Actually, scientists and engineers can prove things as well, also because they are mathematicians and logicians themselves.
It depends on the subject and type "thing" to be proven.
Experimental observations in and of themselves may just be in agreement or conflict with a particular theory, yes. But for example you can still construct solid proofs by construction (can you build a machine that can add numbers is a question about reality, not just abstract mathematics or geometry, yet any of the billion ways to do that are a solid proof of existence or potentiality).
And you construct proofs that hold securely as long as all the premises still hold, that is also much more than just disproving alternatives. In fact proving and disproving something is exactly the same, you set your premises, make reasonably sure they hold true and that everybody can see that, and then use logic to arrive to a conclusion. As long as the premises hold true, the proof holds true forever. If any of the premises turns out to be inaccurate, even something you thought you disproved might end up being true after all. But before anybody starts going all nihilistic, in practice most things get to be pretty accurate or near-perfect after just a few iterations, especially as we use premises that held true over and over.
And even small adjustments are often enough, maybe one of the premises was that your instrument measured the sum of two things instead of just one, the result is still valid, but you might need an extra experiment to separate that sum, etc.
But in agreement to some of what Patrick mentioned, belief doesn't have anything to do with science or technology.
A computer is not working because we believe in it, the term belief is something generally reserved for something that is not part of science or even of the observable reality.
I can believe in invisible unicorns that are completely undetectable and have no impact on reality. That's because there is no way to ever verify or disprove that they really exist or are part of reality, by definition.
If they were, I wouldn't have to believe in them, they would be just a normal observable and reproducible fact of life. I could run any of hundreds of possible tests and the results would always show that they exist.
Now, about special energies like chi/qi/ki etc. scientists do not believe or use it because so far there has never been a need to invoke it to explain any repeatable fact in reality.
We use plenty of special energies already, like electricity and magnetism, gravity, and the strong and weak nuclear forces.
In a sense those are also something somewhat mysterious that we can't quite touch or see directly, but we can see them absolutely repeatably indirectly, for example rubbing tennis shoes on a carpet and making a small electrical shock spark from our fingers to our unsuspecting friends we see the light generated by that spark, or we can see magnetic lines around a speaker using some metal powder, etc.
In contrast, there is nothing repeatable in reality that isn't already explained well by the fundamental forces I already mentioned and that would require a 5th special force, nothing.
In terms of martial arts in particular, everything that you can see repeatedly is quite well-grounded in reality and science.
For example, to break bricks, wood and other objects people use special training that induces a lot of microfractures in their bones, as they repair over time they change the structure of the bone itself, and that makes it much harder and resistant. That's a measurable change you can see in X-rays or even bone samples under the microscope.
And in fact it's similar to well-understood techniques used even in sword-making (the reason why their metal are tempered and refolded many times over) or in material-science in general, where you induce crossing molecular-lattice-structure dislocations to harden a material like a metal (you might have seen if you bend and unbend a piece of metal eventually it becomes harder to bend again, more brittle, but harder)
And the technique, speed and control of recoiling vibrations are also something very much real and therefore perfectly scientific. You can measure those exactly with a lot of instruments (high speed cameras, pressure sensors, computer models etc).
In fact, you can make something with similar material properties as hardened bone, and use a mechanical system to reproduce the same type of collision and obtain the same results, even if most people wouldn't attribute special martial arts energy to a robotic arm connected to a computer for example.
Even other things like taking hits better or worse are grounded in reality and therefore science, for example you can learn to take hits in a way that absorb and dampen harmful vibrations and much of the force etc. You get the idea.
But again none of these are supernatural in any way, because they are actually real, and therefore reproduceable (even by mechanical systems or even simulations and equations) even if they require special training and often even talent.
Even things like "willpower" are still very measurable, dependent on very clear and real mechanisms like total neural output, effects of adrenaline and other chemicals, and are modified by training etc.
Now, on a personal note, I have done a bit of martial arts myself and actually use traditional concepts like chi more as a convenient visualization and coordination concept, so while I still know well it deosn't exist it is still a very useful practical abstraction to use while you practice and it's easier to think in terms of pre-facilitating some motor neural circuits and coordinating breathing and contraction of certain muscle while relaxing others, getting pumped-up with thoughts that release more adrenaline etc. I can do a few of the typical demonstrations of chi without "believing" in it at all, because again they work by very real and scientific mechanisms.
