International Tournament of Young Mathematicians

What is the ITYM ?

The Research phase

This phase begins with the release of the problems in April, and lasts until mid-June. Those 9-12 problems which will be published on our website are difficult and contain parts with no known solution. You can take a peek at the problems from ITYM 2017 here.

The students then collectively work on the problems by themselves: the use of internet forums is prohibited. Similarly, the team leaders must not solve the problems for the students. Instead, they supervise the work and can give directions of research, teach the students about new notions and indicate sources, explain how to write a scientific paper/presentation and review students’ material.

The teams are expected to send preliminary written material to by mid-June. Although those will be graded by the jury, they are not the final work as participants will continue to improve their solutions until the beginning of July. Then, final solutions are to be send 4 days prior to the tournament: they will be used for the debates.

Those papers have to be written in English, and present clearly the team’s work on the problem. The students should properly introduce and give a reference for all sources involved in proofs as well as notions not commonly taught at a high-school level. Finally, there is a 30 pages and 5 MB limit per problem. Written materials from former editions can be found at ITYM official site.


The Competition phase

In July, every team will go to Paris for one week to attend the 10th edition of the ITYM. The schedule and planned activities on site can be found on the webpage Program.

The competition itself consists of 3 phases : a Quiz, two rounds, and the Finals.

The Quiz

The Quiz is a written test of 2 hours. Its aim is to check team’s understanding of the problems of the ITYM, competence in involved mathematical fields and solving skills. It consists of 3 questions for each of the problems: a theoretical question, a particular case of the problem and a question indirectly related to the problem (deviation or generalisation). Each team (high school students only) is gathered in a separate room and works together. Written materials, electronics, literature or other sources are forbidden during the quiz, as well as any external help.

The Rounds

Each of the two rounds begin with the repartition of the teams in groups of 3-4 teams. Via a random draw, every team decide which one of their problems they will present. Two teams in the same group cannot present the same problems, and a team cannot present the same problem twice, so it is important for a team to have addressed enough problems. The first draw will be organised on a public chat three days prior to the tournament.

Before each round, the teams have to read the solutions presented in their groups and review them by highlighting the papers’ qualities and deficiencies. Usually written review are 1/2 pages long.  A model review can be found in the regulations document.

Then the debates on presented problems are held. It consists of scientific and cordial exchanges between the Jury and 3-5 students: Reporter, Opponent, Reviewer, Observer (1 and 2).  The Reporter gives a clear and understandable presentation of the results presented in the final written material, focusing on major results, ideas, methods, and illustrative examples.
The Opponent analyses the Reporter’s solution and presentation and asseses the work by stating weak and strong points. He also asks the Reporter questions about wrong or unclear passages and checks the Reporter’s understanding. He can try to clarify or improve some points.
The Reviewer evaluates the previous dialogue. He can try to settle contentious points or clarify some parts of the discussion. One of the main intentions of the Reviewer is to detect whether the Opponent said anything wrong or overlooked Reporter’s faults.
The Observer only makes important and useful remarks, otherwise he may receive a negative mark from the jury.
During these exchanges, at no time should the Opponent, Reviewer or Observer turn the discussion into an explanation of his/her own proof. At the end of the discussions, the jury can ask questions to all participants so as to extend the debate.


Every debate follows the same pattern, with compulsory and optional steps :

  • Preparation of the Reporter: board and laptop are available for the presentation
  • Presentation of the Jury (1st stage)
  • Presentation of the Reporter (10 min)
  • Questions of the Opponent to the Reporter, answers of the Reporter, and Performance of the Opponent (8 min)
  • Reply of the Reporter (2 min)
  • Questions of the Reviewer to the Reporter and to the Opponent, answers to the questions, and Performance of the Reviewer (5-7 min)
  • Questions and remarks of the Observer 1 (2 min)
  • Questions and remarks of the Observer 2 (2 min)
  • Additional Remarks of the Reviewer (2 min)
  • Additional Remarks of the Opponent (2 min)
  • Concluding Remarks of the Reporter (2 min)
  • Questions and Remarks of the Jury (7 min)
  • Pause. Discussion of the Jury (20 min)
  • The Jury show the marks. Participants may ask questions to jurors (15 min)

The Finals

After the two rounds, the teams are ranked (half the quiz score plus the sum of the rounds scores). Among the teams winning both rounds or with the highest ratings, 3-5 are selected for the Grand Final. The next 3-5 are selected for the Small Final. The Finals are conducted like the former rounds, but weigh more in the final ranking, as the final score is the previous one plus the Finals score times π.

The competition ends with a closing ceremony to announce the final ranking and congratulate all teams.