Gödel's Incompleteness Theorem - Numberphile
Marcus du Sautoy discusses Gödel's Incompleteness Theorem More links & stuff in full description below ↓↓↓ Extra Footage Part One: https://youtu.be/mccoBBf0VDM Extra Footage Part Two:...
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[Marcus du Sautoy] I've been quite obsessed with Gödel's incompleteness theorem for many years because it kind of places this extraordinarylimitation on what we might be able to know in mathematics. In fact, it's quite an unnerving theorembecause at its heart it says there might beconjectures out there about numbers, for example something like Goldbach's conjecture, that might actually be trueSo it might be true that every even number is the sum of two primesbut maybe within theaxiomatic system we have for mathematics, there isn't a proof of that.The real worry is what if there's a true statement that I'm working away on which actually doesn'thave a proof.Now his is a big kind of revelation for mathematic...
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[Marcus du Sautoy] I've been quite obsessed with Gödel's incompleteness theorem for many years because it kind of places this extraordinarylimitation on what we might be able to know in mathematics. In fact, it's quite an unnerving theorembecause at its heart it says there might beconjectures out there about numbers, for example something like Goldbach's conjecture, that might actually be trueSo it might be true that every even number is the sum of two primesbut maybe within theaxiomatic system we have for mathematics, there isn't a proof of that.The real worry is what if there's a true statement that I'm working away on which actually doesn'thave a proof.Now his is a big kind of revelation for mathematic...
