René de Sluze studied at the University of Louvain from 1638 to 1642. He then went to Rome where he received a law degree from the University of Sapienza in 1643. Sapienza was the name of the building which the University of Rome occupied at this time and it gave its name to the University. After this de Sluze studied a large number of subjects in Rome including many languages, mathematics and astronomy.
De Sluze became a canon in the church in 1650, then went to Liège also as a cannon. His knowledge of law meant that he progressed rapidly within the Church and rose to positions of influence quickly. By 1659 he was a member of the privy council of the Bishop of Liège, then he became abbot of Amay in 1666.
De Sluze wrote many books on mathematics. He worked on calculus, having studied the works of Cavalieri and Torricelli while in Rome, in particular he worked on the equation for the cycloid. In his works de Sluze discusses spirals, points of inflection and the finding of geometric means. He extended work by Descartes and Fermat on drawing tangents and finding turning points of functions.
Because de Sluze's position in the church prevented him going to meet with other mathematicians he did most of his mathematical contacts by correspondence. He corresponded with many mathematicians in England, France and other European countries, for example Pascal, Huygens, Wallis and Ricci were among those with whom he was in regular contact.
De Sluze was elected a Fellow of the Royal Society in 1674.
The family of curves yn = k(a-x)pxm for positive integer exponents, are called the pearls of Sluze.
De Sluze did not write exclusively on mathematics. He also wrote on astronomy, physics, natural history, history and theological matters connected with his work in the church.