This question was the title of a 1959 novel by Françoise Sagan – but don't worry, I haven't become a late-life Sagan fan.
There was a time, in the latter part of the 19th century, when, in an early outbreak of identitarianism, the musical world divided into lovers of Brahms, and therefore of the established Romantic tradition, or lovers of Wagner, and therefore of 'new music' and new musical directions. So how you answered the question mattered. For myself, I've had problems with both men, but recently I have definitely been coming round to Brahms, mostly by way of his chamber music, but also with a new appreciation of his symphonies – a CD of the great Carlos Kleiber conducting the Fourth opened my eyes. And then I discovered, to my surprise, that Glenn Gould was fascinated by Brahms's late intermezzos, and rated his own recording of them among his best: 'It's the sexiest interpretation of Brahms's intermezzi you've ever heard – and I really think it's perhaps the best piano playing I have done.'
In his (best) collection, The Cost of Seriousness, Peter Porter has a short, enigmatic poem titled 'A Brahms Intermezzo' –
The heart is a minor artist
hiding behind a beard.
In middle age
the bloodstream becomes a hammock
slowing down for silence –
till then, this lullaby,
arpeggiated thunder
and the streams running
through Arcadia. I, too,
says the black-browed creature,
am in this vale of sweetness,
my notes are added to eternity.
I wonder if this beautiful, melancholy piece was the intermezzo Porter had in mind?