When mathematicians solve the Collatz Conjecture then we'll know. This will likely require creativity and thoughtful reasoning, which are non-algorithmic and can't be accomplished by computers.

> creativity and thoughtful reasoning, which are non-algorithmic and can't be accomplished by computers.

Maybe. When computers solve it then we'll know.

We may use computers as a tool to help us solve it, but nonetheless it takes a conscious mind to understand the conjecture and come up with rational ways to reach the solution.

Human minds are ultimately just algorithms running on a wetware computer. Every problem that humans have ever solved is by definition an algorithmic problem.

Oh? What algorithm was executed to discover the laws of planetary motion, or write The Lord of the Rings, or the programs for training the GPT-4 model, for that matter? I'm not convinced that human creativity, ingenuity, and understanding (among other traits) can be reduced to algorithms running on a computer.

They're already algorithms running on a computer. A very different kind of computer where computation and memory are combined at the neuron level and made of wet squishy carbon instead of silicon, but a computer nonetheless.

I don't see how it could be reasoned otherwise.