Space expands. We know this from our study of general relativity and cosmology. I think an alternate phrasing is also correct. Noting that there is more than one kind of space, one might say: spaces expand. Whatever space it is of, independently of every other, it has a dimension, or more accurately, one or more degrees of freedom, to expand into, which sometimes interact with other spaces' degrees of freedom. We just have to be observant of it and grow harmoniously into the expanded spaces.
To scientists of all callings, the problems they encounter may seem extremely hard before their questions are phrased correctly, while their solutions often have multidimensional uses outside the scientific invention's contexts. Who would have predicted that Einstein's general relativity would have been used to make GPS? Certainly not Einstein himself.
Our engineering skills lived up to the serendipity offered by Einstein's discovery. This is what I loved about watching Edward Boyden's talk about Engineering Serendipity, which I embed here. Please watch it.
The 20th Century's foundational inventions and discoveries were mostly in sociology, computation, mathematics, physics, biology and chemistry. This is not an exhaustive list. Astrobiology and geology are in this list as well.
So now our use cases for these inventions, probably completely unprecedented from that point of view, are in figuring out geography, climate, energy and personal space.
A non-exhaustive unordered list of our future's subjects of study, and my predictions for their uses:
Geography for living space.
Climate for the food, water, the cool breeze and breathing space for all life.
Energy to unlock the productivity space for every one on earth. See Eric Drexler's The Antiparallel Structure of Science and Engineering, and Exploratory Engineering for a discussion of this. He talked about this 7 years ago at the Future of Humanity Institute' inauguration of their program on the impact of future technology:
Biology for the freedom to expand the space for personal growth, by investing in longevity research and development.
Art for the expansion of the space of meaningful conversations.