Just simply telling yourself that something cannot be done is a pretty significant obstacle to actually doing it. It doesn't really much matter what the task is.
A much bigger obstacle is when it actually cannot be done . Let's try to be practical here, not platitudinous...
You can't solve chess but maybe someone else can.😛
Yes. This is known as a fantasy. Imagining that something can happen without any foundation for showing that it actually can happen.
We've been down this road before. If you told me we can create a space elevator ala Fountains of Paradise, I will tell you yes, it's a likely advance that mankind is within striking distance of. We need a filament of the right tensile strength, etc. and we are moving closer all the time in measurable ways.
If you told me we can create a ship that can go through a black hole with human passengers and come out the other side with them alive, I would tell you you are having a fantasy...just like your notion of chess being solved.