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| 1965-1971 | Study of mathematics and physics in Göttingen and Zürich (ETH) |
| 1971 | Diploma at the University of Göttingen |
| 1971-1973 | Scientific assistent at the University of Göttingen |
| 1973 | PhD (Dr. rer. nat.) at the University of Göttingen |
| 1973-1980 | Scientific assistent at the University of Bonn |
| 1980 | State doctorate at the University of Bonn |
| 1981 to date | Professor at the University of Kaiserslautern |
| 1993 to date | Director of the Centre for Computeralgebra at the University of Kaiserslautern |
| 1993 to date | Ombudsman at the University of Kaiserslautern |
| 2002 to date | Director of the Mathematical Research Institute Oberwolfach |
| 2009 | Honorary doctorate of Leibniz Universität Hannover |
| 2010 to date | Chair of ERCOM (European Research Centres on Mathematics) |
| 2011 | Honorary Member of the Real Sociedad Matematica Espanola (RSME) |
| 2012 to date | Editor-in-Chief of Zentralblatt MATH |