Four university professors from American institutions have won Sweden's 2012 Crafoord prizes in mathematics and astronomy.
Each category is worth 4 million kronor ($580,000).
Belgian Jean Bourgain, from Princeton's Institute for Advanced Study, and Australian-American Terence Tao, from the University of California, share the mathematics prize for "exceptional problem-solving" and fundamental contributions to "several branches of mathematics."
American Andrea Ghez shared Thursday's astronomy prize with German Reinhard Genzel for finding "the most reliable evidence" yet that supermassive black holes exist. Both are University of California professors.
Genzel is also scientific director of Germany's Max-Planck-Institut for Extraterrestral Physics.