Nicolaus worked as his father's assistant helping him with correspondence. In particular he was involved with writing letters concerning the famous priority dispute between Newton and Leibniz. He not only replied to Taylor regarding the dispute but he also made important mathematical contributions to the problem of trajectories while working on the mathematical arguments behind the dispute.
Nicolaus worked on curves, differential equations and probability. He died only 8 months after taking up an appointment in St Petersburg at a young age when his talents promised so much for the future. Fleckstein writes in :-
With his brother Daniel he travelled in France and Italy, where both received appointments to the St Petersburg Academy. Within a year, however, he contracted and died of a hectic fever.
Article by: J J O'Connor and E F Robertson