Kurt Friedrich Gödel (1906 - 1978) was an Austrian-American mathematician and logician best known for proving the Gödel's incompleteness theorems. He showed that within any axiomatic mathematical system there are propositions that can not be (dis)proved using the axioms of the system. He is generally considered as one of the greatest logician of all time.
Girolamo Cardano (1501 - 1576) was an Italian mathematician best known for his treatise entitled Ars Magna (Artis magnae sive de regulis algebraicis: The Art of Solving Algebraic Equations) in which he published the solutions of cubic equations (due to Tartaglia) and quartic equations (due to Ferrari). The Cardano's formula (commonly referred to as Cardan's formula) is named after him.
Isaac Newton (1642 - 1727) was an English mathematician and physicist who is considered as one of the greatest intellectuals of all time. He was one of the developers of Infinitesimal calculus and the author of the celebrated Principia and the Opticks.
René Descartes (1596 - 1650) was a French mathematician and philosopher who in order to unify the hitherto largely separate disciplines of algebra and geometry invented coordinate geometry (modern term: 'analytic geometry'). The Cartesian coordinate system is named after him ('Cartesian' /pronounced: kɑrˈtiʒən/ is the adjectival form of 'Descartes').
IPA:
[ʁəne dekaʁt]
Listen:
First your hear 'René Descartes' in French and then 'Cartesian coordinate system' in English.
Sophus Lie (1842 - 1899) was a Norwegian mathematician most famous for initiating the study of transformation groups which has culminated in the modern theory of Lie groups.