Where Modern Mathematics and Academia Fails the Forward Progress of Mankind

There are many areas where academia fails us in the real world, and it doesn't take a rocket scientist to see that. In fact, not long ago, I had contacted a mathematician PhD specializing in astronomy and cosmology equations.

We got to talking about Lagrange Points and how these important points might help humans in their future space explorations, and indeed, my interests are using these points for Space Stations, Space Hotels, Scientific Research, Refueling Depots, Asteroid Mining, etc.
My academic acquaintance told me that Lagrange Points don't have areas or shapes, because they are a point, and the definition of a point is not a shape or area.
Sure, that's true, but pretty irrelevant as to the question of how big are Lagrange Equilibrium areas, especially if we wish to put something there. Okay but, if the present day physics cannot explain the 'Fuzzy Boundaries' of a Lagrange equilibrium areas based on the gravity distribution, motion, and spin of the planetary bodies creating them, then the mathematics used in this area of science are inadequate. In which case, maybe we need to dump the 18th century concept of a "Lagrange Point" being a point, because that definition and description is inaccurate.

Even if the mathematic point happens to be the center of the equilibrium area, it's an inaccurate description because it would be bouncing around and moving constantly.

What is that motion, is it predictable, does it have a harmonic, does it repeat, and who knows what other questions we might come up with if and when we find out those answers? You see, if we do not ask such questions because of pompous academic adherence to an irrelevant use of terminology of days gone by, then we fail to push forward.

If we in this case refuse to consider such questions, due to such nonsense, then indeed, we too are irrelevant to the forward progression of mankind. See that point? I think we can do better than this - seriously, I think we are beyond such meaningless dribble and denial over definitions. Luckily, I am not an academic nor do I understand the vernacular, but I get the concept. Besides, I am not asking to change standard physics, rather I am looking for an upgrade - new thinking on the topic, with new mathematical equations.
Perhaps, my mistake was in thinking that academia really had all the answers, or might be able to come up with such.

If academia fails to accept the challenge, or care not to consider these questions - then maybe humans are wasting our time in trusting their knowledge.

There is no need to play a definitional war of terms, as an excuse not to answer such questions.
It's time to push forward, and if the current leadership of academia won't - we need to get new blood into the system.

Perhaps, why more of our top students should consider such a career, please think on this.