Adami was born in Brussels, Belgium, and graduated from the European School of Brussels I. He obtained a Diplom in physics from the University of Bonn and an MA and a Ph.D. in theoretical nuclear physics from Stony Brook University in 1991. Adami was a Division Prize Fellow in the lab of Steven E. Koonin at the California Institute of Technology from 1992-1995, and was subsequently on the Caltech faculty as a senior research associate.