AI can generate mathematical answers remarkably quickly. But how do we know when an answer sounds right but isn't?

Consider this example.

Suppose we ask an AI to differentiate

[
f(x)=x^x.
]

A common mistake is to treat it like an ordinary power and answer

[
f'(x)=x,x^{x-1}=x^x.
]

Looks plausible. It’s also wrong.

Using logarithmic differentiation,

[
\ln f=x\ln x,
]

so

[
\frac{f'}{f}=\ln x+1,
]

and therefore

[
\boxed{f'(x)=x^x(\ln x+1)}.
]

This is where a mathematical tool such as Maple becomes useful. Instead of relying on whether an AI-generated explanation sounds convincing, we can ask Maple to perform the differentiation and verify the result.

The lesson isn't that AI can't do mathematics.

It's that AI and mathematical computation have different strengths.

AI can suggest an approach, explain the reasoning, and generate code. Maple can perform the symbolic computation and help us verify what the AI tells us.

So perhaps the better question isn't:

“Can AI do the math?”

It's:

“Can AI help us do better math when we have the tools to check it?”