# Math Has a Fatal Flaw

Video Statistics and Information

**Channel:**Veritasium

**Views:**5,402,988

**Rating:**4.9450998 out of 5

**Keywords:**veritasium, science, physics

**Id:**HeQX2HjkcNo

**Channel Id:**undefined

**Length:**33min 59sec (2039 seconds)

**Published:**Sat May 22 2021

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I was really happy he actually went into some of the mechanism behind the incompleteness theorem proof! The idea of creating correspondences between different kinds of objects is such a valuable tool in mathematics, and godel numbering is such a good example.

Nice to see some abstract mathematics getting awareness to a large audience!

This reminds me of one of my favorite observations on the challenge of learning mathematics.

'Most intellectual disciplines require a high degree of abstraction to master; mathematics requires a high degree of abstraction to understand at all.'

Thank you for sharing this.

I am watching this right now amazing stuff

Popular Science channel Veritasium explains some of the history of metamathematics, set theory, uncomputability, and GĂ¶del's incompleteness theorems (including a very nice explanation of how the first theorem is set up). I find it notable that it's both engaging and accurate. It's not perfect, but still very good in my opinion!

I think he said airline ticketing systems are undecidable, but isnâ€™t that just an NP-complete problem?

Although it definitely felt like one of the better videos on the topics, I still feel it is just a tricky subject that more often introduces confusion, or misunderstanding to layman.

The one thing thay often gets neglected, is what is meant with 'truth'? The issue being, that without addressing it, it is not even clear how something is true, but unprovable; what that even means. Like, one has to fill in how one actually shows something is true, other then by proof (which is

notthe case, it just opens up the door to that misconception), and hence claiming it 'true, but unprovable' feels like it can do more hurt than good.If anything, it should have including something about inteprereting a

syntacticstatement into the model of natural numbers or something. To indicate, that such interpretations define when the statement to be 'true'. And that the symbolic jungling (that the videodoesaddress somewhat accuratly), is the 'provability' side of the equation.It keeps leaving the concept of 'incompletness' as alien, even though it is not uncommon (take the abelian property in the theory of groups). I would love a video to include such a concept applied to a different theory, making it clearer what it inherently means.

Again, the video was better than most. I just hope it sparked interest from outsider to investigate what

reallyis going on, instead of viewers filling in the gaps themselves and ending up more confused/misguided and end up in r/badmathematics with random blogpost later down the line.Unusually good video.

I don't understand why Godel's theorem means "there are things we will never know for sure". It says

within the confinesof any reasonable axiomatic system there will be true statements that cannot be proven. But that statement could always be proven in a different axiomatic system! Trivially, you could just add it as an axiom, of course -- but more interestingly there might be "intuitively evident" axiomatic systems which prove the statement you care about (e.g. the twin prime conjecture). So in my opinion if you want to say that we'll never know whether the twin prime conjecture is true, you have to not only prove it's independent of ZFC, but that it's independent of any "reasonably intuitively evident" axiomatic system anybody could ever cook up -- of course such a thing is not rigorously defined, but limiting yourself to one axiomatic system is highly undesirable (for one thing, you'll never know whether it is consistentandsound; also, what's so special about ZFC? it's just one axiomatic system some dudes thought of like 100 years ago).