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Mathematics is not the only kind of reasoning, so your conclusion is false. The human brain also has compartments for different types of activities. Why shouldn't an AI be able to use tools to augment its intelligence?

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I used the mathematics example only because the GP did. There are many other examples of non-reasoning, including some papers (as recent as Feb).

There are many examples of current limitations, but do you see a reason to think they are fundamental limitations? (I'm not saying they aren't, I'm curious what the evidence is for that.)

It's because of how transformers work, especially the fact that the output layer is a bunch of weights which we quite literally do a weighted random choice from. My hunch is that diffusion models would have a higher chance of doing real reasoning - or something like a latent space for reasoning.

Thinking that LLMs are intelligent arises from an incomplete understanding of how they work or, alternatively, having shareholders to keep happy.

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