In 1704 he studied at Basel University under Jakob Bernoulli, receiving maths degree.
In 1709 he received the degree of Jurisprudence with an application of probability to law.
In 1705, he accompanied his uncle, Johann, and his family on their return to Basel from Gröningen.
In 1716, he succeeded Hermann as Professor of Mathematics at Padua (Galileo's old job), where he worked primarily on differential equations and geometry.
In 1722 he returned to Basel as Professor of Logic, exchanging this in 1731 for a Professorship in Law.
He engaged in correspondence with Montmort - the exchange of letters was published by Montmort as part of one of his books. During this exchange the Saint Petersburg Paradox was discussed, a paradox which was considered at length by Daniel Bernoulli in St.Petersburg.
In correspondence with Leibniz he noted that the binomial expansion for (1+x)n diverges for x greater than 1.
He pointed out Newton's misunderstanding of higher-order derivatives which had cause Newton problems with the inverse problem of central force in a resisting medium.
stated the equivalence of second order derivatives in partial differentiation (of those differentiated wrt to the same variables but in different order
In 1713, he published the Ars conjectandi of Jakob and later the Opera Omnia.