Cholesky was born in Montguyon, France. His paternal family was descendant from the Cholewski family who emigrated from Poland at the beginning of 19th century. He attended the Lycée in Bordeaux and entered the École Polytechnique, where Camille Jordan and Henri Becquerel taught. He worked in geodesy and map-making, was involved in surveying in Crete and North Africa before World War I. He is primarily remembered for the development of a matrix decomposition known as the Cholesky decomposition which he used in his surveying work. He served the French military as engineer officer and was killed in battle a few months before the end of World War I; his discovery was published posthumously by his fellow officer Commandant Benoît in the Bulletin Géodésique.
^Commandant Benoit, Note sur une méthode de résolution des équations normales provenant de l'application de la méthode des moindres carrés à un système d'équations linéaires en nombre inférieur à celui des inconnues (Procédé du Commandant Cholesky), Bulletin Géodésique 2 (1924), 67-77.