# Computer cracks Erdős puzzle – but no human brain can check the answer

A puzzle that has confounded mathematicians for almost a century is closer than ever to being solved, it has emerged. But there’s one slight problem.

The calculations which prove a part of what’s known as “Erdős discrepancy problem” have been worked out by a computer. And the sheer amount of data – more than the entire contents of Wikipedia – is so vast that it would be practically impossible to be checked by a human brain.

The “discrepancy problem” was posed in the 1930s by renowned Hungarian mathematician Paul Erdős. It revolves around the properties of infinite sequences of numbers containing nothing but +1s and -1s. Patterns in such sequences can be measured by creating finite sub-sequences.

Professor Enrico Scalas, of the University of Sussex, explained the premise: “You have a sequence of 1s and -1s (for instance, generated by tossing a coin) and a constant C. One is looking for a finite subsequence long enough so that the sum of the elements of the subsequence is larger than C.”

The difficulty lies in actually proving this is the case mathematically. That’s where computers and their ability to perform complex calculations come in. With this aid, computer scientists Dr Alexei Lisitsa and Dr Boris Konev of the University of Liverpool managed to demonstrate that an infinite sequence will always have a discrepancy (the sum of the numbers in a sub-sequence) larger than two.

They took a sequence 1,161 numbers long and the resulting data was a 13-gigabyte file. That’s bigger than the 10GB estimated size of the entire written contents of Wikipedia. It is the start of solving the puzzle – but while computers have helped, they have not yet taken over from humans.

In a statement, the researchers told The Independent: “On the one hand, it is true that our computer-generated solution is beyond the reach of humans to fully understand. On the other, all we can say for now is that at the moment there is no known ‘better’ human-comprehensible solution – but it does not mean that such a solution could not (or will not) be found in the future.”

Mathematicians were philosophical about being beaten by a machine. Matt Parker, Public Engagement in Maths Fellow at Queen Mary, University of London, said: “The computer did the heavy-lifting, but it was the insight and creativity of its human programmers which made it possible.”

Chris Budd, Professor of Mathematics at the Royal Institution of Great Britain, added: “Computers are doing for maths what the printing press did for writing, in that they are opening up unlimited possibilities.”

Arts and Entertainment

comedy
News

news
Life and Style

health
Voices

voices
Life and Style

### A History of The Great War in 100 Moments

ebookNow available in paperback
ebooks

### Mark Hix on Meat

ebookA delicious collection of 50 meaty main courses
News

news
Sport

rugby
News

i100
Sport

sport
Life and Style

### Want to avoid a hangover? Scientists say they've got a 100% effective solution

health
Arts and Entertainment

theatre
News

people
Sport

### Stones starts for Everton as Spurs lie in wait

footballLive: All the latest from today's Premier League matches
News

news
News

i100
Life and Style

love + sex
Sport

football

### Donna Karan leaves Donna Karan, but DKNY soldiers on

##### Independent Dating
and

By clicking 'Search' you
are agreeing to our

### Recruitment Genius: Head of Support Services

£40000 - £55000 per annum: Recruitment Genius: This is an exciting opportunity...

### Recruitment Genius: Business Development Manager / Sales - OTE £40,000

£20000 - £40000 per annum: Recruitment Genius: This IT provider for the educat...

### Recruitment Genius: Front End Developer / Web Designer

£20000 - £25000 per annum: Recruitment Genius: This leader in the e-cigarette ...

### Recruitment Genius: Web Developer - PHP

£32000 - £40000 per annum: Recruitment Genius: With extensive experience and a...

## The Silk Roads that trace civilisation

Long before the West rose to power, Asian pathways were connecting peoples and places

## The honours that shame Britain

Outcry as donors, fixers and MPs caught up in expenses scandal are ennobled

## 'When it comes to street harassment, we need to talk about race'

Why are black men living the stereotypes and why are we letting them get away with it?

## International Tap Festival comes to the UK

Forget Fred Astaire and Ginger Rogers - this dancing is improvised, spontaneous and rhythmic

## Turkey's buffer zone in Syria: self-defence – or just anti-Kurd?

Ankara accused of exacerbating racial division by allowing Turkmen minority to cross the border

## 'A subversive brothel keeper and Communist'

Acclaimed novelist Doris Lessing was kept under MI5 observation for 18 years, newly released papers show

## BBC heads to the Californian coast

The Big Blue Live crew is preparing for the first of three episodes on Sunday night, filming from boats, planes and an aquarium studio

## Victorian fraudster who shook the Bank of England

Conman Austin Bidwell. was a heartless cad who carried out the most daring forgery the world had known

## Car hacking scandal

Security designed to stop thieves hot-wiring almost every modern motor has been cracked

## Take your seat: 10 best placemats

Protect your table and dine in style with a bold new accessory

## Cook not the only one to be caught in The Oval mindwarp

Aussie skipper Michael Clarke was lured into believing that what we witnessed at Edgbaston and Trent Bridge would continue in London, says Kevin Garside

Back at the club he watched as a boy, the pressure is on Benitez to find a winning blend from Real's multiple talents. As La Liga begins, Pete Jenson asks if it will be enough to stop Barcelona

## Beijing witnesses new stage in the Jess and Kat rivalry

The last time the two British heptathletes competed, Ennis-Hill was on the way to Olympic gold and Johnson-Thompson was just a promising teenager. But a lot has happened in the following three years

## Jeremy Corbyn interview: A shrewd operator desperate for power

His radical anti-austerity agenda has caught the imagination of the left and politically disaffected and set a staid Labour leadership election alight

## Isis executes Palmyra antiquities chief

Robert Fisk on the defender of the ancient city's past who was killed for protecting its future