SPS Mathematics Blog

 On Tuesday, 10th June, the brilliant mathematician, Zoe Griffiths, came to St. Paul’s to give some 5th form students a fun and interactive presentation about ‘Mathematics of the Unexpected’. Having entered the John Colet Hall, we sat down at desks in pairs and were immediately greeted by a jovial and comical Zoe. Not only has she appeared on the YouTube Channel Numberphile, but she has also been on BBC Radio 4, performing mathematical comedy sets. Needless to say, she gave off a lot of positive energy, which made us all very excited about the two hours ahead of us. We began by investigating the secrets of some magic tricks, such as the seemingly mind-boggling fact that any 3-digit number repeated after itself (e.g. 738738), when divided by 7, will always produce a whole number. Surely, we would expect only a seventh of the numbers to be a multiple of 7? In fact, this new number divides by 13, 11 and 7. Now, 13 x 11 x 7 =1001 and 1001 multiplied by any 3-digit number produces a n...

Ben Sparks is a Youtuber with over 10,000 subscribers and often has appeared on the popular channel Numberphile. He hosted a session for a group of students from SPS and SPGS united by a love of mathematics. Split into two halves, the initial period was a talk covering a broad range of mathematics - including history and philosophy. Mathematical peaks sighted included irrational numbers, the discovery (invention?) of zero, complex numbers, and the Mandelbrot set. Students were delighted to be met by a QI-esque klaxon and flashing word whenever their answers had been anticipated. After a short break, and some snacks, the students spent some time solving a range of problems related to irrational numbers and folding A4 paper. (Although the highlight here was possibly Ben's metric system supremacist rant). Finally, Ben Sparks finished off with a sprinkle of magic. Michael (6th) played a starring role as assistant and volunteer to Ben's mind-reading trick and later as straight man t...

Students are invited to the Intermediate Maths Challenge (IMC) preparation sessions at their respective problem solving club. These are sessions tailored to the IMC and will continue up to the 29th January.  5th/6th Form Problem Solving: Monday Lunchtime, 12:40, Room 228 The 5th/6th form had the choice of a previous IMC paper or attempting the questions from the Mclaurin. When students sit the IMC they will be battling for the pride of qualifying for the Olympiad rounds - The Cayley (4th), Hamilton (5th) and Mclaurin (6th).  4th Form Problem Solving: Tuesdays Lunchtime, 12:40, Room 227  The most recent session focused on question 25 from the IMC. Often one of the most challenging questions, students were given opportunity to try and discuss a mix of Q25s on various topics.  IMC papers are available on the Maths Hub. Please see the tannoy for more details of the problem solving societies. 

The British Maths Olympiad (BMO) Problem Solving Club meets after school on Fridays. Students who have excelled in the Senior Maths Challenge (SMC) are invited to tackle challenging BMO problems. These problems test advanced mathematical knowledge and problem-solving skills. Despite being held on Friday afternoons, the room is surprisingly lively. Students gather around whiteboards, eagerly discussing mathematical concepts. Dr. Stoyanov and Mr. Morris guide these discussions, helping students develop their ideas and reach solutions. While the BMO itself is an individual competition, the Problem Solving Club fosters a collaborative environment. It's a place where students share mathematical ideas and push each other to excel. The club not only prepares students for the Olympiad but also cultivates a deeper appreciation for mathematics. Through this weekly gathering, students enhance their problem-solving abilities, learn to articulate complex ideas, and experience the joy of c...

The maths society had the pleasure of welcoming one of our own, Mykhailo who presented a captivating talk on problem solving in mathematics. He began by telling us of his journey through mathematics, starting in Ukraine at the humble age of 7, where he agreed to compete in his first Olympiad in return for some Lego - a worthy reward. By the age of 11, however, he began to lose interest until a remarkable geometry teacher reignited his passion. From that point on, he was completely hooked on geometry, so much so that his Olympiad scores r eflected his singular focus: 0/7, 0/7, 0/7, and finally, 7/7, as he excelled in geometry alone. He, therefore, decided that it would be best for his progress if he stopped doing geometry altogether, focusing instead on the other 3 areas of math: Algebra, Arithmetic, and Number theory. He led us through a series of questions, seemingly impossible at the face of it but very manageable after explanation. Among the problems were a complex simultaneou...

With the Senior Maths Challenge (SMC) a week away, 8 th form students are preparing at the Senior Problem-Solving Club. The Senior Problem-Solving club is a lunch time activity where students work through a mix of interesting and stretching questions.  The focus this week was on the hard final question on the paper with Dr Hemery and Mr Morris providing the last 20 years of question 25.  Here is an example: As the final and typically the most demanding question of the SMC, it provided an excellent test for even some of SPS’s best problem solvers.

The teachers in the mathematics department are always looking for ways to give pupils scholarly opportunities beyond the core curriculum topics. Lessons often develop mathematical ideas well beyond the syllabus but pupils require time to research ideas, then spend time reflecting on what they have read before practising questions and developing a deeper understanding for themselves. They then need the opportunity to discuss ideas with others so their understanding can be scrutinised. With this in mind, following the summer exams, the top two 5th form (Year 10) sets embarked on a two week investigation into a non-syllabus topic such as fractals, modular arithmetic and infinite series. At the end, each pupil presented their findings. The class asked some searching questions about anything that wasn’t clear.

The Toller Prize final was held in the John Colet Hall in front of a live audience of parents and students. It was another year of strong lectures, but ultimately, there had to be a winner. The judging panel chose "Trains The Circular Revolution" as the winning lecture of the Toller Prize 2024 A huge well done to the runners up with their lectures "Intuition Mathematics vs Deduction Mathematics" and "Markov Chains": https://vimeo.com/1008202641?share=copy#t=0 https://vimeo.com/1008202785?share=copy#t=0

In the two weeks following the Lower Eighth summer examinations all of the further mathematicians undertake a short research project, culminating in the production of a poster and the giving of a short lecture. Amongst the huge range of topics selected, we had presentations on topology, fluid dynamics, Diophantine equations and the nature of infinity. Click on the poster below to see a selection of the best posters from the group stage: