What does Godël’s Incompleteness Theorem actually mean and imply? I just saw Ted-Ed’s video on this topic and didn’t fully understand what it means or what the implications of this are.
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All valid systems of math will have paradoxical problems that can’t be solved by switching to a “superior” system of math. Paradoxes are unavoidable in math systems, so mathematicians can quite trying to come up with “superior” systems (languages).
Recommend reading Godël, Escher Bach by Douglas Hofstadter if you are intrigued enough to pursue this as a lay person. I started reading it in HS well before I was really capable of understanding a lot of it. (I was a musician and mother was an art teacher so Escher and Bach were quite familiar.) But it was still entertaining and gave me an appreciation of a lot of stuff that later became applicable in college while pursuing a math minor.
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