Late to this conversation, but even with new physics and mathematical models. the concept of faster then light warp travel where you shrink distances in front of your ship and elongate it or normalize it behind your ship have a requirement for negative mass or a ring of negative energy density around your vehicle to bend space time? And negative mass has never been observed.
Maybe this might explain it better then I can.
https://earthsky.org/space/warp-driv...-space-travel/
Its funny when we talk about breakthroughs. Some one mentioned extreme depth exploration, but that was more a question of engineering and materials then defying the laws of physics or nature that were in place.
For example you look at the Atomic Bomb, Science Fiction writers were talking about harnnessing the atom and creating atomic weapons far before the Manhatten project. The laws of physics always supported it. However what changed was on the outside of that.
The ability to manufacture the materials for the explosive core of an atomic bomb made it possible more then changing the rules of theoretical physics. But the first Atomic Bombs were unweildly bruteforce inefficient designs that were built on with material refinements and computer technology. Then we got the leap forward.
Getting man to the bottom of the ocean was always in theory possible. But materials and manufacturing advances made it possible.
I'm not saying FTL travel isn't possible. But we're so far away from it mainly and probably more then anything else because of the energy budget that it would require. In Star Trek they talk about matter and antimatter creating the required power to create a warp bubble, but honestly that wouldn't even come close to creating the energy required.
You, me, our kids, our kids kids and probably a 1000 or more generations is going to pass until we pobably see warp travel.