Karl Gräffe worked as a jeweller in Hamburg from 1813 to 1816 and he thought that he might become a goldsmith. However a lot of hard work saw him manage to pass the entrance examinations of the Carolineum at Brunswick.
In 1824 Gräffe went to Göttingen where he attended lectures by Gauss and Thibaut. While in Göttingen, Gräffe wrote a prize winning dissertation. He became a lecturer in Zurich, becoming professor there in 1860.
Gräffe is best remembered for his method of numerical solution of algebraic equations, developed to answer a prize question of the Berlin Academy of Sciences. It is particularly suitable for methods developed for using computers to solve mathematical problems. This method is today called the Dandelin-Gräffe method after the two mathematicians who independently investigated it. The history of the Dandelin-Gräffe method is discussed in [3] and [4].