Mathematical proofs are becoming harder by the day to verify with absolute certainty, experts say.
"I think we’re now inescapably in an age
where the large statements of mathematics are so complex that we may
never know for sure whether they’re true or false," NewScientist.com
quotes Keith Devlin of Stanford University in California as saying.
"That puts us in the same boat as all the other scientists."
an example, he points to the ‘classification of finite simple groups’ –
a claimed proof announced in 1980 that resulted from an effort in which
members of a group each contributed different pieces.
years later we’re still not sure if it’s correct or not. We sort of
think it is, but no one’s ever written down the complete proof," Devlin
says of the classification.
to Thomas Hales of the University of Pittsburgh in Pennsylvania, part
of the difficulty is the computer code used nowadays to construct
proofs as it makes the proofs less accessible even to experts.
Devlin says all of this uncertainty about new proofs could be good for the discipline of mathematics. "It makes it more human."
and Hales were speaking at the annual meeting of the American
Association for the Advancement of Science in St. Louis in the US.