There are no similarities whatsoever, other than them having opinions on a new tech that affects their field.
> nothing stops mathematicians from doing both of those things
Actually yes, and they explain that pretty clearly in the letter. These problems have been used as "goals" not because the solutions are necessarily worth it, but because they set a clear direction whose process would probably yield very useful theories, and also more conjectures and problems. If the goals get solved by AI models that do not generate comprehension, then the direction gets less clear, it's harder to collaborate and get funding (think what would be easier, to get funding to try and solve Navier-Stokes or to try and understand an already proven Navier-Stokes?), and we get less open problems to work on.
> nothing stops mathematicians from doing both of those things
Actually yes, and they explain that pretty clearly in the letter. These problems have been used as "goals" not because the solutions are necessarily worth it, but because they set a clear direction whose process would probably yield very useful theories, and also more conjectures and problems. If the goals get solved by AI models that do not generate comprehension, then the direction gets less clear, it's harder to collaborate and get funding (think what would be easier, to get funding to try and solve Navier-Stokes or to try and understand an already proven Navier-Stokes?), and we get less open problems to work on.