Roger Penrose explains Godel's incompleteness theorem in 3 minutes

The thing about the sash

theorem

, you see, I heard I used to have a colleague when I was a student in the first place, who was who became a scientist later and we talked about logic and you know how you can do these kinds of mathematical systems I solved the logic and I had heard about this girl's

theorem

, it seems like we say that there are things in mathematics that just can't be proven and I didn't like that idea, but when I heard the when I went to this course, Weisstein and explained what really says and what it says, suppose you have a method to prove things in mathematics and when I say things I mean things with numbers, the famous example is that you must have the last theorem, there is gold, but conjecture is not.

However, they were shown to be very even. A number greater than two is the sum of two prime numbers, that's the kind of example, it's mathematical things about numbers, you can see what they mean, but it can be very difficult to see. whether true or false, but the idea is often that in mathematics you have a system of proof methods and the key to these proof methods is that you can have a computer check whether you have done well to follow these rules. you know they could be adding a and B, it's the same as B and a and things like that and if you give it you tell the computer, it says here's a theorem like the Goldbach conjecture and you see if it can be proven and you say maybe I have a proof and you follow these steps and you give it to the computer and it says yes, you did it right, it's true or maybe it will say you did it right and it's not true or it may not say anything else. it just goes on forever, but these are the kind of results and the point is that if you believe that these procedures give you proof, in other words, that if the algorithm says yes, it is true, then you believe that it is true because you have understood all the rules, you looked at the first one, you say yes, yes, okay, you look at the second, you said mom, oh yes, I see, okay, that's great and you go down to the end and, as long as you're convinced, all those rules work. so if she says yes, that's something you believe in, okay, now what the girl shows as she constructs a very specific sentence, a statement that is a number, like she must have probably lost her arm or something, Think about the numbers, what it shows is whether you trust this algorithm. to prove mathematical things, then you can see from the way it is constructed that it is true, but you can also see from the way it is constructed that it cannot be proven by this procedure.

This was surprising to me because it tells me that okay, you can't formalize your understanding into a schematic that you could put on a computer that you see this statement that the girl comes up with is something that you can see based on the same understanding that you It allows you to trust the rules that it's true but it doesn't actually follow from the rules, you see that it's true by virtue of your belief in the rules and this to me was amazing.