Preda Mihăilescu
fl. 1955, Bucharest, Romania
Romanian-Swiss number theorist who in 2002 proved Catalan's conjecture — that 8 and 9 are the only consecutive perfect powers — 158 years after it was posed.
Preda Mihăilescu was born in Bucharest and left Romania for Switzerland in 1973. He studied mathematics and computer science at ETH Zürich, earning his diploma in 1981 and, after periods working in industry, a PhD in 1997 under Erwin Engeler and Hendrik Lenstra.
Catalan's conjecture, proposed by Eugène Catalan in 1844, states that the only solution in integers greater than one to is — that is, 8 and 9 are the only consecutive perfect powers among the positive integers. In April 2002, after 158 years during which only partial results were known (such as bounds by J. W. S. Cassels and Robert Tijdeman), Mihăilescu proved the full conjecture using deep tools from algebraic number theory: the arithmetic of cyclotomic fields, Galois module structure, and the annihilation of class groups via Francisco Thaine's method. The proof was published in 2004 in Crelle's Journal; the result is now called Mihăilescu's theorem.
After research positions including the University of Paderborn, Mihăilescu joined the University of Göttingen in 2005 as a Volkswagen Foundation Professor, where he has continued work in number theory and cryptography.
Workplaces: University of Paderborn, University of Göttingen
Romania, Switzerland