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Internet Encyclopedia "Wikipedia": an article "Avraham Trahtman"
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From Encyclopedia Britannica http://www.britannica.com/EBchecked/topic-art/1443932/114969/Avraham-Trahtman:
Avraham Trahtman Israeli mathematician
Feb. 10, 1944, Kalinovo,
The astonishing news emerged in 2008 that in September 2007 a 63-year-old Israeli mathematician, Avraham Trahtman, had solved a long-standing problem in graph theory. The road-colouring conjecture, as it was known before being solved by Trahtman, was first suggested in 1970 by the Israeli-American mathematician Benjamin Weiss and the American mathematicians Roy L. Adler and L. Wayne Goodwyn. The theorem concerns a special type of graph, or network, that fulfills certain conditions. The network must have a finite number of vertices (specific locations, or points) and directed edges (one-way paths), be strongly connected (a path must exist from any vertex a to any other vertex b and a path from b to a), and aperiodic (essentially, the cycles, or complete routes following different directions, must be independent). The road-colouring theorem asserts that for such a network, there always exists a synchronized colouring, or method of labeling the edges, to create a map with a simple set of directions, possibly involving many repetitions of the directions, that will lead from any starting point to any other given point. In other words, by following simple directions, such as to take a “red-blue-red” path, it is possible to start from any location and be certain to end up at the desired destination. The existence of such “universal maps” has theoretical implications for real-life problems in computer science, though having a universal map is not the same as having the most efficient route for any individual case.
Trahtman earned an undergraduate degree (1967) and a graduate degree
(1973) in mathematics from
Trahtman’s solution is notable for its brevity: at less than eight pages it is extremely concise and considered quite elegant. The proof is also rather noteworthy in that most major mathematical breakthroughs come from individuals before the age of 40, or even 30. Trahtman proved, however, that age was not a barrier to solving a nearly 40-year-old mathematical conundrum.
MacTutor History of Mathematics, Biographies
Wolfram Research Mathematica
Publisher: Books LLC (Editor) (September 15, 2010) ISBN-10: 1156843480
Die Auserwählten von A.J. kazinski, Krimi-couch, 2011
А. Й. Казински. Последний праведник. : Астрель, 2012.
New Scientist, 186 (2495), 2005, London
Pearce F., Pyramids of dew 52-53
Who'sWho in the World. 2006-2008
Marquis Who's Who, 23th-28th Ed., NY
Dictionary of International Biography
The Times (4 March 2009). M du Sautoy, Sexy maths: ditch the GPS, just follow the colour code,
The Guardian (Friday 21 March 2008). A Heller, Security guard solves 38-year-old maths poser,
The Telegraph (21 March 2008). R Highfield, Directions from anywhere: maths problem solved,
(20 March 2008).Israeli ex-security guard solves 38-year-old math problem
Math in Media, AMS, 03.08
Associated Press, Aron Heller, 20.03.08
The Canadian Press, Aron Heller, 20.03.08
Ediot ahronot, N.
International Herald Tribune, 20.03 08
BBC News, spanish, Mundo, 12.02.08
The Herald, 22.03.08
Math Gateway of AMS, 25.02.08
IsraelNN, AruzSheva, Hillel Fendel, 07.02.08
The Epoch Times,
Physics Today, 21.03.08
Millennium Mathematics Project,
Hacofe, Hadar Rabid, 24.02.08
Evreiskij mir USA, 08.02.08
IsRealli, Israel official, 14.02.08
Israel 21C, Karin Kloosterman. 18 02 2008.
Neue Zürcher Zeitung, George Szpiro, Wie man auf Irrwegen ans Ziel gelangt, 30.03.2008
Forex Times, 18.02.08
Itogi, N9, Astakhova, 06.03.08
Nauka v sviti, Ukraina 22.03.08
Izvestia, D. Varlamova, 04.04.08
REN TV, 04.06.08
Belfast Telegraph 21.03.08
Contemporary Centrist, 21.03.08
Deccan Herald 21.03.08
and other information in dozen of languages
CITATION of the publications
ROAD COLORING, ArXiv downloads
Algebra, finite automata, water problems, algorithms, computing.
1962-1967 Ural State
University, Mathematics, degree II, 1967.
1970-1972 Ural State University, Mathematics, degree III,1973.
1994-1995 Hebrew University - Lecturer, Pre-education Department
1991-1992 Assistant professor,
1969-1984 From assistant to associate professor, Department of Computational Mathematics,
Creation of package TESTAS for verification of local testability and its generalizations (threshold, right, left, bilateral, piecewise and other) for both transition graphs of automata and transition semigroups, for checking synchronizability and finding synchronizing words, for finding transition semigroup of automaton.
The C/C++ compact package TESTAS is mentioned on home pages of several prominent CONFERENCES among the embedded systems for manipulating automata.
English, German, Hebrew, Russian, Polish.