Eliyahu Rips (1948–2024) was a figure of profound complexity, occupying a unique space where elite-level combinatorial group theory met international political dissidence and controversial biblical cryptology. While he became a household name due to the "Bible Code" phenomenon of the 1990s, his enduring legacy in the mathematical community rests upon his foundational contributions to Geometric Group Theory (GGT), particularly his work on hyperbolic groups and actions on trees.
1. Biography: From Dissident to Professor
Eliyahu (born Ilya) Rips was born on December 12, 1948, in Riga, Latvia, then part of the Soviet Union. A mathematical prodigy, he was the first Latvian student to participate in the International Mathematical Olympiad.
His life took a dramatic turn in 1969. Deeply moved by the Soviet invasion of Czechoslovakia and the self-immolation of Jan Palach, the 20-year-old Rips attempted a similar protest. On April 13, 1969, he stood in the center of Riga with a banner reading:
"I protest against the occupation of Czechoslovakia"
and set himself on fire. Bystanders extinguished the flames, and Rips survived, only to be imprisoned by the Soviet government in a psychiatric hospital—a common tactic used to silence dissidents.
Following an international outcry from Western mathematicians, Rips was released and allowed to emigrate to Israel in 1972. He settled in Jerusalem, where he embraced Orthodox Judaism and joined the faculty of the Hebrew University of Jerusalem. He earned his Ph.D. in 1975 under the supervision of Shimshon Amitsur and remained at the Hebrew University for the duration of his career, eventually becoming a Professor Emeritus. He passed away on May 19, 2024.
2. Major Contributions
Rips’s mathematical work is characterized by its ingenuity and its ability to solve "word problems" and structural questions in infinite groups.
- The Rips Construction: This is perhaps his most famous contribution to pure mathematics. In a 1982 paper, he developed a method to construct a specific type of "small cancellation group" that serves as a counterexample to various conjectures. This construction allowed mathematicians to take a "badly behaved" group and embed it into a "well-behaved" hyperbolic group, demonstrating that even hyperbolic groups can have highly complex subgroups.
- Actions on $\mathbb{R}$-trees (The Rips Machine): In the late 1980s and early 90s, Rips revolutionized the study of groups acting on $\mathbb{R}$-trees. He provided a complete classification of finitely generated groups that can act freely on such trees. This work, often referred to as "Rips Theory" or the "Rips Machine," became a cornerstone in the study of 3-manifolds and the solution to the Seifert Conjecture.
- The Bible Code (Equidistant Letter Sequences): In the mid-1990s, Rips gained international notoriety for his research into Equidistant Letter Sequences (ELS) in the Hebrew text of Genesis. He claimed that by skipping a fixed number of letters, one could find names of historical figures and dates of events encoded in the text. While this remains highly controversial and is largely rejected by the broader scientific community as a result of "data mining," the original paper passed rigorous peer review in a statistics journal.
3. Notable Publications
- "Subgroups of small cancellation groups" (1982): Published in the Bulletin of the London Mathematical Society, this paper introduced the "Rips Construction," a vital tool in modern group theory.
- "Equidistant letter sequences in the Book of Genesis" (1994): Co-authored with Doron Witztum and Yoav Rosenberg and published in Statistical Science. This paper sparked the global "Bible Code" craze.
- "Group actions on $\mathbb{R}$-trees": While much of this work was disseminated through lectures and collaborations (notably with Mark Sapir and Zlil Sela), it fundamentally reshaped the landscape of geometric group theory in the 1990s.
4. Awards & Recognition
- The Erdős Prize (1979): Awarded by the Israel Mathematical Union to a young Israeli mathematician for outstanding contributions.
- Invited Speaker at the ICM (1994): Rips was invited to speak at the International Congress of Mathematicians in Kyoto. An invitation to the ICM is considered one of the highest honors in mathematics, recognizing those who have significantly moved the field forward.
- The Aharon Dokshitzer Prize: Awarded for his excellence in research.
5. Impact & Legacy
In the world of Geometric Group Theory, Rips is viewed as a giant. His work provided the machinery that allowed others to solve the Tarski Conjecture (about the elementary theory of free groups) and helped develop the JSJ decomposition for word-hyperbolic groups.
The Rips Complex (or Vietoris–Rips complex) is an essential concept in Topological Data Analysis (TDA) today. It is a way of thickening a set of points into a geometric shape to study its "holes" or topological features. Though based on earlier work by Vietoris, Rips’s application of it to hyperbolic groups brought it into the modern mathematical mainstream.
In the public sphere, his legacy is more divisive. The "Bible Code" (popularized by Michael Drosnin's book, which Rips later distanced himself from) remains a staple of pop-theology and "hidden history" documentaries. However, Rips always maintained that his interest was strictly mathematical and probabilistic.
6. Collaborations
Rips was known for his deep, often decades-long collaborations:
- Zlil Sela: Together, they worked on the structure of hyperbolic groups, producing some of the most difficult and influential papers in the field.
- Mark Sapir: A frequent collaborator on the dynamics of group actions and the complexity of word problems.
- Mikhail Gromov: While not a frequent co-author, Rips’s work was essential in providing the "examples and counterexamples" that fueled Gromov’s theory of hyperbolic groups.
7. Lesser-Known Facts
- The "Unpublished" Machine: For many years, the "Rips Machine" was a piece of mathematical folklore. Rips was known for being more interested in solving problems than in the administrative task of publishing them. Much of his most influential work was initially circulated as preprints or taught in private seminars before being formalized by his collaborators and students.
- Spiritual Transformation: Rips was a secular Jew in the USSR. His move to Israel was not just a geographic shift but a spiritual one; he became a deeply devout member of the Haredi (Ultra-Orthodox) community. He often saw no conflict between his high-level mathematics and his faith, viewing both as a search for underlying truth.
- The 1969 Protest's Aftermath: When he was in the psychiatric ward in Riga, he was allowed a few books. He chose to spend his time solving mathematical problems in his head, a practice he credited with keeping his mind intact during his incarceration.
Eliyahu Rips's life was a testament to the power of the individual mind to resist political oppression and to find hidden structures in the most abstract of spaces—whether in the symmetries of an infinite group or the ancient letters of a sacred text.