From my “watched a YouTube video” understanding of Gödel’s Incompleteness Theorem, a consistent mathematical system cannot prove its own consistency, and any seemingly consistent system could always have a fatal contradiction that invalidates the whole system, and the only way to know would be to find the contradiction.
So if at some point our current system of math gets proven inconsistent, what happens next? Can we tweak just the inconsistent part and have everything else still be valid or would we be forced to rebuild all of math from basic logic?
I’m a math layperson, but isnt this a problem with the application of maths and not math itself? By your logic Einsteins relativity is wrong because it doesn’t work for quantum physics. Which also doesn’t prove math is wrong.
Yes. I chose a more accessible example.
Disproving our concept of maths might be possible as well, but to the best of my knowledge we haven’t done it.
But if we did do it, we would proceed the same way.