I keep on thinking that everything around us is basically just information. Be it DNA, atoms, or spacetime itself. And math is the set of rules that explain the interaction, flow and existence of this information. We did not uncover all the rules yet. Does this make sense?
In: 8
No, actually.
This was proven by Kurt Gödel, who (in a move simplified for an ELI5) created a proof by contradiction that any set of consistent rules would have things that are true and can’t be proven, meaning that it can’t be claimed to be a complete system. One of the things that falls into that hole of incompleteness is a way to fundamentally prove that the system is consistent
Similarly, Alan Turing with the halting problem (also not really easy to do in ELI5 terms, I tried) proved that some problems are absolutely and categorically impossible to solve algorithmically, which for the purpose of this subject is all of math
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