Her father had previously served in the Austro-Hungarian Army as an officer during World War I, and the family moved to Vienna to escape Béla Kun's Hungarian Soviet Republic. Klára Dán, known as Klári to her friends and family, was born in Budapest, Hungary on August 18, 1911, to Károly Dán and Kamilla Stadler, a wealthy Jewish couple.

She was introduced to a lot of her work through her husband, John von Neumann. Klára made significant contributions to the world of programming, including work on the Monte Carlo method, ENIAC, and MANIAC I.

She was the first woman to execute modern-style code on a computer. Klára Dán von Neumann (born Klára Dán 18 August 1911 – 10 November 1963) was a Hungarian-American mathematician, self-taught engineer and computer scientist, noted as one of the first computer programmers.