Formulas are hard to read because you cannot say the symbols out loud

A formula is usually hard to read not because you do not know the subject. It is because you cannot say the symbols out loud.

Skim a row of unfamiliar symbols with your eyes and it just goes past you. But once you can say it — "add everything from zero to infinity" — you can see how the formula is built.

So I learned how to say them before what they mean.

The fifteen I learned first

I did not try to learn fifty at once. These fifteen keep showing up while reading the rest.

Symbol	Say it as	What it means
α	alpha	A value used as a cut-off
β	beta	A value, or the chance of missing something
λ	lambda	A value for how often something happens
μ	mu	The average of everything
σ	sigma	How spread out everything is from the average
σ²	sigma squared	That spread, squared
θ	theta	A value we do not know yet
Γ	capital gamma	The gamma function
f(x)	f of x	The shape of how likely each value is
F(x)	capital F of x	The chance of getting that value or less
E(X)	the expectation of X	The average
Var(X)	the variance of X	How spread out it is
Σ	sigma	Add them all up
∫	integral	Add them all up, for values with no gaps
∞	infinity	A value that grows without end

Three that kept confusing me

σ and Σ — the same name, completely different meanings.

• small σ is how spread out things are
• big Σ means add them all up

You cannot tell them apart by sound, so you tell them apart by size.

Γ and γ — the big one is the gamma function; the small one is a value used in the gamma distribution.

X and x — this one took me longest.

• big X is something whose value is not decided yet
• small x is the value that X actually turned out to be

The difference between capital and small carries the difference between "possibility" and "result."

The squiggle means "is distributed"

X ~ N(μ, σ²) is read like this — "X is distributed normal, with average mu and spread sigma squared."

A formula I actually read out

M_X(t) = ∫₀^∞ e^(tx) · λe^(−λx) dx

Said out loud — "M sub X of t is the integral from zero to infinity of e to the t x times lambda e to the minus lambda x, d x."

Simplified, it becomes this.

M_X(t) = λ / (λ − t),    for t < λ

"M sub X of t is lambda over lambda minus t, for t less than lambda."

Once I could read it, the reason for the condition t < λ came first. Adding things up must not run off to infinity — and that follows the moment you say the symbols.