Chess will never be solved, here's why

Just now - tried to get some things out of the AI about Euler graphs.
Like the seven bridges problem.
Two islands in a river.
After correcting the AI a zillion times it finally represented the bridges in a 2-3-2 format.
And claimed apparently rightly that there's no way to do a tour of the bridges crossing each bridge exactly once.
But struggled with Euler's proof of that. Regarding the 'degrees' at each vertex.
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I told it Euler's 'thing' there looks like a flow diagram not a graph.
After some argument it conceded that an Euler graph could be a flow diagram but a flow diagram doesn't have to be an Euler graph.
But as this was going on I realized that the knight's tour in chess (the knight making its moves to hit all 64 squares just once (will not help your chess) - can be regarded as a flow diagram.
The AI tried to insist - no - the knight's tour cannot be an Euler graph.
And suggested it could be 'Hamiltonian'.
But the AI kept messing that up again and again.
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But it seems that an Euler graph doesn't have to be Eulerian.
Point: the 'rules' of Eulerian.
Eulerian 'path' versus 'circuit'.
The AI kept trying to insist there were more than two odd degrees.
Euler of course is famous for his Euler's identity equation. 
Which he formulated long after the Konigsberg 7 bridges problem.
Point: Descartes' graphs in widespread use everywhere with many uses.
But 'Euler graphs' (which are more like flow diagrams?) seem to come up in narrower contextes.
In trying to figure out why they'd be called 'graphs' ....

That's because the bridge problem is topology. Similar to how if you draw the letters x, y, and z, and the numbers 1, 2, and 3 on a sheet of paper, you will never be able to draw 9 lines connecting each letter to each number once without any of the lines crossing. It doesn't matter where you put the letters and numbers, you will never be able to connect them all without lines crossing unless the surface is a Torus. You'll be able to do 8, but not 9.

Euler diagrams are called graphs for some reason.
Maybe something to do with the etymology of the word 'graph'.
Most of the time when somebody says 'graph' a Descartes style chart is meant.
That's a suggestion - not an insistency.
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So then - 'Euler diagram' versus 'flow diagram' versus 'Venn diagram'.
Euler diagrams apparently were conceived with set theory in mind. In the 1700s.
And pre-dated Cantor. Who apparently introduced the term.
But called a set 'menge' with plural 'mengen.' German in orther words.
That was in the late 1800s.
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Node and vertex and graph and edge seem to be terms borrowed from other disciplines and applied to Euler diagrams in a very jargonish way.
'Tree' is a little better.
'Nodes per second' and 'game states per second' and 'positions per second' look very suspect since the difficulties of positions vary.
I'm not claiming though. I just said 'look'.

[EDIT: I wrote the following thinking @playerafar was expressing uncertainty about the proof. Now I see it was about the understanding of the AI, not him. So feel free to ignore].

Euler's proof is easy.

First formalise the problem as a graph. Every point is a set of real points between which you can move without crossing a bridge. Every bridge is an edge connecting two of the points you have just defined.

(This is a topological viewpoint - you are thinking of all the points on an island as being essentially the same point, as moving between them is irrelevant),

Imagine a continuous path from any point on the graph to any other, i.e. a sequence of bridges that it is possible to cross in order. Then apart from the end points, every other point trivially has the path going into it and out of it each time it reaches it (by definition). Thus every point except for at most 2 must have even order. But more than 2 points in the graph of the Koenigsburg bridges has odd order. Thus is cannot be traversed.

This can be made more formal, but the key thing is each time you pass through a point you add two to its order, with only the two ends of the path allowing any exception.

[Euler has a zillion things names after him: I can't even recall what Eulerian means in this context! But the proof sticks].

This is not a good question for any reason other than etymological interest. It's simply that mathematicians chose the word (which also means something different in common English). Words are labels for concepts, and their only purpose is to communicate from one person to another what concept they mean.

I gave chatGPT a similar problem and it aced it.

Spooky!

I tried to trick it (last question in dialogue) but I was too obvious.

