Ireland achieves three medals at International Maths Olympiad, Shanghai

Team Ireland earned one silver and two bronze medals at the 67th International Mathematical Olympiad (IMO), the world championship in mathematics for second-level students.

The six Irish students – Owen Barron (Cork), Vitalii Halushko (Dublin/Ukraine), Angyang Li (Dublin), Jack McAuliffe (Clare), Ben Maguire (Dublin), Tianci Yan (Dublin) – were selected as Ireland’s most outstanding second-level mathematicians. They competed with 666 of the world’s brightest young minds from 117 countries in Shanghai, China, on July 15th and 16th.

Irish success at International Maths Olympiad

Each participant is given 4.5 hours per day to solve six highly complex mathematical problems. Each question is worth a maximum of seven points, making the maximum possible individual score 42 points. Two of the (easier!) 2026 questions are included below. The threshold in 2026 for a bronze was 16 points, 23 for silver, and 29 for gold. Gold medals are awarded to only the top 16% of competitors.

Ben Maguire earned Ireland’s 5th-ever Silver medal. Angyang Li and Jack McAuliffe got Bronze medals. This is only the second time Ireland has won three medals, after last year’s historic high, and cemented the team’s status as Ireland’s best ever. Owen Barron, Tianci Yan and Vitalii Halushko, who remarkably each medalled at last year’s IMO, all earned Honorable Mentions for a complete and correct solution to at least one problem. The team was led by Prof. Steve Buckley (Maynooth University), Tianyiwa Xie (U. Münster) and Dr Mark Flanagan (UCD).

Following last year’s two silvers and a bronze, Team Ireland’s sustained excellence at this year’s edition of the IMO showcased the level of talent and commitment to mathematics in Ireland. Irish Mathematical Trust (IMT) volunteers provide extracurricular maths training and coaching across the country, with recent expansion enabled by Stripe’s sponsorship of the Irish Maths Trust.

“Maths is the cornerstone of future success in fields as diverse as engineering, finance, medicine, and software development,” said Alison Ahern, Head of Education Partnerships at Stripe. “We are dedicated at Stripe to supporting excellence in maths and STEM education in Ireland, and we are hugely proud of this year’s International Maths Olympiad team, who represent Ireland’s sharpest mathematical minds at secondary level.”

Dr Neil Dobbs, Lecturer in Mathematics at University College Dublin and Chair of the IMT, said: “That all six team members have medalled at the IMO either this year or last is simply extraordinary. The dreams, the hard work and the sense of community throughout the wider squad has been wonderful to witness.”

Team Ireland’s success at IMO is the product of years of work, backed by more than 80 volunteer mathematicians from the Irish Mathematical Trust, many of them former IMO competitors themselves, who ran a rigorous selection process and packed training calendar. Funding was provided by the Department of Education and Youth and our sponsors, Stripe, The Society of Actuaries in Ireland, Abbey Capital, Laminar Shock, Nebular, Emma Waldron Chen, the Irish Maths Teachers’ Association and Susquehanna.

Prior to the IMO, the team participated in the prestigious International Mathematics Summer Camp in Beijing, which incorporated an Olympiad-style contest where Tianci Yan, Vitalii Halushko and Jack McAuliffe got Bronze medals and Owen Barron a Silver. This followed strong performances by Irish Teams at the Junior Balkan Maths Olympiad in Romania in June, the 1st European Maths Olympiad in Lithuania in late April and the European Girls Maths Olympiad in France in early April.

Problem 1

There are 2026 integers greater than 1 written on a blackboard, not necessarily different. In a move, Confucius chooses two integers m > 1 and n > 1 from different places on the blackboard and replaces these two integers with

gcd(m,n)   and   lcm(m,n)gcd(m,n).

He continues to make moves while it is possible to do so.

1. Prove that, regardless of the choices of Confucius, after finitely many moves, exactly one integer M on the blackboard is greater than 1.

2. Prove that the value of M does not depend on the choices of Confucius.

(Note that gcd(m,n) denotes the greatest common divisor of positive integers m and n, and lcm(m,n) denotes the least common multiple of m and n.)

Problem 4

Shan-Yu and Mulan are playing a game. Let ? be an angle with 0º < ? < 180º known to both players. Initially, Shan-Yu makes a paper triangle T with measurements of his choice. Then, they repeatedly perform the following steps:

If T has at least one angle measuring exactly ?, then the game stops and Mulan wins.

Otherwise, Mulan chooses a point P on the perimeter of T, different from its three vertices. She then makes a straight cut from P to the opposite vertex of T, splitting it into two triangles.

Shan-Yu discards one of the two triangles. The remaining triangle becomes the new T.

For which real values of ? can Mulan guarantee her victory in finitely many steps, no matter how Shan-Yu plays?

Full list of problems: https://www.imo-official.org/problems/2026/

Ireland’s IMO results year-by-year: https://www.imo-official.org/results/team/country/IRL/

About the Irish Maths Trust

The Irish Mathematical Trust is a charitable organisation of more than eighty mathematicians from across Ireland, dedicated to inspiring and training Ireland’s next generation of creative thinkers.

For more information on the Irish Mathematical Olympiad and to register interest in Maths Enrichment classes, see www.irmo.ie

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