/sci/ - Science & Math

>>12740006
Also, what exactly is the relationship his undecidability and Turing's uncomputablity? Are they perhaps related by the Curry-Howard correspondence?

>>12740030
If a formal system could derive every true statement (completeness) and only true statements (soundness), then number theory would be decidable (because you could write a program that terminates in finite time that tells you if a given statement of number theory is true or not). And if number theory was decidable by a program, that program could solve the halting problem.

>>12740030
Well not Godels undecidability, rather his incompleteness theorems

>>12740052
What is undecidability in computer science? I read it's related to Collatz Conjecture I've been lost.

>>12740068
a decision problem is undecidable if you can't write an algorithm that correctly answers it 100% of the time

>>12740068
It just means that the given language is not recursive.

>>12740050
>if number theory was decidable by a program, that program could solve the halting problem.
Where can I find the reduction?

>>12740106
look up the Kleene T predicate. If number theory was decidable then so would this predicate, which is statement about Turing machines halting.

>>12740050
[Not the guy who asked, but] Thanks anon! I've tried to understand this concept before but the youtube videos make no sense. Your explanation is nice and simple and to the point.

>>12740082
>>12740083
I must be a brainlet because that's not making sense. Any conerete exampls?

>>12740006

>>12740418
Do you know what a Turing machine is?

>>12740441
Damn, his handwriting is just like mine.

>>12740745
uhhh...maybe just stick to emails anon?

>>12740006
>What was this guy's problem?
Later in his life, Gödel suffered periods of mental instability and illness. Following the assassination of his close friend Moritz Schlick,[32] Gödel had an obsessive fear of being poisoned; he would eat only food that his wife, Adele, prepared for him. Late in 1977, she was hospitalized for six months and could subsequently no longer prepare her husband's food. In her absence, he refused to eat, eventually starving to death.[33] He weighed 29 kilograms (65 lb) when he died. His death certificate reported that he died of "malnutrition and inanition caused by personality disturbance" in Princeton Hospital on January 14, 1978.[34] He was buried in Princeton Cemetery. Adele's death followed in 1981.[35]

>>12740956
Gödel was born in 1906 and Schlick died in 1936. That means Gödel has been a schizo since he was at least 30, kek

>>12740593
No. Nobody does. It's a meaningless term.

>>12740006
There’s an extremely esoteric series on YouTube about Gödel and his philosophy. It also goes in depth about Leibniz.

https://youtube.com/playlist?list=PLC25C694A288E5A03

>>12740956
Dude died rather than learn to cook, what a fucking baby

>>12741270
Where are all the videos?
>3
>19
>22
???

>>12741729
oh nvm
>releasing out of order
>last video 4 years ago

>>12740006
shooting the messenger is a time-honored procedure, but perhaps it is not adequate in this case.

>>12740006
Quick summary of this guy?

>>12740418
>concrete examples
NGMI

>>12742057
Some math guys were trying to make an algorithm to generate math proofs, gurdel proved that they couldnt, math guys got mad

>>12740441
How is point 2 valid at all???? The guy who wrote this must be nutty

>>12742219
>Some math guys were trying to make an algorithm to generate math proofs, gurdel proved that they couldnt
That's the opposite of what happened, retard. Godel constructed an explicit algorithm to generate math proofs. This algorithm was the basis of his incompleteness theorems.

>>12740259
>>12740106
Look up Matiyasevich theorem too.
>>12740418
Problem: given a system of multivariate polynomials with integer coefficients, determine if it has an integer solution. Turns out determining this is impossible in general. There is no algorithm which inputs a system of polynomials and tells you if it has a solution.