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/sci/ - Science & Math

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10777323 No.10777323 [Reply] [Original]

Can someone give me a factual and educational explanation of Godels incompleteness theorem and how big of an impact he had on mathematics?

I see a lot of biased reports and videos making baseless speculations and go way off topic.

>> No.10777326
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10777326

https://www.lesswrong.com/posts/GZjGtd35vhCnzSQKy/godel-s-completeness-and-incompleteness-theorems

>> No.10777759

>>10777326
>lesswrong
yikes

>> No.10777773
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10777773

>>10777759
Not an argument

>> No.10777789

>>10777326
>https://www.lesswrong.com/posts/GZjGtd35vhCnzSQKy/godel-s-completeness-and-incompleteness-theorems
Why does it feel like I'm reading a reddit screencap

>> No.10778932

you cant leave the system to view it from the outside therefore many things, causes and processes are unknowable...
man is the measure of all things.

>> No.10779003

>>10777323
My understanding. Assign axioms to numerical values. Numerical values infinte in states eg axioms infinite in state. Implies incomplete. Relatively associates to axioms.

>> No.10779204

>>10777323

The only way to write down all true theorems in a theory is Theory(Axioms).

>> No.10780400

>>10777323
Here is a quick explanation by our guy

https://youtu.be/V49i_LM8B0E?t=5160

Starts at 1:26:00

>> No.10780704

>>10777323
there are things in this world that are true, but not provable.
math isn't simply basing everything on its axioms.

>> No.10780726

There are 2 theorems. The first states that no formal system strong enough to do arithmetic in can be both consistent and complete. The second says that no such formal system can show that it itself is consistent.