Ralph Herman Abraham (born July 4, 1936) is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He has been 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. It is one of the ten campuses in the University of California syste ...

(where he is currently

professor emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

of mathematics) since 1968.

Life and work

Abraham earned his

BSE BSE may refer to: Medicine * Bovine spongiform encephalopathy, also known as mad cow disease, a neurodegenerative disease of cattle * Breast self-examination Stock exchanges * Bahrain Stock Exchange, Bahrain * Baku Stock Exchange, Azerbaijan * B ...

(1956), MS (1958) and

PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * ''Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. albu ...

(1960) from the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

. Prior to joining Santa Cruz, he held positions at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

(research lecturer in mathematics; 1960-1962),

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

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

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

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

Amsterdam Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the Capital of the Netherlands, capital and Municipalities of the Netherlands, most populous city of the Netherlands, with The Hague being the seat of government. It has a population ...

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...

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. It is south of Coventry, and south-east of Birmingham. It is adjoined with Leamington Spa and Whi ...

Barcelona Barcelona ( , , ) is a city on the coast of northeastern 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 ci ...

Basel , french: link=no, Bâlois(e), it, Basilese , neighboring_municipalities= Allschwil (BL), Hégenheim (FR-68), Binningen (BL), Birsfelden (BL), Bottmingen (BL), Huningue (FR-68), Münchenstein (BL), Muttenz (BL), Reinach (BL), Riehen (BS ...

, and

Florence Florence ( ; it, Firenze ) is a city in Central Italy and the capital city of the Tuscany region. It is the most populated city in Tuscany, with 383,083 inhabitants in 2016, and over 1,520,000 in its metropolitan area.Bilancio demografico an ...

. He founded the Visual Math Institute at Santa Cruz in 1975; at that time, it was called the "Visual Mathematics Project". He is editor of ''World Futures'' and for the ''International Journal of Bifurcations and Chaos''. Abraham is a member of cultural historian

William Irwin Thompson William Irwin Thompson (16 July 1938—8 November 2020) was an American social philosopher, cultural critic, and poet. He received the Oslo International Poetry Festival Award in 1986. He described his writing and speaking style as "mind-jazz ...

Lindisfarne Association The Lindisfarne Association (1972–2012) was a nonprofit foundation and diverse group of intellectuals organized by cultural history, cultural historian William Irwin Thompson for the "study and realization of a new planetary culture". It was in ...

. 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 dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called ' ...

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

chaos theory Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have co ...

and its applications in numerous fields, such as medical physiology, ecology, mathematical economics, psychotherapy, etc. 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 generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...

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

psychedelic drug Psychedelics are a subclass of hallucinogenic drugs whose primary effect is to trigger non-ordinary states of consciousness (known as psychedelic experiences or "trips").Pollan, Michael (2018). ''How to Change Your Mind: What the New Science o ...

DMT ''N'',''N''-Dimethyltryptamine (DMT or ''N'',''N''-DMT, SPL026) is a substituted tryptamine that occurs in many plants and animals, including human beings, and which is both a derivative and a structural analog of tryptamine. It is used as a ...

for "swerv ng hiscareer toward a search for the connections between mathematics and the experience of the Logos".

Works

;Publications * 1978
''Foundations of Mechanics''
2nd edn. With

Jerrold E. Marsden Jerrold Eldon Marsden (August 17, 1942 – September 21, 2010) was a Canadian mathematician. He was the Carl F. Braun Professor of Engineering and Control & Dynamical Systems at the California Institute of Technology.. Marsden is listed as an ISI ...

; 1st edition 1967. * 1982. ''Manifolds, Tensor Analysis, and Applications'', 2nd edn. With Jerrold E. Marsden and

Tudor Ratiu Tudor Stefan Rațiu (born March 18, 1950 in Timișoara) is a Romanian-American mathematician who has made contributions to geometric mechanics and dynamical systems theory. Education His father, Mircea Ratiu, an engineer, was the younger brother ...

. * 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 the responsible use of naturally occurring psychedelic plants. He spoke and wrote about a variety of subjects, including ...

and

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

), * 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. *

film participant. {{DEFAULTSORT:Abraham, Ralph 1936 births 20th-century American mathematicians 21st-century American mathematicians Columbia University faculty Complex systems scientists Living people Chaos theorists People from Burlington, Vermont University of California, Berkeley College of Letters and Science faculty University of California, Santa Cruz faculty University of Michigan College of Engineering alumni Mathematicians from Vermont Fulbright alumni