Mathematics Societies

The Mathematics Department provides a wide range of societies, clubs and competitions.

UK Mathematics Trust (UKMT)

Central to the School’s mathematical profile are the various national mathematics competitions run by the UK Mathematics Trust (UKMT).

The Intermediate and Senior Mathematics Challenges, the Intermediate Olympiad (Cayley, Hamilton and Maclaurin) and the British Mathematical Olympiad rounds 1 and 2.

Junior Problem Solving

Enthusiasm for Junior Problem Solving is exceptional amongst the Fourth Form pupils, with two parallel sessions running throughout the Autumn term just to accommodate demand, and a strong group of problem solvers continuing to attend right up until the summer exams. They work through a variety of challenging questions and their Olympiad marks show that their hard work pays off.

Intermediate Problem Solving

A strong group of Fifth Form pupils attend the Intermediate Problem Solving sessions, building on the problem solving work they did in Fourth Form and putting them in an excellent position for the Olympiad. As an example of the work they do, the pupils tackle a set of questions without access to the solutions, crafting their own solutions as a group, and the session is led by the pupils’ suggestions just as much as they are led by the teacher’s.

Team Maths Challenge

The Team Maths Challenge sessions are always extremely popular, with a large number of Upper Third (from SPJ) and Fourth Form pupils attending each fortnight to battle against each other in crossnumbers and shuttles. Last year this led to an incredible performance in the regional final, where the team of Wentao Huang, Gabriel Treneman, Neil Prabhu and Haolin Zhao lost just four marks out of a total of 236. Their talent and enthusiasm is extraordinary making it an absolute pleasure for the teacher running the sessions.

Intermediate Maths Challenge

We had our highest number of qualifiers for the Intermediate Maths Olympiad (42) since 2015.

Johnny Cubbon, Wentao Huang, Gabriel Treneman and Sava Vujnovic came in the top 50 and Usman Ali, Eamon Coates, Shahzeb Karim, Louis Kirkpatrick, Ryotaro Kusakari, Joseph O’Keeffe and James Roberts came in the top 100 in their year in the whole of the UK. They all received medals.

Also four pupils from SPJ took the Olympiad a year early and all achieved fantastic results. Haolin Zhao and Neil Prabhu came in the top 50 and Ege Isikli came in the top 100 and they received medals.

On the back of his performance in the competition, Johnny Cubbon in the Fifth Form was invited to a UKMT Olympiad Initial Training Camp for a week in August. This is a great achievement.

Senior Problem-solving club

The Senior Problem-solving club has been growing in strength. Once a week the pupils gather at lunchtime and tackle very interesting and sometimes rather challenging mathematics questions that normally appear in mathematics competitions. They do not require pupils to know anything beyond the curriculum taught in lessons, but often in order to answer those questions you have to apply what you know in an unusual way.

Even though they are tackling difficult competition questions, which are normally sat under exam conditions and time pressure, they are always working together, as a group. At the beginning of a problem, they can be completely stuck, but it is amazing to see that after bouncing ideas off each other they gradually start to see ways forward. It may be that not all ideas would work in the end, but they learn new tricks and ideas from each other; sometimes new and original solutions are discovered; and moments like this encourage pupils never to give up.

Senior Maths Challenge

Of the 92 pupils who achieved a Gold in the SMC last year, 29 pupils qualified for Round 1 of the British Mathematical Olympiad (BMO1). After a paper lasting three and a half hours containing six complex and involved mathematical problems, 14 pupils achieved Distinctions, with four pupils awarded bronze medals (top 100) and a further two awarded silver medals (top 50).

Hankun Zhang was the top performer with a score of 47/60 placing him in the top 20 nationally. Ayham Alkhader (Sixth Form) was invited to join a UKMT training camp in Hungary by virtue of a particularly strong performance (40/60) for his age.

Maths Circle

The maths department are heavily involved in outreach, and one of the highlights of the programme is the UKMT Maths Circle which we host. This involves 54 year 10 students from 27 local schools who come to enjoy eight one-hour lectures and break out activities over two days.

Maths Society

Maths Society is open to all pupils. The pupils, with support from Dr Baxter, arrange a variety of events with talks given by pupils, staff and external speakers. The highlights of Maths Society last year included: Mr Toller’s talk about “How many centres does a triangle have?”; Professor Alex Paseau from the University of Oxford on philosophical logic; Dr Asuka Kumon from King’s College London on continued fractions; Dr Davide Rizza from the University of East Anglia on an introduction to Hilbert’s hotel; Mr Hewitt’s talk on Conway’s Soldiers encouraged the audience to experiment on chessboards with the rules behind the puzzle as well as the underlying maths behind this and associated games. The talk about Babylonian maths when the Pegasus Society joined the Maths Society was very intriguing and people liked learning about maths from 2000BC. The lecture by Professor Imre Leader on aspects of Game theory was elaborate and ingenious, and even managed to tie in the distinction between countable and uncountable infinity.

Further Maths Projects

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 presentation. Amongst the huge range of topics selected, we had presentations on topology, fluid dynamics, diophantine equations and the nature of infinity. The best posters and talks went through to a grand final which took place in the Wathen Hall. The best poster prize was The Mathematics of Bridges by Tanmay Lad.

Having made it through the group stage where the pupils presented their work to their peers, the four finalists present to staff and parents. The finalists were Anton Fedotov “Finding Routes in Networks”, George Monro-Davies “The Gauss-Bonnet Theorem”, Sam Little “Dynamical Systems”, and Lunzhi Shi “Topology and the Borsuk-Ulam Theorem”. The adjudicators, Gerry Leverha and Owen Toller, remarked at the incredibly high standard of all the talks. The award for best presentation which earned the Owen Toller Mathematics prize eventually went to George Monro-Davies. It was a showcase for the incredibly talented mathematicians at St Paul’s.

Eight pupils qualified for BMO2. Only 100 pupils across the country qualify for BMO2, so to have eight qualifiers is a great achievement. Those eight pupils were Ayhem Alkhader, Johnny Cubbon, William Isotta, Navonil Neogi, Oliver Parish, Lunzhi Shi, Harry Wright and Hankun Zhang. BMO2 consists of another three and a half hour paper this time containing four questions requiring full written solutions. With 3 merits and 3 distinctions the pupils can be very proud of their performance, and their endurance!