A mathematical mystery that has baffled the top minds in the esoteric field of symbolic dynamics for nearly four decades has recently been cracked — by a 63-year-old former security guard.

Avraham Trakhtman, a mathematician who worked as a labourer after immigrating to Israel from Russia, has succeeded where dozens failed, solving the elusive Road Colouring Problem.

The conjecture essentially 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.

He said the discovery was especially remarkable given Trakhtman’s age and background. “The first time I met him he was wearing a night watchman’s uniform,” he said.

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.

Weiss said he believed that given a finite number of roads, one should be able to draw up a map, coded in various colours, 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 came along and, in eight short pages, jotted the solution down in pencil last year.

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