That does not imply that developing internal combustion engines was a waste of time -- they have been useful for decades for a variety of purposes. Even if they're never used again in the history of mankind, the uses they've already had are enough.
The current state of robotics has allowed some of great things to be built. Industrial automation, mine sweeping robots, goofy little vacuum cleaners, solenoid-driven irrigation systems, etc. So even if it's all ultimately a technological dead end, it's still been justified.
In any case, I don't share any of your certainty about the direction of future robotics. With the increase in accessibility over the last decade of microcontrollers, sensors, and effectors, and the corresponding increasing in accessibility of enabling technologies like 3D printing and CNC, I think it's entirely possible that we're about to see an explosion in the availability of products with embedded robotics in common day-to-day items -- things that start as hobbyist projects built by hackers but quickly become commercialized into consumer products. This may not be what you mean by "robots" but it is an obvious, useful application for the technologies in robotics nonetheless.
Moreover, even if some game-changing development happens after your death, it's still useful to get something done today. The Boston Dynamics rough terrain animal-like cargo bots are probably the most interesting application, although there's lots of industrial robots out there doing incredibly valuable work like pick-and-place.
And you're posting this to Hacker News, where people discuss startups almost all of which will be dead, unrecognisable or absorbed in 20 years time let alone a lifetime.
Breakthroughs don't just happen and change everything. In almost every case there's a lot of background work, like this stuff, that builds up to the breakthrough.
Also, my vacuuming robot is pretty good, I haven't had to manually vacuum in several month and there is virtually no dust. I'd rather have that now than wait for robot researchers to get bored fishing and build something incredibly better.
Exactly what sort of robotics are you railing against? It seems to me that your arguments are essentially the old joke "We're wasting 50% of our money here; if only we knew which 50%". Or, "Things aren't useful, until they are".
>Robotics is not like mathematics
Ever heard of Bayes' theorem?
No he didn't because he failed to abstract it and publish it in a way that would benefit the builders of the first modern computers in the 30-40s - they knew nothing about his Analytical Machine. So, if you were building a technology tree for a CIV-like game, sorry, "Analytical Machine" doesn't appear as a pre-requisite for "Modern Computer". Similarly, today's "robots" will not be ancestors in the technology tree of the first "real" robots, if and when the latter eventuate.
You seem to have this retrospective view of technology creation where anything that didn't pan out or doesn't connect to current technology was therefore a waste of time and effort. The problem is that at the present nobody knows what's going to work out- you just have to try. Some ideas will work, some will not, some ideas will be lost and then re-discovered. It's a messy process. I'm sure there are robotics researchers who are wasting their time in dead end technologies. But I don't know which ones they are, and neither do you. I have opinions, but I'm not prescient.
People thinking about them helps. You don't need the first people designing computers to have heard of an analytic engine and be working from Babbages notes for there to be dependencies. And it is not as though Babbages work did not have an influence on mathematics and technology in its day, it was widely known and discussed in both academic and political circles, and will have certainly influenced many. It would seem unlikely for the people working on the first working computers to not be drawing on some work that had echoes of the earlier attempts in the field, irrespective of whether the researchers themselves were aware of it.