Brahms wrote this symphony in his early 50s while he was at Wiesbaden, a picturesque town on the Rhine river.
The melody of the third movement brings beauty and sadness together. Clara Schumann had described it as "a pearl but a grey one, dipped in a tear of woe". The main theme of the melody, as also for the whole symphony , is the theme incorporating the notes C-A-A (Do-La-La), the musical letters of the name "Clara". Robert Schumann had "invented" this theme for his wife Clara (The "Clara theme") and was incorporating it in his music to make his wife part of it. Brahms borrowed the "Clara theme" and used it in this symphony.
While composing this symphony, Brahms was most probably thinking of his old friend and mentor, Robert Schumann, as he was at Wiesbaden, looking out the window to the mythical river Rhine where Robert had chosen to jump in his suicidal attempt. Following this attempt, Schumann was closed in an asylum for 2 years, during which Brahms fell in love with Clara Schumann. Following Schumann's death, Brahms left Clara, although she remained the love of his life. Therefore, the river Rhine which had also given its name to the symphony was associated in Brahms' mind with Robert Schumann, and all of his intense memories around the triad Brahms-Robert Schumann-Clara Schumann. A remarkable link between music and life which also explains the binding of lyricism and pain.