> Nobody genuinely cares about the moving sofa problem, or about square packing, or about the minimum number of colors needed to draw a map Wild examples. Thes

> Nobody genuinely cares about the moving sofa problem, or about square packing, or about the minimum number of colors needed to draw a map Wild examples. These are all extremely useful. I agree that solving problems along the way is incredibly useful too, but there's no math problem that I'm aware of that's utterly useless. Thing is, math is about abstraction and structure. You're developing tools. Those tools can be used for more than one thing. That's why math is often called a language. It's also why mathematicians and physicists end up being so helpful in other fields, because it was (most of them) about understanding the language of complex problem solving. Even code is math (I find it quite odd programmers are against math and elegance as these are directly in line with their goals, but I guess there's always a Dijkstra EWD already calling this out) Where I fully agree with you is that solving hard problems advances us. TBH, it doesn't matter what it is. Fund NASA and you not only get men to the moon but velcro, GPS, and global wireless communication. Fund particle accelerators and you get the internet. Fund math and, like you said, you get a tool (calculus) which is worth more money than we can even imagine. The thing is that solving hard problems forces the unknown unknowns to become, at least known unknowns.