[1] Beloch studied mathematics at the Sapienza University of Rome and wrote her undergraduate thesis under the supervision of Guido Castelnuovo.
She received her degree in 1908[1] with Laude and dignità di stampa, which means that her work was worthy of publication, and in fact her thesis Sulle trasformazioni birazionali nello spazio (On Birational Transformations in Space) was published in the Annali di Matematica Pura ed Applicata.
In 1920 she moved to Palermo to work under Michele De Franchis, an important figure of the Italian school of algebraic geometry at the time.
[4] She continued working on topological properties of algebraic curves either planar or lying on ruled or cubic surfaces for most of her life, writing about a dozen papers on these subjects.
As a consequence she showed how to extract cubic roots by paper folding,[7] something that is impossible to do by ruler and compass.