Internationally recognised Norwegian scientists include the mathematicians Niels Henrik Abel and Sophus Lie who is recognized as some of the most influential mathematicians of all time. Caspar Wessel was the first to describe vectors and complex numbers in the complex plane. Ernst S. Selmer's advanced research lead to the modernization of crypto-algorithms. Thoralf Skolem made revolutionary contributions to mathematical logic. Øystein Ore and Ludwig Sylow made important contributions in group theory. Atle Selberg was one of the most significant mathematicians of the 20th century, for which he was awarded both a Fields Medal and Abel Prize.