Uniting the sciences is not that trivial.
I’d argue physics has done a lot in terms of breaking down the barriers between the sciences. Each science has their own physics—certain equations of phenomenon that work for their own field.
So in a sense, I can imagine physics as the center of the sciences. Only because physics brings both numbers and theory (math only brings the numbers), and it’s the theory that makes it all make sense.
To give some context, consider all of the physics off-shoots of our central fields: physical chemistry, biomechanics, biophysics, geophysics, etc. Not to mention physics’ attempt at a theory of everything—which is really just a theory of the small (which if correct is technically everything).
But I’m not convinced physics is the best intersection.
I see the problem though stemming from the way we convey physics (not that it isn’t a great choice for an intersection of the sciences). We teach it as separate things, each phenomenon has its own set of equations and rules, though they can be derived from some starting principles (newton, thermodynamics). Ultimately, by building it up as separate ideas, with clearly different models, the unity is lost: how can they work together?
This brings me finally to Biomimicry.
Biology isn’t just a good resource for solutions, it also creates great examples of the separate concepts can work together.
Biology is the application of physics. There are too many organisms that utilize the many types of physics to accomplish a goal. In a sense I would bet that anything we teach in class could be found in an organism.
The point of this is to unify the sciences not through a theory of everything, but rather a unified subject of study. Such that when we learn about physics/chemistry/engineering/mechanics it’s in the context of biology.
Unification through a common application rather than a common equation.
I think this would be a good foundation for someone who is considering an interdisciplinary path; where things are seldom purely one thing.