Ralph Herman Abraham (July 4, 1936 – September 19, 2024) was an American mathematician. In 1968 he became a member of the faculty of the

University of California, Santa Cruz The University of California, Santa Cruz (UC Santa Cruz or UCSC) is a public university, public Land-grant university, land-grant research university in Santa Cruz, California, United States. It is one of the ten campuses in the University of C ...

(UCSC), and later stayed on as a

professor emeritus ''Emeritus/Emerita'' () is an honorary title granted to someone who retirement, retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". ...

of mathematics.

Life and work

Abraham earned his BSE (1956), MS (1958), and

PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

(1960) from the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

. His PhD thesis, titled ''Discontinuities in General Relativity'', was written under the direction of Nathaniel Coburn. Prior to joining UCSC, he held positions at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

(research lecturer in mathematics; 1960–1962),

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

(postdoctoral fellow and assistant professor of mathematics; 1962–1964) and

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

(assistant professor of mathematics; 1964–1968). He has also held visiting positions in

Amsterdam Amsterdam ( , ; ; ) is the capital of the Netherlands, capital and Municipalities of the Netherlands, largest city of the Kingdom of the Netherlands. It has a population of 933,680 in June 2024 within the city proper, 1,457,018 in the City Re ...

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

Warwick Warwick ( ) is a market town, civil parish and the county town of Warwickshire in the Warwick District in England, adjacent to the River Avon, Warwickshire, River Avon. It is south of Coventry, and south-east of Birmingham. It is adjoined wit ...

Barcelona Barcelona ( ; ; ) is a city on the northeastern coast of Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second-most populous municipality of Spain. With a population of 1.6 million within c ...

Basel Basel ( ; ), also known as Basle ( ), ; ; ; . is a city in northwestern Switzerland on the river Rhine (at the transition from the High Rhine, High to the Upper Rhine). Basel is Switzerland's List of cities in Switzerland, third-most-populo ...

, and

Florence Florence ( ; ) is the capital city of the Italy, Italian region of Tuscany. It is also the most populated city in Tuscany, with 362,353 inhabitants, and 989,460 in Metropolitan City of Florence, its metropolitan province as of 2025. Florence ...

. He founded the Visual Math Institute at UCSC in 1975; at that time, it was called the "Visual Mathematics Project". He was editor of ''World Futures'' and for the ''International Journal of Bifurcations and Chaos''. Abraham was a member of cultural historian William Irwin Thompson's Lindisfarne Association. Abraham has been involved in the development of

dynamical systems theory Dynamical systems theory is an area of mathematics used to describe the behavior of complex systems, complex dynamical systems, usually by employing differential equations by nature of the ergodic theory, ergodicity of dynamic systems. When differ ...

since the 1960s and 1970s. He has been a consultant on

chaos theory Chaos theory is an interdisciplinary area of Scientific method, scientific study and branch of mathematics. It focuses on underlying patterns and Deterministic system, deterministic Scientific law, laws of dynamical systems that are highly sens ...

and its applications in numerous fields, such as medical physiology, ecology, mathematical economics, and psychotherapy. Another interest of Abraham's concerns alternative ways of expressing mathematics, for example visually or aurally. He has staged performances in which mathematics, visual arts and

music Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...

are combined into one presentation. Abraham developed an interest in "Hip" activities in Santa Cruz in the 1960s and had a website gathering information on the topic. He credited his use of the

psychedelic drug Psychedelics are a subclass of hallucinogenic drugs whose primary effect is to trigger non-ordinary mental states (known as psychedelic experiences or "trips") and a perceived "expansion of consciousness". Also referred to as classic halluc ...

DMT with "swerv ng hiscareer toward a search for the connections between mathematics and the experience of the Logos". Abraham died at his home in Santa Cruz County, at the age of 88.

Works

;Publications * 1987
''Foundations of Mechanics''
2nd edn. With Jerrold E. Marsden; 1st edition 1967 * 1988.
Manifolds, Tensor Analysis, and Applications
', 2nd edn. With Jerrold E. Marsden and Tudor Ratiu. * 1992. ''Dynamics, the Geometry of Behavior'', 2nd edn. With C. D. Shaw * 1992. ''Trialogues on the Edge of the West''. With

Terence McKenna Terence Kemp McKenna (November 16, 1946–April 3, 2000) was an American ethnobotanist and mystic who advocated for the responsible use of naturally occurring psychedelic plants and mushrooms. He spoke and wrote about a variety of subjects, ...

and

Rupert Sheldrake Alfred Rupert Sheldrake (born 28 June 1942) is an English author and parapsychology researcher. He proposed the concept of morphic resonance, a conjecture that lacks mainstream acceptance and has been widely criticized as pseudoscience. He has ...

* 1992. ''Chaos, Gaia, Eros'' * 1995. ''The Web Empowerment Book''. With Frank Jas and Will Russell * 1995. ''Chaos in Discrete Dynamical Systems''. With Laura Gardini and Christian Mira. * 1997. ''The Evolutionary Mind''. With Terence McKenna and Rupert Sheldrake * 2000. ''The Chaos Avant-garde''. With Yoshisuke Ueda * 2011.
Bolts From the Blue
' * 2016
''Hip Santa Cruz, Vol. 1.''
;Film * 1989. ''The Strange New Science of Chaos'', as himself * 2009

as himself * 2010. '' DMT: The Spirit Molecule'', as himself

References

External links

Personal website
Ralph Abraham. {{DEFAULTSORT:Abraham, Ralph 1936 births 2024 deaths People from Burlington, Vermont Mathematicians from Vermont 20th-century American mathematicians 21st-century American mathematicians Complex systems scientists Chaos theorists University of Michigan College of Engineering alumni University of Michigan College of Literature, Science, and the Arts alumni University of California, Berkeley College of Letters and Science faculty Columbia University faculty University of California, Santa Cruz faculty Princeton University faculty