Mathematicians spark debate with 13 GB proof for Erdős problem

Try fitting THAT in the margins, math wonks

Seven Steps to Software Security

When Pierre de Fermat famously complained that he didn't have space to write the proof of his famous “Fermat's Last Theorem”, he only ran out of space of the margin of a book. Now, a pair of mathematicians at the University of Liverpool in the UK have produced a 13GB proof that's sparked a debate about how to test it.

The mathematicians, Alexei Lisitsa and Boris Konev, were looking at what's called the “Erdős discrepancy problem” (it's appropriate to point to Wikipedia, for reasons you'll catch in a minute).

New Scientist describes the problem like this:

“Imagine a random, infinite sequence of numbers containing nothing but +1s and -1s. Erdős was fascinated by the extent to which such sequences contain internal patterns. One way to measure that is to cut the infinite sequence off at a certain point, and then create finite sub-sequences within that part of the sequence, such as considering only every third number or every fourth. Adding up the numbers in a sub-sequence gives a figure called the discrepancy, which acts as a measure of the structure of the sub-sequence and in turn the infinite sequence, as compared with a uniform ideal.”

For any sequence, Paul Erdős believed, you could find a finite sub-sequence that summed to a number bigger than any than you could choose – but he couldn't prove it.

In this Arxiv paper, the University of Liverpool mathematicians set a computer onto the problem in what they call “a SAT attack” using a Boolean Satisfiability (SAT) solver. They believe they've produced a proof of the Erdős discrepancy problem, but there's a problem.

After six hours, the machine they used – an Intel i5-2500 running at 3.3 GHz with 16 GB of RAM – produced what they offer as a proof, but it's inconveniently large, at 13 GB. A complete Wikipedia (see, I told you it was relevant) download is only 10 GB.

As New Scientist points out, that raises a different problem: how can humans ever check the proof. However, at least one mathematician NS spoke to said “no problem”: after all, other computers can always be deployed to test the proof. ®

The Power of One eBook: Top reasons to choose HP BladeSystem

More from The Register

next story
Bad back? Show some spine and stop popping paracetamol
Study finds common pain-killer doesn't reduce pain or shorten recovery
Malaysian Airlines flight MH17 claimed lives of HIV/AIDS cure scientists
Researchers, advocates, health workers among those on shot-down plane
World Solar Challenge contender claims new speed record
One charge sees Sunswift travel 500kms at over 100 km/h
SMELL YOU LATER, LOSERS – Dumbo tells rats, dogs... humans
Junk in the trunk? That's what people have
All those new '5G standards'? Here's the science they rely on
Radio professor tells us how wireless will get faster in the real world
The Sun took a day off last week and made NO sunspots
Someone needs to get that lazy star cooking again before things get cold around here
Boffins discuss AI space program at hush-hush IARPA confab
IBM, MIT, plenty of others invited to fill Uncle Sam's spy toolchest, but where's Google?
prev story


Top three mobile application threats
Prevent sensitive data leakage over insecure channels or stolen mobile devices.
Implementing global e-invoicing with guaranteed legal certainty
Explaining the role local tax compliance plays in successful supply chain management and e-business and how leading global brands are addressing this.
Top 8 considerations to enable and simplify mobility
In this whitepaper learn how to successfully add mobile capabilities simply and cost effectively.
Application security programs and practises
Follow a few strategies and your organization can gain the full benefits of open source and the cloud without compromising the security of your applications.
The Essential Guide to IT Transformation
ServiceNow discusses three IT transformations that can help CIO's automate IT services to transform IT and the enterprise.