Penniless migrant becomes a maths superstar

A 63-year-old mathematician who worked as a labourer and night-watchman when he first migrated to Israel from Russia has solved a problem which has taxed the world's leading experts in his field for more than a generation.

Avraham Trakhtman has ended the mystery of the Road Colouring Problem by proving the theory of a "universal map" which allows a journey to end at a certain destination whatever the starting point by following the same instructions.

Professor Trakhtman of Bar-Ilan University managed to jot down the proof in pencil on eight pages of paper. In layman's terms, the problem – in the field of symbolic dynamics – can be expressed as whether a man who arrives in a city without street names to visit a friend and telephones for help, could be given directions which would work wherever he was at the time. The solution – which appears to defy logic but which mathematicians believe could have real-life applications in mapping and computer sciences – has excited widespread interest and admiration among Professor Trakhtman's international peer group.

It is all the more remarkable since Professor Trakhtman, who came from Sverdlosk (now Yekaterinburg) in the Urals as a Jewish immigrant to Israel, has achieved the triumph of his career at an age well beyond that at which mathematicians are normally expected to reach their peak.

The Road Colouring Problem was originally posed in 1970 by Benjamin Weiss, an Israeli-American mathematician, and Roy Adler, who both worked at the computer giant IBM. They posited that, given a finite number of roads, they could be depicted in a colour-coded map that would lead to the same destination regardless of the point of origin. Around 100 experts, including the authors of the proposition, have attempted to produce a proof but all failed.

In a diagrammatic version of the conjecture – now a theorem thanks to Professor Trakhtman – a 16-line graph forming one square and eight triangles, with the lines coloured red or green, includes two vertices, each representing different destinations. Following the route "blue red red" repeated three times always leads to one, and following "blue, blue red" always leads to the other, whatever the starting point.

Stuart Margolis, who recruited Professor Trakhtman to Bar Ilan, near Tel Aviv, told Associated Press: "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."

Professor Margolis said that the discovery was all the more remarkable given Professor Trakhtman's age and background. "The first time I met him he was wearing a night watchman's uniform," he said.

Professor Trakhtman said that it took him a year to solve the problem. But he insisted to AP: "The solution is not that complicated. It's hard, but it is not that complicated. Some people think they need to be complicated. I think they need to be nice and simple."

Benjmain Weiss said that it gave him great joy to see someone solve his problem, adding that Professor Trakhtman's solution "is something that is understandable."

PROMOTED VIDEO
News
ebooksNow available in paperback
Arts and Entertainment
booksPhotographer Richard Young has been snapping celebrities at play for 40 years - but he says it wasn’t all fun and games...
News
i100
Sport
Aguero - who single-handedly has kept City's Champions League dreams alive - celebrates his dramatic late winner
footballManchester City 3 Bayern Munich 2: Argentine's late hat-rick sees home side snatch vital victory
News
Muhammad Ali pictured in better health in 2006
peopleBut he has enjoyed publicity from his alleged near-death experience
Arts and Entertainment
Tony breaks into Ian Garrett's yacht and makes a shocking discovery
TVReview: Revelations continue to make this drama a tough watch
News
news
News
peopleSinger tells The Independent what life is like in rehab in an exclusive video interview
News
The assumption that women are not as competent in leadership positions as men are leads to increased stress in the workplace
science... and it's down to gender stereotypes
Arts and Entertainment
Inner sanctum: Tove Jansson and friends in her studio in 1992
booksWhat was the inspiration for Finland's most famous family?
News
i100
Arts and Entertainment
Singer songwriter Bob Dylan performs on stage
films
Have you tried new the Independent Digital Edition apps?
Independent Dating
and  

By clicking 'Search' you
are agreeing to our
Terms of Use.

iJobs Job Widget
iJobs General

Austen Lloyd: Commercial Property Lawyer - Cheshire

Excellent Salary: Austen Lloyd: CHESHIRE MARKET TOWN - An exciting and rare o...

Austen Lloyd: Residential Property Solicitor - Hampshire

Excellent Salary : Austen Lloyd: NORTH HAMPSHIRE - SENIOR POSITION - An exciti...

Recruitment Genius: Gas Installation Engineer

£29000 per annum: Recruitment Genius: A Gas Installation Engineer is required ...

Recruitment Genius: Domestic Gas Technical Surveyor

£28000 per annum: Recruitment Genius: A Domestic Gas Technical Surveyor is req...

Day In a Page

Homeless Veterans Christmas Appeal: Drifting and forgotten - turning lives around for ex-soldiers

Homeless Veterans Christmas Appeal: Turning lives around for ex-soldiers

Our partner charities help veterans on the brink – and get them back on their feet
Putin’s far-right ambition: Think-tank reveals how Russian President is wooing – and funding – populist parties across Europe to gain influence in the EU

Putin’s far-right ambition

Think-tank reveals how Russian President is wooing – and funding – populist parties across Europe to gain influence in the EU
Tove Jansson's Moominland: What was the inspiration for Finland's most famous family?

Escape to Moominland

What was the inspiration for Finland's most famous family?
Nightclubbing with Richard Young: The story behind his latest book of celebrity photographs

24-Hour party person

Photographer Richard Young has been snapping celebrities at play for 40 years. As his latest book is released, he reveals that it wasn’t all fun and games
Michelle Obama's school dinners: America’s children have a message for the First Lady

A taste for rebellion

US children have started an online protest against Michelle Obama’s drive for healthy school meals by posting photos of their lunches
Colouring books for adults: How the French are going crazy for Crayolas

Colouring books for adults

How the French are going crazy for Crayolas
Jack Thorne's play 'Hope': What would you do as a local politician faced with an impossible choice of cuts?

What would you do as a local politician faced with an impossible choice of cuts?

Playwright Jack Thorne's latest work 'Hope' poses the question to audiences
Ed Harcourt on Romeo Beckham and life as a court composer at Burberry

Call me Ed Mozart

Paloma Faith, Lana del Ray... Romeo Beckham. Ed Harcourt has proved that he can write for them all. But it took a personal crisis to turn him from indie star to writer-for-hire
10 best stocking fillers for foodies

Festive treats: 10 best stocking fillers for foodies

From boozy milk to wasabi, give the food-lover in your life some extra-special, unusual treats to wake up to on Christmas morning
Phil Hughes head injury: He had one weakness – it has come back to haunt him

Phil Hughes had one weakness – it has come back to haunt him

Prolific opener had world at his feet until Harmison and Flintoff bounced him
'I have an age of attraction that starts as low as four': How do you deal with a paedophile who has never committed a crime?

'I am a paedophile'

Is our approach to sex offenders helping to create more victims?
How bad do you have to be to lose a Home Office contract?

How bad do you have to be to lose a Home Office contract?

Serco given Yarl’s Wood immigration contract despite ‘vast failings’
Green Party on the march in Bristol: From a lost deposit to victory

From a lost deposit to victory

Green Party on the march in Bristol
Putting the grot right into Santa's grotto

Winter blunderlands

Putting the grot into grotto
'It just came to us, why not do it naked?' London's first nude free runner captured in breathtaking images across capital

'It just came to us, why not do it naked?'

London's first nude free runner captured in breathtaking images across capital