The Guardian reports that he had carved himself out a successful scientific career, but :
... ultimately he could not escape the legacy of being the offspring of one of the most famous and tragic literary relationships of the 20th century.Sylvia Plath was famously very ill with depression and also died at her own hand. Depression often runs in families, and Sylvia had at least one other close relative who suffered from it (according to Kay Jamison's Touched with Fire). But Judith Flanders in The Guardian quite rightly has a go at those who would sensationalise these deaths, calling them a kind of curse of poetry.
The picture shows Sylvia with baby Nicholas taken from The Daily Mail which has a very good piece.
Nicholas was immortalised in his mother's poetry, including in this poem, Morning Song written just months before she died:
Love set you going like a fat gold watch.
The midwife slapped your footsoles, and your bald cry
Took its place among the elements.
Our voices echo, magnifying your arrival. New statue.
In a drafty museum, your nakedness
Shadows our safety. We stand round blankly as walls.