Israeli ex-security guard solves 38-year-old math problem
Avraham Trakhtman, a mathematician who worked as a laborer after immigrating to Israel from Russia, succeeded in solving the elusive Road Coloring Problem. The conjecture assumes that it is possible to create a universal map that would direct people to arrive at a certain destination, at the same time, regardless of their original location. Experts say this proposition, which seems to defy logic, could actually have real-life applications in the fields of mapping and computer science.
"In math circles, we talk about beautiful results. This is beautiful and it is unexpected. Even in layman's terms it is completely counterintuitive, but somehow it works," said Stuart Margolis, a colleague who recruited Trakhtman to Bar Ilan University near Tel Aviv.
"The first time I met him he was wearing a night watchman's uniform," said Margolis.
The Road Coloring Problem was first posed in 1970 by Benjamin Weiss, an Israeli-American mathematician, and a colleague, Roy Adler, who worked at IBM at the time.
Weiss said he believed that given a finite number of roads, one should be able to draw up a map, coded in various colors, that would lead to a certain destination regardless of the point of origin.
For eight years, he tried to prove his theory. Over the next 30 years, some 100 other scientists attempted to as well. All failed, until Trakhtman jotted solved it in eight pages in pencil last year after working on it for twelve months.
Originally from Yekaterinburg, Russia, Trakhtman was already an accomplished mathematician before he came to Israel in 1992, at the age of 48. But like many immigrants in the wave that followed the breakup of the former Soviet Union, he struggled to find work and ended up employed in maintenance and security before landing a teaching position at Bar Ilan in 1995.
Trakhtman says he was lucky to be recognized, but plays down his recent achievement.
"The solution is not that complicated. It's hard, but it is not that complicated," he said. "Some people think they need to be complicated. I think they need to be nice and simple."
Trakhtman's solution is available for viewing on the Internet and will soon be published in the Israel Journal of Mathematics.
Weiss said it gave him great joy to see someone solve his problem.
Joel Friedman, a math professor at the University of British Columbia, said probably everyone in the field of symbolic dynamics has tried to solve the Roadmap Coloring Problem at some point, as well as experts in related disciplines graph theory, discrete math and theoretical computer science.
Trakhtman's achievement is not the longest open problem ever solved. In 1994, British mathematician Andrew Wiles solved Fermat's last theorem, which had been open for more than 300 years.
Margolis says the solution could have many applications.
"Say you've lost an e-mail and you want to get it back - it would be guaranteed," he said. "Let's say you are lost in a town you have never been in before and you have to get to a friend's house and there are no street signs - the directions will work no matter what," he said.
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