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Education and early works

In 1902, Prokofiev's mother met Sergei Taneyev, director of the Moscow Conservatory, who initially suggested that Prokofiev should start lessons in piano and composition with Alexander Goldenweiser. Unable to arrange that, Taneyev instead arranged for composer and pianist Reinhold Glière to spend the summer of 1902 in Sontsovka teaching Prokofiev. The first series of lessons culminated, at the 11-year-old Prokofiev's insistence, with the budding composer making his first attempt to write a symphony. The following summer, Glière revisited Sontsovka to give further tuition. When, decades later, Prokofiev wrote about his lessons with Glière, he gave due credit to his teacher's sympathetic method but complained that Glière had introduced him to "square" phrase structure and conventional modulations, which he subsequently had to unlearn. Nonetheless, equipped with the necessary theoretical tools, Prokofiev started experimenting with dissonant harmonies and unusual time signatures in a series of short piano pieces he called "ditties" (after the so-called "song form", more accurately ternary form, on which they were based), laying the basis for his own musical style.

Despite his growing talent, Prokofiev's parents hesitated over starting their son on a musical career at such an early age, and considered the possibility of his attending a good high school in Moscow. By 1904, his mother had decided instead on Saint Petersburg, and she and Prokofiev visited the then capital to explore the possibility of moving there for his education. They were introduced to composer Alexander Glazunov, a professor at the Saint Petersburg Conservatory, who asked to see Prokofiev and his music; Prokofiev had composed two more operas, Desert Islands and The Feast during the Plague, and was working on his fourth, Undina. Glazunov was so impressed that he urged Prokofiev's mother to have her son apply for admission to the Conservatory. He passed the introductory tests and enrolled that year.

Several years younger than most of his class, Prokofiev was viewed as eccentric and arrogant and annoyed a number of his classmates by keeping statistics on their errors. During that period, he studied under, among others, Alexander Winkler for piano, Anatoly Lyadov for harmony and counterpoint, Nikolai Tcherepnin for conducting, and Nikolai Rimsky-Korsakov for orchestration (though when Rimsky-Korsakov died in 1908, Prokofiev noted that he had only studied with him "after a fashion"—he was just one of many students in a heavily attended class—and regretted that he otherwise "never had the opportunity to study with him"). He also shared classes with the composers Boris Asafyev and Nikolai Myaskovsky, the latter becoming a close and lifelong friend.

As a member of the Saint Petersburg music scene, Prokofiev developed a reputation as a musical rebel, while getting praise for his original compositions, which he performed himself on the piano. In 1909, he graduated from his class in composition with unimpressive marks. He continued at the Conservatory, studying piano under Anna Yesipova and continuing his conducting lessons under Tcherepnin.

In 1910, Prokofiev's father died and Sergei's financial support ceased. Fortunately, he had started making a name for himself as a composer and pianist outside the Conservatory, making appearances at the St Petersburg Evenings of Contemporary Music. There he performed several of his more adventurous piano works, such as his highly chromatic and dissonant Etudes, Op. 2 (1909). His performance of it impressed the organisers of the Evenings sufficiently for them to invite Prokofiev to give the Russian premiere of Arnold Schoenberg 's Drei Klavierstücke, Op. 11. Prokofiev's harmonic experimentation continued with Sarcasms for piano, Op. 17 (1912), which makes extensive use of polytonality. He composed his first two piano concertos around then, the latter of which caused a scandal at its premiere (23 August 1913, Pavlovsk). According to one account, the audience left the hall with exclamations of "'To hell with this futuristic music! The cats on the roof make better music!'", but the modernists were in rapture.

In 1911, help arrived from renowned Russian musicologist and critic Alexander Ossovsky, who wrote a supportive letter to music publisher Boris P. Jurgenson (son of publishing-firm founder Peter Jurgenson); thus a contract was offered to the composer. Prokofiev made his first foreign trip in 1913, travelling to Paris and London where he first encountered Sergei Diaghilev 's Ballets Russes.