Sur les Ensembles de Distances. Des Ensembles de Points d'un Espace Euclidien.

Neuchâtel: Secrétariat de l'Université, 1939. Octavo. Original grey wrappers printed in black. Text block unopened. Wrappers tanned along the edges and spine, a little creasing at the edges, small chip at the top of the upper wrapper, contents faintly toned in the margins. An excellent copy. First edition of this significant work on set theory, an unopened copy in the original wrappers. Author Sophie Piccard (1904-1990) showed great mathematical ability from an early age. She was born and completed her first undergraduate education in Russia, but fled to Switzerland with her parents in 1925. Piccard then completed a second mathematics degree, and obtained her doctoral dissertation on probability at the University of Lausanne. Following her father's death, she worked as an actuary and then an administrative secretary, but continued doing research, and in 1936 became assistant in geometry to at professor at the University of Neuchâtel. She succeeded to his position in 1938, and from 1943 held the chair of higher geometry and probability theory, becoming the first female full professor in Switzerland. "Her research interests were set theory and group theory. She published papers in other areas as well: function theory, the theory of relations, probability theory, and actuarial science" (Ogilvie, p. 1020). "In 1939 Piccard published her book 'Sur les ensembles de distances des ensembles de points d'un espace Euclidean.' If A and B are point sets of a Euclidean space, the distance set of the pair (A,B), denoted by D(A,B), is the set of all numbers d such that there is a pair of points, one in A and the other in B, whose distance is d. Piccard's book made a detailed study of various questions concerning D(A,B). The review of the book in Mathematical Reviews said that 'a few results in the field under investigation are due to Steinhaus, Sierpinski and Ruziewicz, but after chapter I, the results are almost entirely new'" (Biographies of Women Mathematicians, Agnes Scott College website).