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. The talent and enthusiasm of the pupils are extraordinary, making it an absolute pleasure for the teacher running the sessions.

Intermediate Maths Challenge

In 2022 we had 261 pupils achieve a Gold and 49 pupils qualify for the next round – the Olympiad.

Year 2019 2020 2021 2022
Cayley 9 21 17 16 27
Hamilton 10 10 17 16 12
Maclaurin 11 11 11 25 10
Total 42 45 57 49
GKang 9 69 78 81 118
PKang 10,11 104 85 120 155
GOLD all 204 171 205 261
SILVER all 98 108 164 132
BRONZE all 48 63 111 43
Total 350 342 480 436

Pupils finishing in the top 20 in the UK receive a Gold medal, top 50 receive a Silver medal and top 100 receive a Bronze medal.

In 2022 the pupils achieved 3 Gold, 4 Silver and 8 Bronze medals.

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 learning from each other. 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 150 pupils who achieved a Gold in the SMC last year, 32 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, 3 pupils achieved Medals, 17 pupils achieved Distinctions and a further 20 achieved Merits.

  2019 2020 2021
BMO1 Qualifiers 17 34 32
Gold 114 119 150
Silver 117 149 143
Bronze 63 57 40
  2019 2020 2021
Distinction 20 14 17
Merit 10 22 20
Other 4 21 16
  2019 2020 2021
Distinction 0 4 5
Merit 3 5 2

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 have 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 on the The Mathematics of Bridges.

Having made it through to the group stage where the pupils presented their work to their peers, four finalists presented to staff and parents. In 2022 the finalists were:

Arjun Rajkumar: Mathematics in Poker

Axel La Pira: Mathematical Logic

Jash Jhaveri: The Basel Problem

Eliyahu Gluschove-Koppel: Mathematical Modelling in Biology

The adjudicators, Owen Toller, Dr Hemery and Dr Franjic 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 Jash Jhaveri. It was a showcase for the incredibly talented mathematicians at St Paul’s.