Rudolf Wolf attended the University of Zurich where he studied under Raabe. He also studied at Vienna and Berlin where he attended lectures by Encke, Dirichlet, Poggendorf, Steiner and Crelle. In 1838 he visited Gauss then the following year he became a teacher of mathematics and physics at the University of Bern. He became professor of astronomy there in 1844.
Wolf became director of the Bern Observatory in 1847. In 1855 he accepted a chair of astronomy at both the University of Zürich and the Federal Institute of Technology in Zürich. An observatory was opened at Zürich in 1864, largely due to Wolf's efforts.
Wolf wrote on prime number theory and geometry, then later on probability and statistics - a long paper discussed Buffon's needle experiment. He estimated p by Monte Carlo methods.
Wolf's main contribution, however, was his work on the 11 year
sunspot cycle. He extended earlier work by A H Schwabe and he was the
codiscoverer of the connection of the cycle with geomagnetic activity on Earth.
In 1848 he devised a system now known as Wolf's sunspot numbers. This system is
still in use for studying solar activity by counting sunspots and sunspot
groups.