AlphaZero is not general AI. It can play Go (and chess and shogi) but that's very literally all it can do- it can't process speech or recognise objects in images, or any other task you might choose to test it against. It is extremely powerful, but also extremely limited, in the same way that computers have been for a very long time.

For instance, computers are decidedly better than humans at arithmetic. Yet nobody (today) thinks that just because computers can do arithmetic very quickly and accurately, they are more intelligent than humans.

Is there anything special in Go or chess that makes a specific skill at them a necessary and suficient condition for general intelligence? We are impressed at the performance of AlphaZero because humans find it very hard to play Go etc well. On the other hand, we also find it extremely hard to, e.g. divide two arbitrary 100-digit numbers -but we are not impressed by a pocket calculator as much as we are by AlphaZero. Might there be an element of psychological bias in our ability to be impressed, then?

Go and chess are different in that they are designed as a competition for human thinking in a similar way that say marathons are designed to show off human running. Dividing 100 digit numbers less so. Also there was something human like in the way alphazero learns unlike say stockfish which is more calculator like.

There are competitions where people try to do arithmetic with very large numbers [1], or memorise very long sequences. The point is not what is an actual competition, which is a matter of tradition or culture; but what is easy and hard for a human to do, which is not (entirely) culturally determined.

I guess you could say that the difference between human and computer intelligence is that humans don't have total recall, while computers do. This allows computers to add large numbers without trouble or play millions of entire games at random and choose the best, etc.

On the other hand, there's always a chance that humans' incomplete recall is a hallmark of general intelligence.

>> Also there was something human like in the way alphazero learns unlike say stockfish which is more calculator like.

That's a matter of interpretation. AlphaZero plays by searching a huge space of possible moves- humans dont' play like that. It learns by playing itself millions of times. Again, humans don't learn like that.

There's nothing human about AlphaZero, nor Stockfish far as I can tell.

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[1] https://en.wikipedia.org/wiki/Mental_Calculation_World_Cup