Modern group theory can be said to have been born at the beginning of the twentieth century. As with many fields in mathematics, World War I caused a hiatus in the study of group theory. In 1932, Wilhelm Magnus solved the word problem for one-relator groups, and combinatorial group theory blossomed from the 30’s through the 60’s, laying the foundation for today’s research in the areas of geometric and probabilistic group theory, as well as public key cryptography and group theory.

We will talk about some of the personalities involved and the advances they made in group theory during the twentieth century.