The ICMC (Imperial–Cambridge Mathematics Competition) aims to provide undergraduate and master's students with an opportunity to enjoy non-bookwork, competitive mathematics. It is run by students and graduates of Imperial College London and the University of Cambridge, and is open to students studying in Europe. Since 2017, we have seen undergraduate students from across the UK and beyond take part in the events, which include a two-round Individual Competition and a Team Competition.

We welcome undergraduate and master's students from all departments. Although the problems on our papers may require knowledge from the first year of an undergraduate degree in maths, our papers are designed to test the contestants' abilities to solve problems creatively rather than their knowledge.

Why did you change your name?

Our name was Imperial College Mathematics Competition, but since 2022 we have changed our name to Imperial–Cambridge Mathematics Competition. This better reflects the involvement of students at the University of Cambridge in organising and running the competition, and reflects internal changes in the running of the competition.

How many contestants qualify to Round Two?

Up until the 5th ICMC, this was 50. However, since the 6th ICMC, the top 100 students qualify.

How does the ICMC work?

The ICMC consists of both an Individual Competition and a Team Competition.

The Individual Competition has two rounds: Round One takes place on the last Sunday of November and Round Two on the last Sunday of February. The Round One question paper consists of six problems, and will be held simultaneously at multiple universities, so that most contestants will not have to travel afar. The top 100 contestants from Round One are invited to Imperial College London for Round Two, which consists of five harder problems. For qualifying contesteants in the UK, Round Two will be held at Imperial College London, but we may be able to partially reimburse travel expenses for some contestants. For those not in the UK, check to see if it is possible to have your travel reimbursed by your university. If not, it is possible to sit Round Two at your own university.

On the afternoon of Round Two, we will run our Team Competition event at Imperial College London, open to Round One participants. Registration for this event will be emailed to eligible participants closer to the date. For more information see the team competition page.

How difficult are the problems?

The problems will be of a very similar difficulty range and scope to our past papers and the problems in the Putnam Archive.

What is the scope of the problems?

The problems will be selected from calculus and analysis (e.g. limits, summations, and integrals), abstract algebra, combinatorics, geometry (including discrete and combinatorial geometry), number theory, probability, game theory, and so on. The problems will only assume knowledge from a typical first year undergraduate course in mathematics.

Am I eligible to take part?

To take part in the Competition, you must be an undergraduate or master's student currently enrolled at a European university who has completed less than four years of university education. Students studying in Turkey and Russia are eligible. All students are welcome to take part regardless of what they are studying.

What if my university has not partnered with ICMC?

Please encourage your university's mathematics society (or mathematics department, if your university does not have a mathematics society) to partner with us by reading the Partners page and contacting us.

How is the competition similar/different when compared to the Putnam competition?

If you're familiar with the Putnam competition, then the difficulty and style of the problems will be very similar — the major differences are in the format of the competition. Whereas Putnam has two papers on a single day, our two papers are around four months apart to allow time for the marking of Round One and invitations to Round Two.