British Mathematical Olympiad (BMO)
A UK mathematical olympiad where students solve demanding proof-based problems across two rounds. Open to full-time secondary-school students through registered UKMT centres, with progression based mainly on performance in the Senior Mathematical Challenge and BMO Round 1. Rated Expert Level, with difficulty mainly coming from advanced problem-solving, rigorous proofs and highly selective progression.
Verified information
Competition details can change. Always confirm dates, eligibility and entry requirements on the official organiser's website.
Official website ↗OVERALL COMPETITION LEVEL
Expert Level
5 evaluation dimensions have source-backed automatic scores; 0 dimensions need conflict review.
Competition overview
Key information
Eligible ages
14–19
School level
Upper secondary / sixth form (selection from UKSMC performance)
Registration method
School Only
Competition stages
BMO1 then BMO2 (invitation and discretionary/fee pathways)
Fee
BMO2 additional entry may require payment (see official BMOS rules)
Online / in-person
In-person
Dates
Competition timeline
Registration opens
Not yet announced by the organiser
Registration closes
19 Nov 2025
Competition starts
19 Nov 2025
Competition ends
21 Jan 2026
Editorial perspective
Our Take
The British Mathematical Olympiad is best understood as a two-stage senior Olympiad pathway rather than a single event. BMO1 gives a wider group of strong senior students their first experience of proof-style competition; BMO2 narrows the field further and asks the strongest students to work at greater depth. Together, the rounds offer a route from Challenge-style problem solving towards the kind of mathematical thinking associated with national Olympiad teams. The pathway normally begins with the Senior Mathematical Challenge. Students who reach the relevant standard may be invited to BMO1, and the strongest BMO1 performers may progress to BMO2 or later selection opportunities. The exact invitation thresholds and discretionary entry rules can change by cycle, so families should always check the current UKMT information rather than assuming that a previous year's score guarantees entry. What makes BMO distinctive is the change in output. In a Challenge paper, a correct answer is usually enough. In an Olympiad, the student must make the reasoning visible: define the key idea, justify each important step and handle edge cases. That transition can be exciting for students who enjoy mathematical writing, but frustrating for those who have only practised speed. We rate the BMO pathway at the Expert Level. Its value lies less in collecting two results than in developing a durable habit of rigorous, creative problem solving. Students should build towards it through regular proof practice, not treat it as a short-term examination course.
Read full guide →Preparation support
Recommended resources
British Mathematical Olympiad Past Papers
Open resource ↗BMO1 and BMO2 papers and reports for sustained proof-based practice.
Official · Free · Past papers & reports · Essential
BMO Video Solutions Archive
Open resource ↗Official solution videos to study after writing a complete proof attempt.
Official · Free · Video solutions · Recommended
Notes on BMO Marking
Open resource ↗Annotated guidance on proof scoring, justification and examiner expectations.
Official · Free · Marking and proof-writing guide · Essential
A Mathematical Olympiad Primer II
Open resource ↗Structured analysis of BMO1 problems from 2011–2022 for building olympiad techniques.
Official · Paid · Preparation book · Recommended