By Rajaram Nityananda
Recently NASA scientists analysed the crazy variations in the brightness of small moons orbiting the planet Pluto and figured that the cause is their irregular shape and even more irregular rotation, which presents different faces to the farway sun, sending back varying amounts of light to NASA on faraway Earth. It turns out that the mathematical problem – of a rigid body under external forces – has a long history, in which a woman mathematician, Sofia Kovalevskaya played a stellar role.
Here she is aged 30 (photography was quite mature by 1880).
As a young woman she moved from Russia, where she learnt mathematics but was barred from higher studies. Switzerland was the nearest country with universities that were open to young women. Kovalevskaya, with the help of her older sister, a radical young woman, entered a ‘fictional’ marriage to gain permission from her father to leave the country. Eventually she ended up in Germany, where she was sometimes barred from classes but still won a doctorate from University of Gottingen with ‘private tuition’ from Karl Weierstrass, one of the best mathematicians of the time. She later went to Sweden where she won a full professorship (the first woman to do so in Northern Europe), and the editorship of Acta Mathematica, a peer-reviewed mathematical journal. The French Academy was in the habit of awarding prizes for solutions of outstanding problems and she won one in 1888, for her work entitled “Mémoire sur un cas particulier du problème de le rotation d’un corps pesant autour d’un point fixe, . …..” Did you guess ‘a memoir on a particular case of the problem of rotation of a rigid body about a fixed point?’ Sort of.
The legends of that time were trying to solve this problem. As it turns out, they tried the general case, which is, like Pluto’s moons, chaotic. Sofia (who was Sonya by then, for unknown reasons) was the lady (ahem) who put her finger (ahem) on the one and only case, which was not chaotic. We still don’t understand why exactly this works. It belongs to the mysterious particular cases of mathematics. Much of Ramanujan’s work is of that nature or was when it was done. The general theories come later.
Sofia/Sonya contributed one major general theory as well, to the field of PDEs (those who are partial to differential equations will know what this stands for), a theorem in all the textbooks. Suffice it to say that this field is alive and well in Bengaluru, if one includes satellite town Yelahanka.
And as a last teaser, why did George Eliot have this passage, “In short, woman was a problem which, since Mr. Brooke’s mind felt blank before it, could hardly be less complicated than the revolutions of an irregular solid” in her novel Middlemarch? It turns out that Sofia wrote fiction, spent time in England, and was part of Eliot’s circle.
Every one of the mathematicians’ names mentioned in connection with her today — Euler, Lagrange, Weierstrass, Mittag-Leffler — were legends of their time and are all mentioned in textbooks today. She moved among them first as a star student but later as an equal. Since she died at 41, clearly the volume of her work would not match theirs, but the depth and quality would.
Rajaram Nityananda is a theoretical physicist working at the Azim Premji University, Bengaluru. He was earlier with the Raman Research institute, Bengaluru and the National Centre for Radio Astrophysics Pune. His research includes mechanics, optics, and statistical phenomena mainly in astronomy, and he is keen to write and lecture about about these areas.