Ralph Abraham Ph.D

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

He was involved in the development of the theory of dynamical systems in the 1960s and 1970s. He is editor of World Futures and for the International Journal of Bifurcations and Chaos.

Another interest of Dr. Abraham’s concerns alternative ways of expressing mathematics, for example visually or aurally. He founded the Visual Math Institute at UC Santa Cruz in 1975 (at that time it was called the Visual Mathematics Project).

He has staged performances in which mathematics, visual arts and music are combined into one presentation. Students were often allowed to earn extra credit by writing papers on the history or social impacts of mathematics, which is a subject which Dr. Abraham wrote about extensively.

Ralph Abraham is a member of cultural historian William Irwin Thompson’s Lindisfarne Association.

Partial bibliography

By Ralph Abraham:

  • Foundations of Mechanics, 2nd edn. 1978 (with J.E. Marsden)
  • Manifolds, Tensor Analysis, and Applications, 2nd edn. 1982 (with J.E. Marsden and T. Ratiu)
  • Dynamics, the Geometry of Behavior, 2nd edn. 1992 (with C.D. Shaw), transl. in Japanese
  • Trialogues on the Edge of the West, 1992 (with Terence McKenna and Rupert Sheldrake), transl. in French, German, Portuguese, Dutch
  • Chaos, Gaia, Eros, 1992, transl. in Korean
  • The Web Empowerment Book, 1995 (with Frank Jas and Will Russell)
  • Chaos in Discrete Dynamical Systems, 1995 (with Laura Gardini and Christian Mira)
  • The Evolutionary Mind, 1997 (with Terence McKenna and Rupert Sheldrake), transl. in German
  • The Chaos Avant-garde, 2000 (with Yoshisuke Ueda), transl. in Japanese.


  • July 2004: Award of NSF Proposal 0436509 (with Prof. Dan Friedman, UCSC) for 2005-2006 in Mathematical Economics
  • May 2004: Three-week Fulbright visit to Japan
Jan 2004: Award of Fulbright Senior Specialist Program [FULSPEC] last year, contacts underway with Austria, India, Italy, Japan, Sri Lanka for short trips this year

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