On resolving singularities of plane curves via a theorem attributed to Alfred Clebsch (Q2041104)

This paper discusses a theorem in birational geometry that J. L. Coolidge attributed to Alfred Clebsch which states that ``any arbitrary plane algebraic curve can be birationally transformed into another having only double points as singularities''. The background is reconstructed from letters Felix Klein exchanged with Max Noether in 1894, when Noether was completing work on a lengthy report with Alexander Brill on the history of algebraic functions. Noether was deeply troubled to learn that Klein had informed him back in 1869 about relevant results that Clebsch and Leopold Kronecker had discussed in Berlin. These exchanges with Klein led to revisions in the Brill-Noether report, made in part to ensure Noether's own priority rights and larger intellectual legacy.