Although the first viscount had fought for the Crown in the Anglo-Scots war of 1639, malicious gossip said that he paid the then enormous sum of £1200 for the title and was almost ruined as a result.

Until 1660 he played no part in public life: being a staunch Royalist, he felt it best to live quietly and devote himself to his mathematical studies.

[1] Although his attendance at the Royal Society had become infrequent, and he had quarrelled with some of his fellow members, he was nonetheless greatly displeased to be deprived of the presidency in 1677.

[1] Brouncker never married, but lived for many years with the actress Abigail Williams (much to Samuel Pepys' disgust) and left most of his property to her.

His mathematical work concerned in particular the calculations of the lengths of the parabola and cycloid, and the quadrature of the hyperbola,[2] which requires approximation of the natural logarithm function by infinite series.