How to know what the letters mean in math formulas? For example, see this Wikipedia section on Newton's laws of motion:

Newton's Second Law states that an applied force, $\mathbf F$, on an object equals the rate of change of its momentum, $\mathbf p$, with time. 
   Mathematically, this is expressed as:
  $$\mathbf F =\frac{\mathrm d \mathbf p}{\mathrm dt} =\frac{\mathrm d(m \mathbf v)}{\mathrm dt}.$$

Based on this chart of symbols I understand they are saying $A / B = C / D$ and that $\mathrm d$ is a function and $m \mathbf v$ is the input to that function, but how do I figure out what "$\mathrm d \mathbf p$", "$\mathrm dt$", "$\mathrm d$", and "$m \mathbf v$" mean? Please don't give me the answer, but instead, pretty please tell me what method a math person would use to always know what there mean (without asking anyone).
I can sort of guess that $m \mathbf v$ might mean motion/velocity or something, but surely you're not just supposed to guess at the symbols. A see formulas like this all the time and I can never find a key that explains what the letters mean. What am I missing?
 A: A mathematical text would define the notation it uses, either within the body of the text or in an index of symbols at the start or end of the text, unless the notation is really common. For example, a high school text would not define the symbol for ordinary addition or subtraction.
If you are ready to see what the notation in your example means, read on. Otherwise, stop here.
In your example $F=\frac{dp}{dt}=\frac{d(mv)}{dt}$, $t$ is time, $m$ is mass, $v$ is velocity, $p=mv$ is momentum, and $\frac{d}{dt}$ is not a fraction but the derivative function. You will learn about taking derivatives in a calculus course.
A: You take classes, and hopefully the people teaching those classes explain what the symbols they're using mean. Alternately, you read textbooks, and hopefully the people writing those textbooks explain what the symbols they're using mean. In this particular case, taking a physics class and a calculus class (alternatively, reading a physics textbook and a calculus textbook) would tell you what all of the relevant symbols mean. 
(In particular, in this case $d$ is not (quite) a function and the bar does not (quite) denote division. This is not something you can just figure out.) 
I don't understand how you're supposed to know what symbols mean without asking anyone. Do you expect that you can learn what Chinese characters mean without asking anyone (not even a dictionary)? Did you learn what English characters meant without asking anyone? 
A: Some letters or symbols have a standard meaning. Sometimes, the writer of the formula chooses letters so that the letter is the first letter of the definition of the letter.
Examples of formulas and their common meanings:
x - used in simple equations. Also used as a left/right coordinate in a graph.
y - used in simple equations as a second variable. Also used as a up/down coordinate in a graph.
z - used in equations for 3 dimensional calculations. How close something is to you.
A - used for area formulas. Also for number of amps.
H - Height. Used in geometry.
M - Angle of a line in geometry.
B - Offset of a basic line equation in geomoetry. Y = MX + B
a b c - used to solve quadratic equations with the quadratic formula.
t - used to denote time.
d - used for distance or diameter.
r - used for radius.
p q - used for RSA public key cryptography calculations.
Σ - used as a sum for calculus.
Δ - Delta used for difference. Also rate of change in calculus.
θ - Theta used for angle calculations in trigonometry.
Π - Pi = 3.14159
μ - 1/1,000,000. Prefix used in electronics.
F - Number of Farads in a capacitor.
V - Number of Volts
W - Number of Watts
Ω - Electrical resistance

Examples in Business Calculus:
C - Cost
P - Profit
R - Revenue
D - Demand
dx - Derivitave of X. X is usually an input.
dt - Derivative of T (Time)
dy - Derivative of Y (Dependent variable)

Theory of Relativity/Newtonian Mechanics:
E = Energy
M = Mass of an object
C = Speed of light
G = Gravitational constant of the universe
D = Distance between two objects
V = Velocity
S = Speed
