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Computer generated math proof is too large for humans to check

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Posted February 20, 2014
Computer generated math proof is too large for humans to check
Credit: arXiv:1402.2184 [cs.DM]
A pair of mathematicians, Alexei Lisitsa and Boris Konev of the University of Liverpool, U.K., have come up with an interesting problem—if a computer produces a proof of a math problem that is too big to study, can it be judged as true anyway? In a paper they’ve uploaded to the preprint server arXiv, the two describe how they set a computer program to proving a small part of what’s known as “Erdős discrepancy problem”—the proof produced a data file that was 13-gigabytes in size—far too large for any human to check, leading to questions as to whether the proof can be taken as a real proof.

Anyone who has taken a high level math course can attest to the fact that math proofs can sometimes grow long—very long. Some mathematicians have dedicated years to creating them, filling whole text volumes in the process. Quite naturally then, mathematicians have increasingly turned to computers to perform some of the more mundane parts of proof creation. It wasn’t long, however, before some began to realize that at some point, the proofs spit out by the computer would be too long, complicated or both for a human reader to fully comprehend. It appears, with this new effort that that day might have come.

Read more at: Phys.org

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