FAMILY BACKGROUND 
Sophia Kovalevskaya (nee Korvin-Krukovskaya) was born on January 15, 1850 in Moscow. Her father, Vasily Krukovsky, an artillery officer, came of an ancient family ennobled for the military services of their ancestors—Ukrainian Cossacks. But it took him 15 years before his right to the privileged status of an ancient noble family was formally recognized. Krukovsky received the name of Korvin-Krukovsky because his family's coat-of-arms resembled that of the Polish family Korwin-Kjukowski. He entered the army in 1817, and took part in the 1828 and 1829 campaigns in the Balkans against Turkey. He retired in 1858 with the rank of Lieutenant-General. 
Krukovsky was a stern, reserved man. He was 40 years old when he married his young bride Yeliziaveta Shubert. Well educated himself, he gave his children ia good education, but did not approve of their progressive views. He was very angry when he learned that his elder daughter Anna had written a story for Dostoyevsky's magazine and had been paid for it. But gradually, under the influence of his daughters, he changed his outlook, and towards the end of his days became reconciled with their views. 
Y. F. Litvinova, Kovalevskaya's first Russian biographer and a friend of the family, wrote that Sophia inherited her father's intellect and strong character. 
Sophia's mother, Yelizaveta, was the daughter of a general, a geodesy specialist. She had received a good schooling and was well-read. Among her friends were Nikolai Pirogov, the famous surgeon, educationalist and public figure; the Mathematics Professor Pyotr Lavrov, who was arrested by the tsarist government and then left the country, and the progressive artist Fyodor Moller, a friend of Gogol's. Yelizaveta liked to recall the evenings she had spent in their company discussing education, family life, etc. 
Her acquaintance with Pirogov, who held progressive views on education, was of great interest. Pirogov advanced his views on education in an article published in 1856 entitled Questions of Life, in which, in particular, he wrote about the harm of special training.without a broad back-ground. 
Although Yelizaveta was well versed in educational questions and had read Jean Jacques Rousseau, she paid little attention to the upbringing of her own children. 
One day her two little daughters went to the woods by themselves and got lost. This incident, coupled with the elder daughter Anna's poor progress in her studies, brought home to Krukovsky that his children's upbringing was being neglected. He discharged their governess and engaged new teachers. 
Sophia showed her aptitude very early. At the age of five she taught herself to read with the aid of the adults wihom she would ask the meaning of this or that letter in a newspaper. 
She was put into the hands of expert teachers. But there was one sorrow that clouded her childhood and of which Kovalevskaya herself spoke. Her parents had wanted a boy when she was born, and they were consoled only five years later, when her brother Fedya was born. Anna, the first-born, seven years Sophia's senior, was was Fedya. But Sophia got less attention and she was jealous and suffered greatly.

CHILDHOOD IN POLIBINO 
When Korvin-Krukovsky retired from the army in 1858, the family went to live on their Polibino estate (formerly Palibino, Vitebsk Gubernia).
There Sopihia spent her childhood, of which she later wrote in Childhood Reminiscences. 
Polibino lies between Velikiye Luki and Nevel, to the right off the main road, about 17 miles from Velikiye Luki. The landscape has retained much of its beauty. The road rises and falls between the undulating spurs of the Valdai Hills; on both sides stretch endless fields, spotted here and there with young groves. There are many beautiful lakes in the region, and huge boulders—solitary sentinels of the ice age—are not infrequently to be seen. But the impenetrable pine forest which a century ago surrounded the estate is no more. Gone too .are the packs of wolves which used to stage fearsome "concerts" in the vicinity of the estate in the winter. A birch-tree avenue leads to a beautiful old park. The avenue of limes where Sophia used to walk with her governess has grown very thick and shady. 
The house was destroyed by the fascist invaders during the Second World War, and now only the shell-pierced thick walls remain. 
In the summer-time, many tourists visit the estate where two outstanding Russian women spent their childhood and youth. 
The house was a very massive affair, topped by a rectangular tower with a spire. This tower was the girls' favourite retreat, and it was here that Anna told Sophia about her first steps in writing. Here, too, they dreamed of their future, of a better life for the people. 
Their new teacher—Margaret Smith—was the daughter of English parents living in Russia. Miss Smith tried her best to transform the Russian girls into well-bred English girls. Anna, however, had already matured into a "free Cossack" iand was not susceptible to foreign influence. 
Sophia was therefore the object of Miss Smith's full attention. Sophia had to get up at seven o'clock. In winter it was still dark and she longed to sleep a little longer. Then came the cold shower which Kovalevskaya describes as "a breath-taking second of icy cold, followed by a sensation of boiling water throbbing through my veins; then I felt a wonderful surge of suppleness and energy spreading all through my body." After breakfast she had a music lesson at which Miss Smith kept time by tapping loudly with a cane. This was followed by an extremely dull 90-minute walk up and down the avenue with Miss Smith. 
