In 1948, he made a mathematical conjecture on coefficients of -valent functions, first published in his
Columbia University dissertation thesis and then in a closely following paper. After the proof of the Bieberbach conjecture by Louis de Branges, this conjecture is considered the most interesting challenge in the field, His researches in the field continued in the paper
Univalent functions and nonanalytic curves, published in 1957: in 1968, he published the survey
Open problems on univalent and multivalent functions, which eventually led him to write the two-volume book
Univalent Functions. Apart from his research activity, He was actively involved in teaching: he wrote several college and high school textbooks including
Analytic Geometry and the Calculus, and the five-volume set
Algebra from A to Z. He retired in 1993, became a Distinguished Professor Emeritus in 1995, and died in 2004. ==Selected works==