> Mathematicians will be less likely to work on a problem if there is a solution

Yes, that is Tao's premise, I'm just not sure I buy it. Suppose an oracle existed which could answer any question truthfully. Let's ignore the mechanics of this for now, but it could say things like "the Riemann hypothesis is False" or whatever and we would take it as gospel.

Does this mean that we wouldn't have mathematicians or physicists or computer scientists or biologists anymore? I genuinely don't think so.

Yes, but presumably they'll work on another problem instead, because they're mathematicians who enjoy doing mathematics.

Is there value lost in them working on problems that don't have solutions instead of problems that do?