As DL says, not all natural language can be expressed in math terms. IE, "Love is like a red red rose" can't be expressed mathematically.

However, to say that the converse is true, that anything written in math cannot be understood in natural language is a complete logical fallacy, in my opinion.

If that were so, we would have no text books, and we would not be able to effectively communicate math to one another. Like it or not, we think in natural language. Each symbol in math has a natural language equivalent. + is equivalent to "plus"

1 + 1 is equivalent to "one plus one."

r is a mathematical-lingustic shorthand for radius
r^2 is mathematical shorthand for "radius squared" or "radius time radius" or "radius times itself"

4*Pi*(R^2) is the equivalent of saying "Four times Pi times radius squared" or "four times the ratio of the circumference of a square to the circumference of a circle times the radius squared."

We understand math in natural language. To say that we don't is ridiculous. If anything math is a specific set of more formal language, with more specific definitions than english language. Perhaps each symbol is specifically defined. But where we string symbols and digits and variable together we get a mathematical syntax and in some cases, the syntax CAN mean different things depending on how it's interpreted.

Granted, the expression of force F=Kg*A appears to be quite straightforward, with only a single definition. However, we have other knowledge. A=V/T

So we can alterantely write Force a Kg * V/T This conjures a slightly different understanding of the equation (Mass times the change in velocity over time). Granted, it's still equivalent to the same thing, but it make use of different real world understandings. It can further be broken down into Kg *((D/T)*(1/T)). Again, a slightly different real-world understanding emerges. Now we understand it as mass time the change in the change in distance over time.

However, this can be rearranged yet again, still equivalent mathematically, but again with a different real-world understanding: (Kg*(D/T)) * (1/T). Now we understand an alternate meaning of force as Momentum over time, rather than mass time acceleration.

The point here being that we think conceptually in real-language and real-world concepts. We don't think in math. Whatever we think is generally rooted in our internal monologue, which is in natural language. We may see 1 + 1 = 2. But these symbols are mapped to real-language equivalents, and associated with concepts, such as numbers, addition and equality.

To say that we must divorce mathematics from real-world language is to say that we must cease to understand mathematics at all. We cannot think without translation into real-language and into conceptualization. That's just part of the human cognitive process. To say otherwise is madness.

If we must divorce mathematics from definition and/or meaning, then mathematics becomes useless because it then ceases to have meaning. It becomes gibberish. It becomes a collection of symbols, numbers and letters without meaning. Meaning and definition are intrinsic to language, any language. And if we cannot define our terms, we cannot talk rationally.

In order to define terms, we must have a conceptual understanding of said terms. And any conceptual understanding, as stated, will be in natural language or it will be useless.

In and of itself, r^2*4*Pi is just a sequence of characters on a page, it is only our connection with specific concepts that makes them into "math."

If I wanted to I could write a string of such characters with no associated meaning:

r^2*4*n/39,000*(24^9)+49Pi(n^39002). But it's nothing more than a string of characters, and gibberish. One could probably attempt to work it out mathematically, and it may even form some interesting if slightly bizarre graph. But it would be meaningless, because none of the terms are defined, three is no real-world meaning to the equation.

This is my point. There MUST by definition, be a definition in order for anything we say in any language to have meaning.

My only question is what is the definition of Mass? So far we've only been able to define it in a roundabout fashion as "that which resists acceleration."

My inquiry is "why," "how do we describe mass in real-world terms," and "what is the structure of mass, such that it resists acceleration." It's a fairly straightforward question relating to definitions. Inevitably, in science and math, all things should trace back to first causes. We know why division works. We know why addition works. We know why exponentiation works. These all proceed from simpler concepts back to the simplest concepts. Theoretically, anything we observe should derive from simpler concepts, back to what is relatively indivisible. Hope that makes sense.

I certainly understand that formulae are the way they are for a reason. There has been much testing and freeting that went into deriving them. But they're generally all based on specific concepts and foundations, or specific observations. And these observations, theoretically stem fom real-world things.

As Alcaray said, mathemtical equations are used to describe real-world things like a car rolling down a hill, and back up. Forces can be felt. Acceleration seen and experienced and measured (with the right equipment). Math is just another language to describe what we see or imagine. But inevitably it traces back to real-language in our brains, as we think about it. And it traces back to specific thoughts/concepts. So, to say that something doesn't trace back to a real-world thought, makes one question whether that thing is valid and makes one wish to explore/further understand it. I still question how we can define one mathematical concept in real world terms but not another. It simply makes me wonder if our definition of mass is complete and/or legitimate, if we can't articulate it fully...

IE, we throw around the term "mass" but seem to thus far have a problem with definition of how mass works and exactly what it is. My question is simply one of defintion.

So, again, we come back to it. I ask "what is mass?" You say "resistance to acceleration." I ask "okay, how does that resistance to acceleration work?" Thus far, the answer seems to be, for all intents and purposes, "I don't know," "it's not important," or "shut up, and don't ask that, 'cause we don't know."

I'm not satisfied with those answers. ;o]