At that time, a few universities in western Europe recruited female students. In order to get rid of the shackles of family and win the opportunity to go abroad, Sophie adopted the method of "fake marriage", chose a like-minded man who also wanted to study abroad, and formally married him, so that he could go abroad together without family constraints. She and her "husband" Vladimir Kovaliv, a graduate of the Department of Paleontology of Moscow University, held a "wedding" in September 1868. The following spring, Sophie left Petersburg with Sophie's sisters Anna and Vladimir to study in Germany. Under the recommendation of physicist Professor Kirchhoff, Sophie finally entered the school gate of Heidelberg University after all kinds of difficulties. She abandoned the comfortable and luxurious life of the aristocratic family and lived a hard study life in a strange foreign city. Sophie arrived in Berlin on August 1870. After strict examination, Professor Wilstrass (a professor at the University of Berlin) realized that Sophie was a rare mathematical genius. However, at that time, the University of Berlin refused to recruit female students. The professor sympathized with Sophie's desire for science and decided to teach her alone in her own home. Under the careful training of Wilstrass, Sophie received a good education from a master of mathematics. She studied hard and gave full play to her talent in mathematics. During her four years in Berlin University, she not only completed all the university courses, but also completed three important math papers. At this time, she was only 23 years old. Sophie's three papers, each one is enough to make her a "mathematician". 1874 In July, on the recommendation of Wilstrass, the German mathematics center G? ttingen University awarded her the "highest honorary doctorate in mathematics" degree (no examination and defense), and Sophie became the first female doctor in mathematics in history.

1874-1880 she temporarily left mathematics research and fought for the equality of women's rights (especially education) in Russia. She returned to Berlin on 188 1. 1883 On the recommendation of Swedish mathematicians, she was hired as a lecturer at Stockholm University. 1884 promoted to professor. Sophie attended the International Conference of Scientists held in Copenhagen. During this period, the unresolved problem of "mathematical water demon" for more than 100 years occupied her whole body and mind. The problem of "mathematical water demon" is the rotation of a rigid body around a fixed point. Because of its importance in theory and application, in order to make a major breakthrough in the research on this issue, the French Academy of Sciences offered three awards with the "Bolding Prize" of 1888. 1888, when the French Academy of Sciences announced the new prize again, Sophie broke through this difficult problem with her efforts and published "On the Rotation of Rigid Bodies around Fixed Points", and won a prize of 5,000 francs by the method of hyperelliptic function integration. A woman has achieved such a great success that the whole European scientific community has caused a sensation. 10 February 10, Sophie Kovalevskaya died of pneumonia in Stockholm.