(Provably) Unprovable and Undisprovable... How??

No matter how hard we try to axiomatise mathematics, there will always be strong, independent propositions that don't need no proofs... but how do we show that a proposition can't be proven nor disproven? __________ Timestamps: 00:00 - Motivation(al) 01:14 - What is logical independence? 02:47 - An axiomatic foundation of "integers" 04:45 - A provable proposition 05:36 - An unprovable proposition 06:29 - An unprovable and undisprovable proposition 07:35 - The usual integers 08:35 - The undisprovability of the Freshman's Dream 10:08 - The big idea 10:41 - Thx 4 watching