Claire Falkenstein was born on July 22, 1908, in Coos Bay, Oregon. She studied at the University of California, Berkeley, specializing in art but also studying philosophy and anthropology. She had not yet graduated when she held her first solo exhibition in 1930 at the East-West Gallery, San Francisco. In the 1930s, while teaching to support herself, she devoted her time to sculpture and created ceramic pieces, which are among the first examples of nonobjective American sculpture. Her series of wooden sculptures titled Exploded Volumes date from the first half of the 1940s. These were made of movable parts that could be combined in different ways by the viewer. In 1948 she started teaching at the California School of Fine Arts, where she met Richard Diebenkorn, Clyfford Still, and other Abstract Expressionists.
Falkenstein moved to Paris in 1950 and associated with artists Jean Arp and Alberto Giacometti. She joined a group of American artists that included Sam Francis and Paul Jenkins and whose ideas were promoted by the art connoisseur Michel Tapié. The group was interested in drawing connections between the Art Informel movement and Einsteins's theories on mathematics and physics. Falkenstein developed a new type of artistic expression called Topology, based on the relation between matter and space. Falkenstein started to make sculptures by soldering scrap material and by the mid-1950s she went on to produce airy metal structures of increasingly bigger sizes and volumes.
In 1954 the Galleria Montenapoleone in Milan held a major solo exhibition of her work, and four years later she was asked to make the railing of the Galleria Spazio in Rome. On this occasion she inserted pieces of colored glass in an open, grid-like structure of soldered metal. She used a similar technique in 1961 to create the gates for Peggy Guggenheim's museum-house in Venice. Her design employed a uniform, linear metal structure that extended in all directions, thus creating a seemingly endless construction. In 1962 she moved back to the United States, where she set up her studio in Venice, California, and received many public commissions, such as the fountain for the San Diego Art Museum and the windows for St. Basil's Cathedral, Los Angeles. Late in life, the artist turned to painting. Falkenstein died in Venice, California, on October 23, 1997.