You care because Pierre de Fermat 16th century work on modular arithmetic was of “no intest to anyone else” except other theorists but it got to shine in the twentienth century in modern cryptography.

Doing theory is what gives you a chance to push the envelope to places you can’t even imagine when you’re knee deep in real world problems. And proving something is possible (if impractical) gives an incentive to find a better algorithm and may attract others.

For example see the first graph here: http://klotza.blogspot.com/2016/06/the-fall-of-twin-prime-ga...

I think you are free not to care about what they are doing. It turns out that big O notation has some useful properties, and in particular it is a useful definition as it allows you to define complexity classes which are a very useful tool for analyzing algorithms in general.

Much of our 'practical' understanding of algorithms also in part came from theoretical advances.

> If algorithmic theorists don't care about practical performance then why should we care about what they're doing? It's just a strange game they're playing, of no interest to anyone else.

You don't need to care. But every so often breakthroughs in theory can be turned into breakthroughs in practice.

> It seems like rather than coming up with more "galactic" algorithms, a more useful thing to do might be to come up with a replacement for big-O that's not so exploitable, and to convince theoreticians to play that game instead.

There's plenty of replacements.

Btw, we already have the optimal (in big-O terms) algorithm for every NP hard problem. We just don't know whether it runs in polynomial time or takes longer. And, yes, that algorithm called Levin's Universal Search is a galactic algorithm. Simplifying a lot, Levin's Universal Search does some clever interleaving to essentially try all possible algorithms in sort-of parallel.

Lo and behold, even the theorists you complain about don't see that 'loophole' as a solution, declare victory and go home. They still keep researching.

They do care. They also care about partial results. As of last week, we thought we knew the best possible algorithm. We now know that there's a galactic algorithm that's an asymptotic improvement. The question then becomes "Is there a non-galactic algoritm that does the same, or is any such algorithm necessarily galactic?"

The problem is that proving an algorithm is necessarily galactic is incredibly hard. If you knew how to do this, you would become one of the most celebrated complexity theorists of the age. Stanford would be calling.