Kurepa graduated from the University of Belgrade Faculty of Mathematics under Aleksandar Milojević, and later electrical engineering in the United Kingdom, under J. D. Craggs.
In 1964, Kurepa joined the newly founded Institute of Physics at the University of Belgrade as a research scientist.
At present, about a dozen of Kurepa's students are scientists and professors at leading universities in Australia, Belgium, the UK, France, Germany, Slovenia, Sweden, and the United States.
During the isolation of Yugoslavian scientists from the rest of the world due to United Nations sanctions, Kurepa organized a very successful meeting of SANU in 1997 to celebrate the 100th anniversary of the discovery of the electron.
AUPR has organized protest meetings at Serbian universities, published statements regarding university autonomy and freedom of opinion, appealed to international academic associations for intervention with the Serbian government, and engaged in similar activities.