematics Blog

 Yesterday, six months after kicking off the 2024-25 Hans Woyda season with our annual friendly against SPGS, we were at long last on our way to the final. There was a palpable tension around the school site and an unmistakable atmosphere of excitement and anticipation, making it abundantly clear that the entire school had their minds on that afternoon’s Mathematics fixture. As I set off for the match with Yidong (4 th ), Shyamak (6 th ), Adavya (L8 th ), and Eason (U8 th ), accompanied by Dr Stoyanov for moral support and intimidation, pupils and staff had even gathered by the towpath to wish them well; unfortunately, they all seemed to be facing the wrong direction, but it was touching nevertheless. We made our way to the City of London School (which offered its services as neutral territory for the final), discussing tactics on the tube and working through a set of warm-up questions. We met the King’s College School Wimbledon side in the lobby as we arrived, and based on previou...

I had been watching the girls’ school’s results so far with growing unease; while the nature of the competition makes it difficult to compare scores between matches, I couldn’t help but notice that they had beaten our totals in the last two rounds, and I had not forgotten the speed and accuracy on display from their squad in the mixed friendly we hosted back in September. However, there was no doubt in my mind that if anyone could give them a run for their money, it was Yidong (4 th ), Shyamak (6 th ), Adavya (L8 th ) and Eason (U8 th ). One thing was certain; it would be a thrilling match.   Both teams started strong on the starter questions, but an early mistake from SPGS gave us a 2 point lead after the first four. I started to imagine that lead snowballing into an insurmountable gap, but in a sign of things to come, a slip on our side in the remaining questions brought the two teams back level. Up next was the geometry section, all of which concerned overlapping isosceles trian...

Two students who joined St Paul's in L8th, Conrad and William, discuss the their experience of joining the school. Arav of the Maths Society volunteered to interview the students. 

Harry gave a talk on other possible worlds using quantum mechanics. After explanation, we showed that when a quantum object in superposition gets entangled with another object, a parallel world is formed. We proved this using a theoretical experiment with light; when observing, the way light behaves differs from if you hadn’t observed it, which should be impossible in classical physics. This led to a discussion with questions such as how many possible worlds exist, how energy is conserved, and whether this idea is real or conceptual.

This week in Maths and Phil Soc, Aman gave a talk on mathematical constructivism. This is a branch of maths where you reject one of the foundational axioms (law of excluded middle) and so common mathematical proofs, such as proof by contradiction, do not work - constructivists believe that if (P or Q) you should be able to prove (notP) and (notQ). If (P or Q) is true, you cannot rely on proving (notP) is true to prove Q is true. The following discussion included queries about how constructivists can deal with the idea that mathematics is discovered.

This week in Maths and Phil Soc, Aman gave a talk on whether mathematics can prove God, using the unreasonable effectiveness of mathematics in describing the universe, such as in the laws of physics. Many mathematical theories, such as complex numbers and matrices, are developed in pure maths but have extremely surprising applications to physics, like quantum mechanics. This unreasonable effectiveness cannot easily be explained by the atheist, which suggests that we should believe in God. After the talk, the crowd discussed potential objections, ranging from limited access to science in the current day to the idea of multiple possible universes . Many students and teachers attended to enjoy the session, and it was a great way to end the half-term.