Joseph Saurin was educated at home, being brought up as a Calvinist by his father, Pierre Saurin, who was a Calvinist minister. Joseph was the youngest of his parents three children, who were all boys. His brother, Élie Saurin, went on to become a famous Protestant theologian. Pierre Saurin was the only tutor for all three of his sons and he wanted them all to enter the ministry. He taught them to read and write and then took them on to more advanced topics eventually teaching them theology and Hebrew.
Saurin entered the Calvinist ministry as a curate in Eure in 1684 but was soon in trouble for his outspoken views which he delivered in sermons from the pulpit. He was forced to leave France and went first to Geneva in Switzerland. He then became a curate at Bercher, Yverdon. However, although he established himself in this position, he continued to be too outspoken for his own good and, in 1685, refused, despite strong pressure being exerted on him, to sign the Consensus of Geneva. This document had been drawn up by John Calvin in 1552 in an attempt to unite the Swiss Reformed churches with regard to the doctrine of predestination. This had become a fundamental part of the Calvinist belief but created divisions within the Protestant Churches. Saurin, always someone with strong opinions of his own, did not accept the doctrine of predestination as presented in the Consensus.
On 18 October 1685, Louis XIV had revoked the Edict of Nantes and deprived the French Protestants of all religious and civil liberties. This now put Saurin in a very difficult position, unable to return to France as a Protestant minister. Fontenelle writes in  that of the two systems of religion, he found one too severe, the other too soft. He went to Holland where he had discussions with many elders regarding his religious problems.
Saurin had married a daughter of the noble family de Crouzas in Switzerland; they had at least one son Bernard-Joseph who became a poet and writer of plays. Saurin now, however, found himself in difficulties since in October 1688 a French army marched into the Palatinate and a war had begun. However he was able to go to France to discuss his religious problems with the Roman Catholic Bishop Bossuet and, on 21 September 1690, he converted to Roman Catholicism. He made the difficult return to Switzerland to be reunited with his wife, frightened of religious persecution after his religious conversion. After some adventures (recounted in ) he was able to return to France with his wife.
Back in Paris in 1690 he had to seek a new career and he felt that it was either to be mathematics or the legal profession. Eventually he decided on mathematics and he began first to learn the subject and then to teach it. He became friends with de L'Hôpital, Malebranche and Varignon but, by 1702, he was in dispute with Rolle over the calculus. This came about because of his role as mathematics editor of the Journal des Sçavants. He appealed to the Académie Royal des Sciences but, although Saurin was correct, they had no wish to come out against Rolle who was a member. Perhaps to be diplomatic, Saurin was elected to the Académie Royal des Sciences in 1707.
He spent several months in jail for writing libellous poems about Rousseau. However on 7 April 1712 he was exonerated by the Parliament and Rousseau was sent into exile. Then he retired to spend the rest of his life working on mathematics.
Saurin made contributions to the calculus, wrote on Jacob Bernoulli's problem of quickest descent and Huygens' theory of the pendulum. Mahoney writes :-
Saurin made no original contributions to mathematics. Rather, firmly committed to the new infinitesimal calculus, he explored the limits and possibilities of its methods and defended it against criticism based on lack of understanding. Rolle, for example, assumed that the new method of tangents could not handle singularities of multivalued curves where dy/dy took the form 0/0. In reply [Réponse à écrit de M Rolle de l'Académie Royale des Sciences inséré dans le Journal du 13 Avril 1702, sous le titre de Règles et Remarques pour le Problème général des Tangentes par M Saurin (1702), Remarques sur les courbes des deux premiers exemples proposés par M Rolle dans le Journal du jeudi 13 Avril 1702 (1703), and Remarques sur un cas singulier du problème général des tangentes (1716)], Saurin explicated the nature and treatment of such indeterminate expressions on the basis of de L'Hôpital's theorem ...
His contributions to the problem of curves of quickest descent amount first to solving the original problem and then to solving a generalisation. His two papers on this topic both appeared in 1709, the first being Solutions et analyses de quelques problème appartenants aux nouvelles méthodes, and the second Solution générale du problème .... Other contributions by Saurin include Manière aisée de démontrer l'égalité des temps dans les chutes d'un corps tombant par une cycloude ... (1703) in which he gave proofs of Huygens' theorems on centrifugal force and the cycloidal path. He defended Huygens' theory of the pendulum after it was attacked by le Chevalier de Liouville in éclaircissement sur une difficulté proposé aux mathématiciens par M le Chevalier de Liouville (1722). In 1709 he proposed a modification of Descartes' vortex theory of gravity in Examen d'une difficulté considérable proposée par M Huygens contre le système cartésien sur la cause de la pesanteur. Johann Bernoulli considered it the best theory of gravity so far proposed and, as Aiton points out in , Saurin could have brought together the ideas of Newton and Descartes with his proposed theory. He did not go down that road, however, choosing to attack Newton's ideas as being a return to ancient style philosophies.
It is clear from the biographical details that we have related above that Saurin fell out with many people around him. In fact Fontenelle  says that he had few friends other than de L'Hôpital and Malebranche, and that he adopted the somewhat strange working routine of sleeping in the day and doing mathematics throughout the night. He died of lethargic fever at the age of 78.
Article by: J J O'Connor and E F Robertson