Prokofiev and Stravinsky restored their friendship, though Prokofiev did not particularly like Stravinsky's later works ; it has been suggested that his use of text from Stravinsky's A Symphony of Psalms to characterise the invading Teutonic knights in the film score for Eisenstein's Alexander Nevsky ( 1938 ) was intended as an attack on Stravinsky's musical idiom.

Eisenstein's first film, Glumov's Diary ( for the theatre production Wiseman ), was also made in that same year with Dziga Vertov hired initially as an " instructor.

Strike ( 1925 ) was Eisenstein's first full-length feature film.

Eisenstein's idiosyncratic and artistic approach to cinema was incompatible with the more formulaic and commercial approach of American studios.

The thing which appeared to save Eisenstein's career at this point was that Stalin ended up taking the position that the Bezhin Meadow catastrophe, along with several other problems facing the industry at that point, had less to do with Eisenstein's approach to filmmaking as with the executives who were supposed to have been supervising him.

This was started, completed, and placed in distribution all within the year 1938, and represented not only Eisenstein's first film in nearly a decade but also his first sound film.

Prokofiev composed the score for Eisenstein's film and Eisenstein reciprocated by designing sets for an operatic rendition of War and Peace that Prokofiev was developing.

Eisenstein's film, Ivan The Terrible, Part I, presenting Ivan IV of Russia as a national hero, won Joseph Stalin's approval ( and a Stalin Prize ), but the sequel, Ivan The Terrible, Part II was criticized by various authorities and would go unreleased until 1958.

Eisenstein's health was also failing: he was struck by a heart attack during the making of this picture, and soon died of another at the age of 50.

Eisenstein's experiment was a mixed success ; he " was disappointed when Potemkin failed to attract masses of viewers ", but the film was also released in a number of international venues, where audiences responded more positively.

The Irish born painter Francis Bacon ( 1909 – 1992 ) was profoundly influenced by Eisenstein's images, particularly the Odessa Steps shot of the nurse's broken glasses and open mouthed scream.

It was this reenactment which provided the inspiration for the scenes in Sergei Eisenstein's film October: Ten Days That Shook the World.

In 1241, it was taken by the Teutonic Knights, but Alexander Nevsky recaptured it several months later during a legendary campaign dramatized in Sergei Eisenstein's 1938 movie.

Eisenstein's montage experiments met with official disapproval ; the authorities complained that October was unintelligible to the masses, and Eisenstein was attacked — for neither the first time nor the last — for excessive " formalism ".

It was produced by Goskino via the Mosfilm production unit, with Nikolai Cherkasov in the title role and a musical score by Sergei Prokofiev, Alexander Nevsky was the most popular of Eisenstein's three sound films.

The film was the first of Eisenstein's dramatic films to use sound.

It was at the Cinémathèque Française that he befriended the head, Henri Langlois ( later claiming that he worked for Langlois for twelve years ) and was allowed to rummage through the Cinémathèque's archives, in which he found prints of Sergei Eisenstein's Que Viva Mexico !, which he attempted to put into Eisenstein's original order.

It has been used as an alienating Brechtian technique ( the Verfremdungseffekt ) that makes the audience aware of the unreality of the film experience, in order to focus the audience's attention on the political message of a film rather than the drama or emotion of the narrative — as may be observed in some segments of Sergei Eisenstein's The Battleship Potemkin.

Alexander Nevsky is less experimental in its narrative structure than Eisenstein's previous films: it tells one story with a single narrative arc and focuses on one main character.

Because of this romantic aura, a spirit of struggle for a just cause imbues such diverse works about that period as Sergei Eisenstein's film The Battleship Potemkin and Boris Pasternak's narrative poems " 1905 " and " Lieutenant Schmidt " as well as Shostakovich's symphony.

Another of Eisenstein's films, 1927's October, depicted the Bolshevik perspective on the October Revolution, culminating in the storming of the Winter Palace which provided Soviet viewers with the victory that the workers and peasants lacked in Battleship Potemkin, ending with Lenin ( as played by an unknown worker ) declaring that the government is overthrown.

The 1930s saw Prokofiev's scores for Sergei Eisenstein's epic movies, and also soundtracks by Isaak Dunayevsky that ranged from classical pieces to popular jazz.

