In 1874 she began her doctorate on a study of Saturn's great rings while studying at Gottingen University. Denied a Chair (a noted profession) because of her gender didn't surprise her, yet still she managed to find mentors to assist her. Arriving at the University of Stockholm, Sweeden in 1884 for a five year professorate in Astronomy. She is the first women to ever hold a professorate in mathematics, however both Laura Bassi (1711-1778) and Maria Agnesi (1718-1799) preceded her.
Her family was scandalized from her love affair with mathematics. Working at night, while tending to her family throughout the day, she resembled ancient pagan priests/astronomers and cartographers who had to work in extraordinary solitude with little institutional support. She was forced into marriage so as to travel abroad, she's buried a few miles from where she worked at the University of Stockholm. Her work on differential equations and integral analysis or Abelian integrals is still studied today.