| 1971-1974 | Van Mildert College, Durham University |
| 1974-1977 | Magdalen College and Department of Astrophysics, Oxford University |
| 1977-1978 | Astronomy Department, University California Berkeley (Lindemann Fellow) |
| 1977-1980 | Christ Church and Department of Astrophysics, Oxford (Junior Research Lecturer) |
| 1980-1981 | Physics Department, University California Berkeley (Miller Fellow) |
| 1981-1988 | Lecturer, Astronomy Centre, University of Sussex |
| 1986-1987 | Nuffield Foundation Science Fellow, University of Sussex |
| 1988-1989 | Senior Lecturer, Astronomy Centre, University of Sussex |
| 1989 | Reader, Astronomy Centre, University of Sussex |
| 1989-1999 | Professor, Astronomy Centre, University of Sussex |
| 1989-1990 | Acting Director, Astronomy Centre, University of Sussex |
| 1992-1993 | Royal Society Leverhulme Fellow, University of Sussex |
| 1994-1999 | PPARC Senior Fellow, University of Sussex |
| 1995-1999 | Director, Astronomy Centre, University of Sussex |
| since 1999 | Professor of Mathematical Sciences, University of Cambridge |
| Director, Millennium Mathematics Project, University of Cambridge |
| Professorial Fellow, Clare Hall, Cambridge |
| 2004-2007 | Vice President, Clare Hall, Cambridge |
| 2003-2007 | Gresham Professor of Astronomy, Gresham College, London |
| 2005 | First Eastern Visiting Cambridge Professor (China and Hong Kong) |
| 2006 | Li Ka Shing Foundation Visiting Scholar (China and Hong Kong) |
| since 2007 | Fellow of Gresham College |
| since 2008 | Gresham Professor of Geometry, Gresham College |
| 1984-2009 | Ressort Innenpolitik in der Radio-Information, ORF - Österreichischer Rundfunk |
| 1991-1997 | Ressortleiterin, ORF - Österreichischer Rundfunk |
| 1997-2002 | Sendungsverantwortliche "Report", Moderation des politischen TV-Wochenmagazins des ORF "Report" |
| 1999 | Sendungsverantwortung für "Report International" |
| 2001 | Sendungsverantwortung für "Europa-Panorama" |
| 2002-2005 | Moderation von "Modern Times", des Zukunftsmagazins des ORF |
| 2002-2009 | Leiterin der Hauptabteilung "Bildung und Zeitgeschehen", ORF - Österreichischer Rundfunk |
| seit 2009 | Freie Journalistin und Moderatorin |
