January 1, 2007 - December 31, 2010
| President: | L. Lovász | (Hungary) |
| Vice-Presidents: | Z.-M. Ma | (China) |
| C. Procesi | (Italy) | |
| Secretary: | M. Grötschel | (Germany) |
| Members at Large: | S. Baouendi | (USA) |
| M. de León | (Spain) | |
| R. Piene | (Norway) | |
| C. Praeger | (Australia) | |
| V. Vassiliev | (Russia) | |
| M. Viana | (Brazil) | |
| Ex-officio: | J. Ball | (UK), Past President |
January 1, 2007 - December 31, 2010
| President: | S. Dani | (India) |
| Secretary: | G. Gonzalez-Sprinberg | (France) |
| Members at Large: | G. Boente | (Argentina) |
| P. Cordaro | (Brazil) | |
| J-P. Gossez | (Belgium) | |
| M. T. Niane | (Sénégal) | |
| M. Sanz-Solé | (Spain) | |
| J. Zhang | (China) |
January 1, 2007 - December 31, 2010
| C. Houzel | (France) | |
| P. M. Neumann | (UK) |
January 1, 2010 - December 31, 2012
| President: | William (Bill) Barton | (New Zealand) |
| Vice Presidents: | Mina Teicher | (Israel) |
| Angel Ruiz | (Costa Rica) | |
| Secretary-General: | Jaime Carvalho e Silva | (Portugal) |
| Members at Large: | Mariolina Bartolini Bussi | (Italy) |
| Sung Je Cho | (Korea) | |
| Roger Howe | (USA) | |
| Renuka Vithal | (New Zealand) | |
| Zhang Yingbo | (China) |
January 1, 2007 - December 31, 2010
| Chair: | Sir John Ball | (UK) |
| Committee Members: | Olga Caprotti | (Italy) |
| James Davenport | (UK) | |
| Michael Doob | (Canada) | |
| Carol Hutchins | (USA) | |
| Peter Olver | (USA) | |
| Ulf Rehmann | (Germany) |
January 1, 2007 - December 31, 2010
| Chair: | Charles Herbert Clemens | (USA) |
| Members: | Jill Adler | (South Africa) |
| Hajer Bahouri | (Tunisia) | |
| John M. Ball | (United Kingdom) | |
| Shrikrishna G. Dani | (India) | |
| Jean-Pierre Gossez | (Belgium) | |
| Andreas Griewank | (Germany) | |
| Lê Dung Trang | (Italy) | |
| Jacob Palis | (Brazil) | |
| Peter Pang Yu Hin | (Singapore) | |
| Ragni Piene | (Norway) | |
| Michel Jambu | (France) | |
| Sheung Tsun Tsou | (United Kingdom) | |
| ex officio: | Professor László Lovász | (Hungary) |
| Body | Representative/liaison person | (end of) Term |
| COSPAR | Alain Bensoussan | 2010 |
| Gruber Foundation Cosmology Prize | Roger Penrose | 2011 |
| ICSU | Manuel de León | 2010 |
| ICSU Ad hoc Group on Weighted Voting | Marcelo Viana | 2010 |
| ICSU Regional office for Asia and the Pacific (ROAP) | Manuel de León | 2010 |
| Zhiming Ma | 2010 | |
| Cheryl Praeger | 2010 | |
| ICSU Regional office for Latin America and the Caribbean (ROLAC) | Marcelo Viana | 2010 |
| ICMI | Cheryl Praeger | 2010 |
| CEIC | John Ball | 2010 |
| Niels Henrik Abel Memorial Fund | Ragni Piene | 2010 |
| Ramanujan Prize | Marcelo Viana | 2010 |
| ICHM | Peter Neumann | 2010 |
| Christian Houzel | 2010 | |
| IMU archive at Helsinki university | Guillermo Curbera | 2010 |
| UNESCO | Michèle Artigue | 2010 |