The United Kingdom Mathematics Trust (UKMT) is far more than a competition organiser — it is a thriving community of students, volunteers, educators, and mathematicians united by a shared passion for problem-solving. While its annual competitions attract over 700,000 participants, the Trust's enrichment programmes — particularly its National Mathematics Summer Schools and Mentoring Scheme — offer transformative experiences that shape the next generation of mathematical thinkers.
UKMT summer school participants collaborating on challenging mathematical problems
The National Mathematics Summer School: Where Talent Meets Inspiration
UKMT's National Mathematics Summer Schools (NMSS) are residential events that run for one week, bringing together some of the brightest young mathematicians from across the United Kingdom. These events are specifically designed for students aged 14–16 who demonstrate an exceptional interest and aptitude in mathematics.
Summer school students engage with advanced mathematical concepts in a supportive environment
Who Gets Invited?
Invitations are extended to students selected at random from the top 1.5% of results from the Intermediate Mathematical Challenge, specifically those in Years 10–11 (England and Wales), S3–S4 (Scotland), and Years 11–12 (Northern Ireland). The selection process is deliberately designed to ensure diversity: half of the students invited are girls, and 90% come from state schools. To promote wider access, only one student per school can be invited, and schools cannot send students two years in a row.
Peer-to-peer learning is a cornerstone of the UKMT summer school experience
What Happens at Summer School?
Each day is filled with thought-provoking and exciting sessions run by dedicated volunteers — many of whom are current university students or recent graduates in mathematics. The programme covers topics far beyond the standard school curriculum, from number theory and combinatorics to geometry and algebraic structures.
As one volunteer from NMSS 61 (2023) reflected: "I loved working with younger students and exploring their insights on complex problems, and exploring maths to a higher level than I had before. While some people found some sessions too easy or too difficult, everyone had fun and found something which challenged them."
Workshop sessions at the NMSS encourage deep mathematical thinking and discussion
A student attendee shared: "I had a great time; although the maths was challenging, I felt like we had a lot of support that successfully helped people with varying levels of confidence. I learned a lot and, more importantly, I found things that really interested me that I'm excited to pursue further. Being away from home wasn't as hard as I thought — I enjoyed the evening activities and made new friends."
Beyond the classroom: building friendships and a lasting mathematical community
The Mentoring Scheme: Personalised Mathematical Growth
While summer schools offer an intensive, week-long experience, UKMT's Mentoring Scheme provides sustained, year-long support for aspiring mathematicians. The scheme pairs students with experienced mentors who guide them through increasingly challenging problem sets each month.
UKMT mentors provide one-to-one guidance to students throughout the academic year
Nine Programmes, Named After Mathematical Giants
The Mentoring Scheme features nine distinct programmes, each named after a renowned mathematician and designed for a different level of experience:
Pythagoras — The entry level, designed for in-school mentoring starting from Year 7
Hypatia — Building on foundational skills, now available for UKMT-led mentoring
Archimedes — Developing deeper problem-solving abilities
Cartwright — Named after mathematician Mary Cartwright, advancing mathematical rigour
Robinson — Named after Julia Robinson, tackling Olympiad-style problems
Noether — Named after Emmy Noether, exploring abstract mathematical structures
Neumann — Named after John von Neumann, for highly advanced problem-solving
Hardy — Named after G.H. Hardy, approaching competition-level mathematics
Ramanujan — The most advanced level, for students aiming at the highest Olympiads
Collaborative learning: students work through challenging problems together
Applications for 2026/27 Are Now Open!
Teachers can nominate one student from their school for the mentor-led programmes. The application deadline for the 2026/27 academic year is 16th September 2026. Each student works through eight sets of problems over the course of the year, with concepts progressively developing in complexity. The scheme emphasises not just finding answers, but developing the ability to write clear, rigorous mathematical explanations.
Developing clear mathematical communication is a key goal of the mentoring programme
The Volunteer Community: The Engine Behind UKMT's Success
None of UKMT's enrichment programmes would be possible without its dedicated community of volunteers. From summer school session leaders to one-to-one mentors, these individuals — many of them current or former mathematics students at top universities — give freely of their time to nurture young talent.
The dedicated volunteers who make UKMT's enrichment programmes possible
The Trust's governance structure reflects this volunteer-driven ethos. The Board of Trustees, chaired by Dr Geoff Smith MBE, is composed of mathematicians and mathematics enthusiasts from diverse professional backgrounds. Supporting the Board are dedicated Board Committees of volunteers who advise on specific operational areas, ensuring that UKMT remains responsive to the needs of students and schools.
Guiding the next generation: teachers and volunteers making a lasting impact
Team Challenges: Building Collaboration and Camaraderie
UKMT also recognises that mathematics is not always a solitary pursuit. Its Team Maths Challenges bring a collaborative dimension to competitive mathematics:
The Senior Team Maths Challenge (STMC) brings teams from schools across the UK to compete in a fast-paced, multi-round event, culminating in a prestigious National Final.
The Team Maths Challenge (TMC) offers a similar experience for younger students, also culminating in a National Final.
These events develop not only mathematical skills but also teamwork, communication, and the ability to think under pressure — qualities that serve students well far beyond the competition hall.
The team challenges combine mathematical rigour with the thrill of collaborative competition
Looking Ahead: The 2026–27 Year
As UKMT prepares for another exciting year, several key milestones are on the horizon:
The 2026/27 Mentoring Scheme applications are currently open, with a deadline of 16 September 2026.
A new competition format is being trialled for the Senior Mathematical Challenge (7 October 2026): the last three questions will shift from multiple-choice to a 000–999 answer format, requiring students to calculate and enter three-digit answers.
The Mathematical Competition for Girls, launched in 2025, returns for its second year alongside the established Mathematical Olympiad for Girls on 22 September 2026.
UKMT's impact continues to grow, reaching hundreds of thousands of young people each year
How to Get Involved
Whether you are a student, teacher, parent, or mathematics enthusiast, there are many ways to connect with UKMT:
Schools in the UK, Crown Dependencies, and British International Schools can register as UKMT centres to enter students into competitions.
Teachers can access past papers, video solutions, and classroom resources through the Dr Frost Maths partnership.
Volunteers can apply to become mentors by emailing volunteering@ukmt.org.uk.
Donations help sustain and expand UKMT's charitable work in mathematics education.
