Ralph H. Abraham (b. July 4, 1936, Burlington, Vermont) is an American mathematician. He has been a member of the mathematics department at the University of California, Santa Cruz since 1968.

Contents 1 Life and work 2 Publications 3 References 4 External links

[edit] Life and work

Ralph Abraham earned his Ph.D. from the University of Michigan in 1960, and held positions at UC Santa Cruz, Berkeley, Columbia, and Princeton. He has also held visiting positions in Amsterdam, Paris, Warwick, Barcelona, Basel, and Florence.

He founded the Visual Math Institute^[1] at UC 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's "Lindisfarne Association".

Abraham has been involved in the research frontier and the development of dynamical systems theory in the 1960s and 1970s. He has been a consultant on chaos theory and its applications in numerous fields, such as medical physiology, ecology, mathematical economics, psychotherapy, etc.^[2]

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 are combined into one presentation.

[edit] Publications

• 1978. Foundations of Mechanics, 2nd edn. With J.E. Marsden
• 1982. Manifolds, Tensor Analysis, and Applications, 2nd edn. With J.E. Marsden and T. Ratiu.
• 1992. Dynamics, the Geometry of Behavior, 2nd edn. With C.D. Shaw.
• 1992. Trialogues on the Edge of the West. With Terence McKenna and Rupert Sheldrake),
• 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.

Further reading

• Thomas A. Bass. The Eudaemonic Pie: describes some early experimenting with roulette prediction.

[edit] References

[edit] External links

• Ralph Abraham at the Mathematics Genealogy Project
• Personal website Ralph Abraham.
• Chaos in Discrete Dynamical Systems
• Notes from the Lindisfarne Symposium
• [1] Ralph Abraham expresses his personal ideas and philosophy in the smart movie Cognition Factor.