He originally studied the violin at the Franz Liszt Academy of Music in his native Budapest.

[1] In 1963, Fürst founded the Irish Chamber Orchestra, and developed his conducting career from that point.

In 1978 he conducted the premiere of Salome by Sir Peter Maxwell Davies and subsequently recorded it.

A number of his students at the Paris Conservatoire won prestigious conducting competitions.

Late in life he was invited to become head of orchestral conducting at Royal College of Music in London, but he did not live enough to take up the post.