Johannes Brahms was not only a great composer, but also an accomplished musical scholar. He was fascinated with music of the past and even owned the first complete publication of J.S. Bach's entire compositional output.
In addition to Bach, Handel and Beethoven, he particularly idolized Joseph Haydn. In fact, Brahms' Variations on a Theme of Joseph Haydn is based on one of Haydn's one chorale tunes, the "Saint Anthony Chorale".
Brahms composed two arrangements of this particular work. One arrangement is the one we just heard for full orchestra. The other, however, is for a much smaller ensemble: two pianos. Brahms composed the two-piano version of the Haydn variations first before later orchestrating the work.