In 1968 he became a member of the faculty of the University of California, Santa Cruz (UCSC), and later stayed on as a professor emeritus of mathematics.

His PhD thesis, titled Discontinuities in General Relativity, was written under the direction of Nathaniel Coburn.

He has been a consultant on chaos theory and its applications in numerous fields, such as medical physiology, ecology, mathematical economics, and psychotherapy.

Abraham developed an interest in "Hip" activities in Santa Cruz in the 1960s and had a website gathering information on the topic.

[4] He credited his use of the psychedelic drug DMT with "swerv[ing his] career toward a search for the connections between mathematics and the experience of the Logos".