Ashley JaegerProfessor BrewerMAT 267 May 6, 2008Women in Mathematics: The Remarkable Life and Worksof Sofia Kovalevsky “Say what you know, do what you must, come what may.”~Sofia KovalevskySofia Kovalevsky, a prominent Russian mathematician, is arguably the greatest woman mathematician of the 19th century. She was a woman of great aptitude who, despite many obstacles, made notable contributions to a male dominated society. A distinguished and brilliant writer, she founded the mathematical journal, Acta Mathematica. Perhaps her greatest accomplishment however was her composition on rotational motion of a rigid body that won her the prestigious Prix Bordin (“Bordin Prize”). In addition to her contributions to the scientific realm as a brilliant mathematician, Sofia also actively contributed to the political realm as an advocate for women’s rights. Her life and works are truly fascinating and admirable; neither deserves to be overlooked or forgotten by scientific history. Although her name is tied to manyimportant mathematical theorems, little is commonly known about her remarkable life. Instead allowing her life to gather dust in our historical archives, Sofia Kovalevsky should be recognizedfor all her many contributions.The fact that Sofia Kovalevsky commonly worked under a pseudonym makes it increasingly more difficult to research and credit her accomplishments. Sofia most commonly used the name “Kovalevsky” to work and publish under. “Kovalevsky” however is actually masculine version of her surname “Kovalevskaya”. To add more confusion, Sofia, Sonya Sonia, and Sofya are all common variations of her given name and its infinite alternative spellings. I will hereon refer to her as Sofia Kovalevsky to avoid misunderstanding. Sofia's passion and interest in mathematics was sparked at a very young age. It is rumored that her father papered his old calculus notes on her nursery wall due to a shortage of wallpaper and that as a child she studied “the writing on the wall”. Sofia secretly began her education against her father’s wishes at the age of thirteen. Using books written by a neighboringprofessor, Sofia self-educated herself on the concepts of algebra, trigonometry, and physics. Sofia showed extreme brilliance in both literature and mathematics but her heart belonged to math. Sofia strongly believed that "Many who have never had occasion to learn what mathematics is confuse it with arithmetic, and consider it a dry and arid science. In reality, however, it is the science which demands the utmost imagination....It seems to me that the poet must see what others do not see, must look deeper than others look. And the mathematician must do the same thing.” Believing Sofia to be the next Pascal, her neighbor pleaded and convinced her father to permit her to continue studying mathematics.Sofia avidly desired to continue her education after her private tutoring, but unfortunatelyRussian universities would not yet admit women. Thus, her only alternative to pursue mathematics was to study abroad. However her father refused to let her travel alone. Sofia let nothing stand in her way and resolved these problems by entering into a fictitious marriage with a young paleontologist by the name of Vladimir Kovalevsky. This fictitious husband enabled her to travel abroad for her education because a married woman did not need her father’s signature for a passport. In 1869, they left Russia with her sister and went to Heidelberg, Germany where she obtained special permission of the math professors to study at the University. After two years sheleft Heidelberg to study in Berlin with Karl Weierstrass, an illustrious German mathematician. Because the university in Berlin would not permit women to attend class, Weierstrass had to privately tutor Sofia for four years. At the end these four years, Sofia presented three papers for her Ph.D. dissertation, all of which were deemed more than acceptable by Weierstrass. The three papers she presented for her degree were “On the Theory of Partial Differential Equations”, “On the Reduction of a Certain Class of Abelian Integrals of the Third Rank to Elliptic Integrals”, and “Supplementary Remarks and Observations on Laplace’s Research on the Form of Saturn’s Rings.” Sofia was amazingly the first women to apply for a degree in mathematics in Germany and was granted her degree summa cum laude from the Göttingen University without ever being allowed to attend class (in absentia)! Sofia Kovalevsky then became a noted Professor of Mathematics at the University of Stockholm in 1884 and it was four years later when she won the aforementioned Prix Bordin for her paper, “On the Rotation of a Solid Body about a Fixed Point," In this paper Sofia developedthe theory for the rotation of an unsymmetrical top where its center of mass is not on an axis within the body. This special case of rotation came to be known as the Kovalevsky top. Not only was Sonya Kovalevsky indispensable to the field of mathematics, but she also played a large role as an advocate for women’s rights. Sonya Kovalevsky continuously strived toobtain the greatest education available to her in time where universities had just begun to open their doors to women. The road to acceptance and esteem by mathematical society was exceedingly difficult; Sonya faced many disadvantages and barriers due to her gender. As a woman in a male dominated discipline, Kovalevsky’s innovative work in mathematics caused scientific and mathematic society re-envision their foolish preconceptions of feminine inferiority.Despite many obstacles, Sonya’s incredible brilliance, passion, and drive contributed to her well-merited success. She was a woman of many firsts, first female member of the Russian Academy of Sciences (although oddly she was unable to attend actual meetings), first German woman to receive a Ph.D. in mathematics, first European woman to attain a full, prestigious professorship, and first female winner of the Bordin Prix. This long list of “firsts” developed a strong sense of esteem for Sofia Kovalevsky and also caused society to recognize the capabilitiesof women for the first time.The Cauchy-Kovalevskaya TheoremThe Cauchy-Kovalevskaya Theorem“On the Theory of Partial Differential Equations,” the first paper presented by Sofia for her Ph.D., received the high honor of being published in Crelle’s journal in 1875. This was a very high honor for