Nielsen began writing this work (Det Uudslukkelige in Danish) during the summer of 1915, and completed it two weeks before the first performance, which he conducted in Copenhagen on February 1, 1916. In addition to triple winds and full brass, Nielsen specified two sets of timpani, as far apart as possible on the stage. While Symphony No. 3, the Espansiva of 1910-1911, proclaimed his indubitable maturity, the Fourth (which he started planning in 1914) became Nielsen's equivalent of Beethoven's Eroica, just as the Fifth would be his counterpart of Beethoven's Fifth. Years before, he had written, "It is a fact that he who brandishes the hardest fist will be remembered the longest." Certainly the proximity and brutality of World War I influenced the conflicts in his Fourth Symphony, although the Fifth of 1921-1922 expressed his real horror. In the score of The Inextinguishable Nielsen wrote, "Under this title the composer has endeavored to indicate in one word what music alone is capable of expressing to the full: the elemental Will of Life. Music is Life, and like it is inextinguishable. The title...might therefore seem superfluous; the composer, however, has employed the word to underline the strictly musical character of his subject. It is not a program, but only a suggestion about the right approach to the music."

Taking a cue from Mendelssohn's Scottish and Schumann's D minor symphonies, he wrote all four movements of The Inextinguishable to be played without pause, beginning with a violent struggle between the keys of C major and D minor. More even than Franck's D minor Symphony, however, Nielsen's Fourth is a "motto" symphony based on the E major second theme of his opening Allegro. This is introduced in "sweet-sounding" thirds by a pair of clarinets, replaced by flutes, horns, and strings before the strident main theme returns to do battle—not only in the development but during the recapitulation—a contest won by the motto in the coda, although not decisively enough to forestall a later, even more vehement challenge in the finale. Without pause, the folk-colored Poco allegretto in G replaces a scherzo, piquant writing for winds that remembers Serenata invano of 1914 as much as it anticipates the Quintet of 1922 and the flute and clarinet concertos. Its principal subject derives from the motto theme, but Nielsen puts this on hold in the ensuing Poco adagio quasi andante, whose searing, starkly scored main theme is developed in two-part counterpoint, derived from old Netherlands polyphony according to one Nielsen scholar. A nervous, stuttering new theme increases the tension. While the movement climaxes in E major, this crumbles in the struggle between themes. Suddenly, the strings begin a wild race that plunges into a terminal Allegro whose swaggering main theme in E major declares itself, only to be challenged by two sets of timpani that duel brutally for control until E major can finally assert itself and hold. Triumphant, the motto theme invites both timpanists to punctuate the "inextinguishable" victory.

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