We said we didn't want a protracted discussion of science, math, and philosophy, but I don't quite feel I can let this go.
You got it the other way around.
Actually, I don't. Some mathematical disciplines are developed specifically in order to help model the real world. This is generally called "Applied Mathematics". One of the first well codified examples of this is Euclidean Geometry. Classical EG is based upon 3 undefined terms: the point, the line, and the plane. Now the fact nothing in nature even remotely resembles any one of the three is irrelevant to EG itself. It doesn't invalidate any theorem in EG. The closest thing to a point in real world physics is the center of a black hole, and it does not seem to be a point, either. Line segments and plane segments can be used to great effect to model vast numbers of real world objects and particularly human artifacts, but in reality nothing completely flat or straight actually exists, and certainly nothing infinite nor anything truly infinitesimal. Furthermore, EG is universally used to model virtually all human artifacts and Earth-bound phenomena. Non-Euclidean Geometry, however, produces wildly different forms than the more restrictive EG. In EG, for example, the sum of the three angles in any triangle is always precisely 180 degrees. In Non-EG, any triangle can exist which has vertices whose angles add up to any value whatsoever, including more than 360 degrees and less than zero. In EG, any two unique lines either intersect at exactly one point, or not at all. Non-EG lines can intersect many, many times, even an infinite number of times, and still be unique, provided there is at least one point on one line where they do not intersect. It would be all but insane to try to model most of the world nearby to us using Non-Euclidean Geometry, yet the reality is every bit of the universe, right down to the very most fundamental objects, are more closely modeled by non-Euclidean constructs. Note furthermore that both EG and non-EG are both perfectly valid, perfectly complete mathematical disciplines, yet neither conforms to the other, and constructs in one form are not consistent with constructs in the other, at all, and constructs in either form are only approximately consistent with real world phenomena.
The universe at every level is approximate. Mathematics is exact. Pi is a transfinite number of completely precise value. An approximate value is 3.1415926535897932384626433832795. The ratio of the circumference to the diameter of the most precisely manufactured disk ever made is perhaps 3.1416. That is quite close in real terms, but infinitely separate in mathematical terms. There are precisely as many points between the actual value of Pi and 3.1415926535897932384626433832795 as there are between 0 and infinity. Nothing of which I know in the real world approximates that. It is a simple fact that, whether any mathematical construct conforms in any way or not to any external form, the construct is still valid as long as it is consistent with the foundation postulates, undefined terms, and formal logic. The construct may conform moderately well to forms in the real world, and it may well be intended to do so from the outset, but it is not a requirement. It may also be true it is extremely difficult, almost impossible, for us to create any mathematical construct that cannot be utilized in some way to model some aspect of the universe, but that may be for any number of reasons, none of which hold any restrictions upon Mathematics.
everything in the world *can be described* and understood with math
"Modeled" is a better word, and that is an assumption. It is not one with which I would quibble, but it is an assumption, nonetheless. Just because we have never come across any phenomena than cannot be approximately modeled via Mathematics does not prove none such exists. There is the very crux of the matter. In Mathematics, every form can be reduced to some exact value or range of values, and everything other than a postulate can be proven without deviation. In Science - especially Applied Science - nothing is ever exact and nothing can ever be proven.
Before Einstein, nobody knew there's an universal speed limit
A "universal speed limit" is a common misconception. Nothing in relativity precludes the existence of an object moving faster than the speed of light in a vacuum, but I will roll with it.
When Einstein created his Theory of Relativity and proved
Einstein didn't prove anything, a notion of which he himself was at some pains to discredit.
that in a mathematical sense, speed of light became a theory.
That the speed of light in a vacuum is constant for every observer regardless of their frame of reference is the First Postulate of Relativity. It remains a postulate. That it should not be possible through any known means to accelerate a massive object to the speed of light is a simple consequence of the fact it would require an infinite amount of energy to do so.
Now that many scientist have proved his theory with countless experiments to be correct over the years
No one has proved the theory, as Einstein himself would stress. There is no other theory in all of science with more supporting evidence than the General Theory of Relativity. Rather oddly, there is significantly less evidence supporting the Special Theory of Relativity, but there is a vast amount of evidence supporting it, as well. Outside of the Quantum realm, no theory is more complete, and there has never been observed an irreconcilable measurement relating to either. They are still, nonetheless, theories. By a vast margin the best supported ones in all of history, but still theories.
everybody knows that there's a constant, and it is the universal speed limit.
Then what "everybody knows" is wrong.
Ask any scientist
You mean like me? What's more, I shouldn't ask a botanist or a psychologist, or even most chemists about it. They are not likely to have much of a good notion.
they will tell you that the speed of light is indeed a *fact*.
The speed of light in a vacuum is indeed a fact. Galileo made some qualitative measurements (or at least attempts to do so) in the 1400s. Subsequent attempts to measure it continue to this day. The first fairly accurate measurements were done in the 1800s. Einstein made the clearly stated assumption the velocity of light in a vacuum is a constant for all observers based upon Michael Faraday's conclusion the velocity of light is equal to the square root of the permeability of free space multiplied by the permittivity of free space. Faraday had been widely discredited in scientific circles, but Einstein thought he had it right.
Shortly before Einstein wrote his first paper on Relativity, Albert A. Michelson had demonstrated that both extant hypotheses concerning the nature of light, based upon the notion there existed a limuniferous aether, were dead wrong. This blasted apart nearly every notion concerning the nature of light except, as it turned out, Faraday's. It is unclear whether Einstein knew about the Michelson - Morley experiment when he first formulated his hypothesis, or not.
Upcoming theories can rely on it safely as a premissa without the need of further proving it.
Since nothing in science is ever proved, the statement isn't well formed. It is true that any new hypothesis is likely to be based upon extant inferences, such as the notion no ordinarily massive object can quite reach the speed of light WRT any observer in the universe, regardless of how strong or tenuous the inferences might be.
One final comment I would like everyone to consider, and also research if it sounds bizarre, impossible, or or just interesting. The notion that no observer will ever measure the velocity of any normal object relative to himself to be greater in magnitude than the speed of light in a vacuum says something much more important about the observer's frame of reference than it does about the object or any "speed limit". You see, it is perfectly permissible for an object to travel at, say, 3/4 the speed of light relative to an observer. If the object has any significant mass at all, it is damnably difficult, but certainly theoretically possible. Indeed, it is quite possible to have three observers, we will call them A, B, and C, with A traveling at 3/4c to the left relative to B and C traveling at 3/4c to the right relative to B. Isaac Newton would have concluded A and C would measure each other's speed relative to each other to be 1.5c. It seems he would have been wrong. A would measure B's speed to be 3/4c, but he would measure C's speed to be .96c. C would also measure B's speed to be .75c, and A's speed to be .96c. The important notion is not so much an object can't "travel" at c, it is that no observer will ever measure the speed of any normally massive object to be c. The other important notion is that this is not just a limit of the method of measurement. After all, SONAR will never measure an object to be traveling at or beyond the speed of sound, which *IS* merely a limitation of the method of measurement. The limitation for light, however, is assumed to be fundamental to the nature of the universe itself.
Conceptually, the physics of a system in an inertial frame
Sure. Too bad there is actually no such thing as an inertial frame in the real world. It is also too bad that, even if there were such a physical thing, a hologram or projection is not an inertial frame, and is definitely not so in the larger system. It could indistinguishably appear so in the smaller frame.
