Re:Titans of Mathematics Clash Over Epic Proof of ABC Conjec...
by ericsoderstrom on Thursday September 20, 2018 @05:00PM
(#18035427)
Math is different in that one feels there should be something close to "absolute truth." That is, given a set of axioms, it is possible to verify with complete certainty whether a proof follows from those axioms or not. Though when proofs become so long and abstruse that only a handful of people can even read them, perhaps that's no longer true. In other fields, it's more clear that nothing is known with 100% certainty. That differences of opinion or experimental error could always lead to uncertainty.
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Re:Titans of Mathematics Clash Over Epic Proof of ABC Conjec...
by atmanthedog on Thursday September 20, 2018 @06:20PM
(#18035895)
Unfortunately, math doesn't really permit this type of truth: if your axioms are strong enough to prove general statements about arithmetic, there is no effective procedure to determine whether an arbitrary proof follows from those axioms.
Re:Titans of Mathematics Clash Over Epic Proof of ABC Conjec...
by smadge on Thursday September 20, 2018 @08:32PM
(#18036401)
Did you mean to write “there is no effective procedure to determine whether an arbitrary formula follows from those axioms?”
A proof is exactly how we demonstrate that a formula follows from the axioms.
Re:Titans of Mathematics Clash Over Epic Proof of ABC Conjec...
by rocqua on Thursday September 20, 2018 @06:58PM
(#18036060)
Still, given a set of axioms, statements will fall into one of three categories. 1) Provably True, 2) Provably False, 3) Undecideable
Claims that a statement is in category 1 are fully verifiable (by providing the proof). The same goes with claims that a statement is in category 2.