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From Encyclopedia Britannica http://www.britannica.com/EBchecked/topic/1443932/Avraham-Trahtman:
Avraham Trahtman Israeli mathematician
born
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.
Encyclopedia Britannica.
Encyclopedia Britannica Australia.
Wikipedia (English, German, Russian, France
…)
MacTutor History of Mathematics, Biographies
http://www.techhap.com/sciencehistory/279150.html#.Wb5ddbIjFMv
Wolfram Research Mathematica
Israeli Mathematicians: Adi
Shamir, Giulio Racah, Saharon Shelah,
Zlil Sela, Robert Aumann, Michael
O. Rabin, Oded Schramm, Avraham Trahtman
Publisher: Books LLC
(Editor) (September 15, 2010) ISBN-10: 1156843480
Den sidste gode mand A.J.
kazinski, Politiken. 2010 (18
translations)
The Last Good Man A.J. Kazinski Translated by: Tiina
Nunnally Simon @Schuster 2010
Die Auserwählten von A.J. kazinski, Krimi-couch, 2011
А. Й.
Казински.
Последний
праведник. :
Астрель, 2012.
Arthur Benjamin, Gary Chartrand & Ping Zhang
The Fascinating World of Graph Theory
Popular Math., press.princeton.edu, 360, 2015
New Scientist, 186 (2495), 2005, London
Pearce F., Pyramids of dew 52-53
Наука
и жизнь 2020 № 2
Максимов
Универсальный
алгоритм
, NEW YORK TIMES
Published: April 24,
1988 DAVID K. SHIPLER
Excerpts from some
recently published letters
Ogonyok, No. 15 April
1988 A. Trakhtman
Timeline Israel 1961-1995 (1970)
Timelines (1970)
Who'sWho in the World. 2006-2008
Marquis Who's Who, 23th-28th Ed., NY
Dictionary of International Biography
33th Ed., London, 2006
The Times (
The Guardian
(Friday
The
Telegraph (21 March 2008). R Highfield, Directions from anywhere: maths problem
solved,
The.
Haaretz Newspaper (
Math in Media, AMS, 03.08
Associated Press, Aron Heller, 20.03.08
The Canadian Press, Aron Heller, 20.03.08
Ediot ahronot, N. Mozgovaja, 06.02.08
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, in
Physics Today, 21.03.08
Millennium Mathematics Project,
Hacofe, Hadar Rabid, 24.02.08
Evreiskij mir USA, 08.02.08
BecomingJewish, 10.02.08
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
Kristeling Dagblat, 12.02.08
Red
CloudWatcher, 09.02.08
ProphecyNewsWatch, 09.02.08
Forex Times, 18.02.08
Lenta.ru, 09.02.08
Itogi, N9, Astakhova, 06.03.08
Nauka v sviti, Ukraina 22.03.08
Izvestia, D. Varlamova, 04.04.08
Novosti, 10.04.08
REN TV, 04.06.08
Belfast Telegraph 21.03.08
Contemporary Centrist, 21.03.08
Deccan Herald 21.03.08
Izmirdeyasam, 22.03.08
http://avva.livejournal.com/2260452.html
and other information in dozen of languages
CURRICULUM VITAE
Prof. Dr.
Avraham Trahtman
Academic
interests
Algebra,
finite automata, water problems, algorithms, computing.
Education
1962-1967
Ural State University, Mathematics, degree II, 1967.
1970-1972 Ural State University, Mathematics, degree III,1973.
Work
experience
1995- 2012
1994-1995 Hebrew University - Lecturer, Pre-education Department
1991-1992 Assistant professor, Sverdlovsk
Pedagogical University, Department of Mathematics.
1969-1984 From assistant to associate professor, Department of Computational
Mathematics, Ural Technical University.
Computing
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.
See http://www.cs.biu.ac.il/~trakht/Testas.html
Languages
English, German, Hebrew, Russian, Polish.