As someone lucky enough to have found a programming job in an organization that is dedicated to something I believe in, I can confirm this perspective. The big picture mission helps keep me motivated, but my day-to-day is pretty abstracted from that mission.
My advice to OP would be to try to diversify your sources of fulfillment. That may be unsatisfying advice - I know that there was a time in my life that I would have rejected it - but from where I stand now, it is the most reliable path to overall happiness.
I doubt this is true. Lots of amazing math has been done since the 70s. I guess your sentiment comes from the fact that what we learn in school/university is necessarily old math, as the newer stuff is just too advanced. Also, from the old stuff it's easy to pick out the important parts, making it look like it was better.
I forgot who said this (possibly Knuth?), but it rings true to me: "When I was young, I thought every step of progress takes out one more thing that could be discovered. Now I know it just opens several more new avenues."
Most tech jobs today are highly commercial and not about making life better. Even if you manage to find something that is somewhat relevant to the real world, like green energy research, chances are it might be something highly technical, abstract, and difficult to relate back to the final product.
For everything else, you'll likely just work on the arms race to the bottom -- whether it be an arms race to fight for attention in the narcisstic space of social media, improving database read times at Google, making some new AI to replace millions of humans, wasting people's time with more advertising, or making poor people buy more stuff they don't need.
In my opinion, if you want to have something truly fulfilling, you'll have to first ask yourself how you can actually make the world better, and then strike out on your own to do it. 95% of modern tech jobs are just a weight on society's back, dragging us down.