* Sergei Eisenstein prepared a screenplay in the late 1920s which he hoped to have produced by Paramount or by Charlie Chaplin during Eisenstein's stay in Hollywood in 1930.

For example consider, in which the coefficient 1 of x is not divisible by any prime, Eisenstein's criterion does not apply to H. But if one substitutes for x in H, one obtains the polynomial

An important class of polynomials whose irreducibility can be established using Eisenstein's criterion is that of the cyclotomic polynomials for prime numbers p. Such a polynomial is obtained by dividing the polynomial by the linear factor corresponding to its obvious root 1 ( in fact its only rational root if ):

This argument is much more complicated than the direct argument by reduction mod p. It does however allow one to see, in terms of algebraic number theory, how frequently Eisenstein's criterion might apply, after some change of variable ; and so limit severely the possible choices of p with respect to which the polynomial could have an Eisenstein translate ( that is, become Eisenstein after an additive change of variables as in the case of the p-th cyclotomic polynomial ).

This shows that this polynomial satisfies the hypotheses of the generalization of Eisenstein's criterion for the prime ideal since, for a principal ideal, being an element of is equivalent to being divisible by.

It is important to notice how early Mexican cinematographers were influenced and encouraged by Soviet director Sergei Eisenstein's visit to the country in 1930.

This is already apparent in his breakthrough piece, The Deluge ( 1957 – 58 ), which is inspired by Eisenstein's notes for a film based on a writing by Leonardo da Vinci ; in other words Goehr writes music about a director's notes for a film based on the writings of a painter!

*** Battleship Potemkin ( album ), a 2005 album of electronic and orchestral music written by Neil Tennant and Chris Lowe from Pet Shop Boys to accompany Eisenstein's film

Soviet cinema played an important part in cultivating the leader's cult of personality: from 1937 and onward, in a gradual process, Stalin's reign was legitimized by depicting him as Vladimir Lenin's most devout follower and by positively presenting historical autocrats-like in Sergei Eisenstein's Ivan the Terrible.

Sergei Eisenstein's famous motion picture The Battleship Potemkin commemorated the uprising and included a scene where hundreds of Odessan citizens were murdered on the great stone staircase ( now popularly known as the " Potemkin Steps "), in one of the most famous scenes in motion picture history.

The Untouchables finale shoot out in the train station is a clear borrow from the Odessa Steps sequence in Sergei Eisenstein's The Battleship Potemkin.

Marker begins the film with the Odessa Steps sequence from Sergei Eisenstein's film The Battleship Potemkin, which Marker points out is a fictitious creation of Eisenstein which has still influenced the image of the historical event.

The scene is perhaps the best example of Eisenstein's theory on montage, and many films pay homage to the scene, including Terry Gilliam's Brazil, Francis Ford Coppola's The Godfather, Brian De Palma's The Untouchables, Tibor Takacs ' Deathline, Laurel and Hardy's The Music Box, George Lucas's Star Wars Episode III: Revenge of the Sith, Chandrashekhar Narvekar's Hindi film Tezaab, Shukō Murase's anime Ergo Proxy and Peter Sellers ' The Magic Christian.

* The movie being shown to American prisoners at the Soviet camp near Calumet is Alexander Nevsky ( 1938 ), Sergei Eisenstein's Soviet anti-Nazi film.

This scene is notable because it became the legitimate, historical depiction of the storming of the Winter Palace owing to the lack of print or film documenting the actual event, which led historians and filmmakers to use Eisenstein's recreation.

In this particular example it would have been simpler to argue that H ( being monic of degree 2 ) could only be reducible if it had an integer root, which it obviously does not ; however the general principle of trying substitutions in order to make Eisenstein's criterion apply is a useful way to broaden its scope.

For example, the final shot of Keaton is a reference to Ingmar Bergman's Persona, the sequence with the stone lions is a parody of Sergei Eisenstein's Battleship Potemkin.

For example, a letter from Gauss to Humboldt dated 1846 April 14 says that Eisenstein's talent is one that nature bestows only a few times a century (" welche die Natur in jedem Jahrhundert nur wenigen erteilt ").

In mathematics, Eisenstein's theorem, named after the German mathematician Gotthold Eisenstein, applies to the coefficients of any power series which is an algebraic function with rational number coefficients.

Then Eisenstein's theorem states that there is a finite set S of prime numbers p, such that every prime factor of a number d < sub > n </ sub > is contained in S.