Sophia was glad when bad weather kept them indoors. There she was usually able to deceive Miss Smith and do a little reading in the library instead of playing in the adjoining corridor. Sophia loved to write poetry iand at the age of 12 she was convinced that she would become a poetess. She was especially proud of two poems: A Bedouin Speaks to His Horse, and A Pearl Diver's Sensations. One poem she devoted to the Panama Canal project which the press wias widely commenting on at the time. Miss Smith, however, frowned on this poetry-making and tore up her verses whenever she had the chance. When Sophia misbehaved she would pin a paper to her back telling everyone of her offence. 
But Miss Smith taught Sophia how to work systematically, and as the child was very painstaking and persistent she did not find it difficult to comply with her teacher's demands. 
Sophia's first teacher on general subjects was Iosif Malevich, who was considered to be a very good tutor. Malevich began teaching Sophia in October 1858, when she was eight years'old. "She was a sweet attractive child," he wrote in his memoirs, "of rather sturdy build, with hazel-brown eyes which sparkled with intelligence and kindliness." She wias very attentive, quickly grasped a subject, punctually executed her tasks and knew her lessons well. 
As Malevich's favourite subject was literature he at first was proud of Sophia's literary inclinations. He especially recollected her poem about the pearl diver. 
"Surprised and delighted at her realistic, sensible, well-expressed point of view, which a philologist would have not been ashamed of," he wrote, "I would return to my room after a lesson and ponder for hours, 'not so much on the extraordinary 'success of my capable pupil, as on the future of a girl of a rich and esteemed family. What if she were ordained to traverse a different path in life? What would happen if fortune deprived her of excessive means for a livelihood and only provided her with moderate means for a higher education, which, unfortunately, women cannot receive in our universities? Then, oh yes! then I was positive that my talented pupil could occupy a prominent position in the literary world." 
Malevich wrote that Sophia's progress in arithmetic was not unusual. One day at dinner her father asked her whether she liked arithmetic and she replied that she did not. But four months later she said she did like arithmetic. 
Some four years of studies passed by smoothly, and Sophia made good progress. When she learned about the ratio of the diameter of a circle to its circumference she substituted her own solution for the one Malevich had explained. Malevich saw that she was correct, but insisted that she use his method, admonishing ;her for solving problems in a roundabout way. He wrote: "I don't know whether she was taken aback by my unexpected demand, or I may have pricked her pride, but she flushed, cast down her eves, and burst into tears." 
When Malevich told Sophia's father about this incident the latter praised her, saying: "Good girl, Sophia. You're not like me. I used to be very glad to know my lesson anyhow and you, a slip of a girl, propose your own solution!" It was very gratifying for Sophia to be encouraged by her father. 
Sophia studied arithmetic for two and a half years, then algebra and geometry for three and a half years, finishing with plane to be papered. But we had many rooms and there was mot sufficient wall-paper for one of the children's rooms. As we got our wall-paper from St. Petersburg it was not worth while ordering a small amount, thus the slighted room remained for a (number of years pasted with sheets of paper which, by happy coincidence, turned out to be Ostrogradsky's lectures on differential and integral calculus which my father had bought in his student days.
 "These sheets with their strange formulas soon drew my attention. I used to spend hours on end before the mysterious walls, trying at least to decipher separate phrases and find out the proper order of the sheets. By daily scrutiny the formulas and even the wording became imprinted on my brain, although at the time they were Greek to me."
Sophia relates how she studied mathematics with her cousin Michael, the only son of a widowed landowner. His mother wanted Michael to enter a secondary school, and he was being prepared for the 7th form. Michael, however, wanted to be ;an artist and considered all this swotting unnecessary. 
He came with his mother to Polibino for one summer and Malevich began teaching him. Michael, however, was very insolent. He used to interrupt the lessons with all kinds of 'nonsense. He had to be made to study. 
Sophia's help was enlisted. She was to show that even a girl who was younger than he could easily learn things. The ruse succeeded. Michael became ashamed of himself, and covered an extensive course of algebra and geometry that summer. 
Nikolai Tyrtov (1822-1888), teacher of physics at the Naval School, presented his friend Korvin-Krukovsky with a copy of his Rudiments of Physics. 
When he visited the Korvin-Krukovskys, he was surprised to learn that fourteen-year-old Sophia was studying his text-book independently. In the chapter on optics she came across the concept of the sine which hitherto she not known. She began to ponder on the mysterious formulas and unravelled their meaning. Tyrtov was amazed when Sophia explained to him the simple theorems of trigonometry. He called her a new Pascal and (advised Korvin-Krukovsky to have her taught higher mathematics. 
At a family council it was decided that Sophia would study mathematics during her visits to St. Petersburg with her mother and sister.
Yalta and Crimea Private Tour Guide Sergey Tsarapora