**1687**(October 21st), son of another Niklaus, the brother of Johann and Jakob Bernoulli, from both of whom he received training in Mathematics.

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*.