Eureka! Former security guard solves 38-year-old maths puzzle

A MATHS puzzle that baffled the top minds in the esoteric field of symbolic dynamics for nearly four decades has been cracked — by a 63-year-old immigrant who once had to work as a security guard.

Avraham Trahtman, a mathematician who also toiled as a labourer after moving to Israel from Russia, succeeded where dozens failed, solving the elusive “Road Colouring Problem”.

The conjecture essentially assumed it is possible to create a “universal map” that can direct people to arrive at a certain destination, at the same time, regardless of starting point. Experts say the proposition could have real-life applications in mapping and computer science.

The “Road Colouring 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.

For eight years, Weiss tried to prove his theory. Over the next 30 years, 100 other scientists attempted as well. All failed, until Trahtman came along and, in eight short pages, jotted the solution down in pencil last year.

“The solution is not that complicated. It’s hard, but it is not that complicated,” Trahtman said. “Some people think they need to be complicated.

“I think they need to be nice and simple.”

Weiss said it gave him great joy to see someone solve his problem.

Stuart Margolis, a mathematician who recruited Trahtman to teach at Bar Ilan University near Tel Aviv, said the solution could have many applications. He said what makes the result especially remarkable is Trahtman’s age and background.

“The first time I met him he was wearing a night watchman’s uniform,” said Margolis.

“Math is usually a younger person’s game, like music and the arts. Usually you do your better work in your mid 20s and early 30s. He certainly came up with a good one at age 63.”

Originally from Yekaterinburg in Russia, Trahtman was an accomplished mathematician when he came to Israel in 1992, aged 48.

Like many immigrants in the wave that followed the breakup of the Soviet Union, he struggled to find work in the Jewish state and was forced into stints working maintenance and security before landing a teaching position at Bar Ilan in 1995.

His solution is available on the internet and will be published in the Israel Journal of Mathematics.