Try it on the cat and mouse game (2x2 grid with two lines added to an edge of the bottom right cell to form a triangle, cat top left corner of the grid, mouse centre, cat and mouse to move 1 edge alternately starting with cat, cat wants to land on mouse or mouse to land on him.)

Well it might be able to be solved because of the minimax thereom but it would be hard

Let v(P) represent the value of a position P

Then for any chess position the optimal move corresponds to maximizing this value according to the minimax principle

v(P)=Player A’s move (max) and Player B’s response (min ) value of the resulting position

Chess has a finite number of positions so there has to be a definitive strategy for both players that would lead to a minimax solution which would be a singular optimal move

I gave chatGPT a similar problem and it aced it.

Spooky!

I luv the word spooky ...I feel like in the next 5 yrs or so AI will be a good thing. But in 10-20 yrs ?...it could end up harming society (ppl dont discern so easily right ?). must we regulate now ? ...not sure, but i feel we'll hafta one day.

@Elroch
If you're saying that 'traversing' changes the 'degree' at a vertex ...
well the AI was not saying that.
It kept saying the degree of a vertex was/is the number of bridges that connected to an island.
Then it kept insisting that the number of vertices with odd degrees was three.
But there's only two that are odd.
The two islands each have five degrees.
The two mainlands each have two degrees.
In order to stop it repeating its mistake over and over - I started over. New session.
Finally - it conceded that there were only two islands with odd degrees.
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Etymololgy and terminology.
An Euler 'graph' would be better called a 'flow diagram'.
But maybe in DevWorld (a term I coined a while back) they don't say 'flow diagram' or 'flow chart' anymore. Maybe they don't use those terms in the Stack Overflow website.
I don't know because I don't go there.
Are we allowed to criticize jargon terminology here? Yes.
'Edge' is a poor choice of words for a route or arrow or bridge.
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Regarding Euler diagram versus Venn diagram
there's apparently at least one intersection (overlap) of 'bubbles' in all Venn diagrams.
Or - there's supposed to be.
Even if its a 'null set'. In other words if two sets have no common elements.
Whereas Euler diagrams have no such requirements. 
An intersection (real or theoretical) not required.

'graphic' as a noun would be a better choice for an Euler diagram than 'graph'.
An Euler graphic.
We get to discuss the terminologies used.

We could also say diagram. Right?
Game tree diagram. And 'game tree' could refer to the mathematical entity of the game tree as opposed to a diagram or graph or graphic.
Right?
Not arguing - just suggesting.
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So to prevent ambiguity - I could say 'Euler-style game tree graph' every time but that would be inappropriate.
So instead I'll call it 'game tree diagram'.
Now lets see if I've got it right about what MARattigan is saying ...
Regarding game tree diagrams (Euler style) that display or use 'nodes' I'm starting to get the impression that such diagrams would not have axes - even though the AI indicated that they would.
It was suspect as soon as the AI suggested that the x-axis would be the dependent variable.
Next: try and find out if the term 'flow diagram' is not in common usage in DevWorld.

We could. We could also say kettle or Basingstoke. But why would we want to? We're already using diagram for something completely different, why confuse the issue?

But it’s not about the exact play style of an engine it’s about identifying a definitive outcome from any position

It’d remove any variation in the style of play, because whether an engine plays tactically or strategically, whatever it does will ultimately align with the optimal moves according to the architecture

You suggested no axes.
No attempt to confuse.
What might be helpful is an actual diagram (game tree diagram) of 'nodes' in its chess computing context.
Or diagrams. Displayed here.
If they were already displayed including recently I missed it.
(19,000 posts. Not Guilty)

You’re thinking in terms of human comprehension and philosophy I’m thinking in terms of objective mathematical reality

The fact that you have to calculate to the end of the game doesn’t make it impossible, it’s still possible, you’re looking at it from an “endgame” perspective, but the way chess will eventually end up getting solved is if a system ends up successfully calculate every single possibility from every possible position

This is indeed possible even if it takes an absurd amount of computing power to do so

Because finite doesn’t mean “impossible,” it means calculable