I was about to comment with something similar to what Martín said. I think what you want is an AI that solves problems that can be fully specified with a low Kolmogorov complexity in some programming language. A crisp example of this sort of AI is AlphaProof, which gets a statement in Lean as input and has to output a series of steps that causes the prover to output “true” or “false.” You could also try to specify problems in a more general programming language like Python.
A “highly complicated mathematical concept” is certainly possible. It’s easy to construct hypothetical objects in math (or Python) that have arbitrarily large Kolmogorov complexity: for example, a list of random numbers with length 3^^^3.
Another example of a highly complicated mathematical object which might be “on par with the complexity of the ‘trees’ concept” is a neural network. In fact, if you have a neural network that looks at an image and tells you whether or not it’s a tree with very high accuracy, you might say that this neural network formally encodes (part of) the concept of a tree. It’s probably hard to do much better than a neural network if you hope to encode the “concept of a tree,” and this requires a Python program a lot longer than the program that would specify a vector or a market.
Eliezer’s post on Occam’s Razor explains this better than I could—it’s definitely worth a read.
I was about to comment with something similar to what Martín said. I think what you want is an AI that solves problems that can be fully specified with a low Kolmogorov complexity in some programming language. A crisp example of this sort of AI is AlphaProof, which gets a statement in Lean as input and has to output a series of steps that causes the prover to output “true” or “false.” You could also try to specify problems in a more general programming language like Python.
A “highly complicated mathematical concept” is certainly possible. It’s easy to construct hypothetical objects in math (or Python) that have arbitrarily large Kolmogorov complexity: for example, a list of random numbers with length 3^^^3.
Another example of a highly complicated mathematical object which might be “on par with the complexity of the ‘trees’ concept” is a neural network. In fact, if you have a neural network that looks at an image and tells you whether or not it’s a tree with very high accuracy, you might say that this neural network formally encodes (part of) the concept of a tree. It’s probably hard to do much better than a neural network if you hope to encode the “concept of a tree,” and this requires a Python program a lot longer than the program that would specify a vector or a market.
Eliezer’s post on Occam’s Razor explains this better than I could—it’s definitely worth a read.