He worked on mathematics both with his father and as an independent worker. He had the remarkable distinction of winning the Prize of the Paris Academy on no less than four separate occasions. On the strength of this he was appointed to his father's chair in Basel when Johann Bernoulli died.
However, quoting :-
... thereafter his mathematical production dwindled to occasional academic papers and a treatise, although he lived to almost as old as his father. His shyness and frail constitution did not, however, prevent him from engaging in extensive scientific correspondence (about 900 items) and from furthering the publication, in four volumes, of his father's Opera Omnia. He personified the mathematical genius of his native city in the second half of the eighteenth century.Johann(II) Bernoulli worked mainly on heat and light.
Maupertuis, who was President of the Berlin Academy, was accused by Samuel König of plagiarising Leibniz's work. Voltaire was so critical of Maupertuis' work that eventually he left Berlin and, in 1756, travelled to Basel where he took refuge in Johann(II) Bernoulli home. Maupertuis remained in Johann's home for the last three years of his life.
Article by: J J O'Connor and E F Robertson