# Why do mathematicians use single-letter variables?

I have much more experience programming than I do with advanced mathematics, so perhaps this is just a comfort thing with me, but I often get frustrated when I try to follow mathematical notation. Specifically, I get frustrated trying to keep track of what each variable signifies.

As a programmer, this would be completely unacceptable no matter how many comments you added explaining it:

float A(float P, float r, float n, float t) {
return P * pow(1 + r / n, n * t);
}


Yet a mathematician would have no problem with this:

$$A=P (1+rn)ntA = P\ \left(1+\dfrac{r}{n}\right)^{nt}$$

where
$$AA$$ = final amount
$$PP$$ = principal amount (initial investment)
$$rr$$ = annual nominal interest rate (as a decimal)
$$nn$$ = number of times the interest is compounded per year
$$tt$$ = number of years

So why don’t I ever see the following?

$$final_amount=principal(1+interest_rateperiods_per_yr)periods_per_yr⋅years\text{final_amount} = \text{principal}\; \left(1+\dfrac{\text{interest_rate}}{\text{periods_per_yr}}\right)^{\text{periods_per_yr}\cdot\text{years}}$$

As an example, when we choose to talk about the matrix $(a_{ij})$ instead of the matrix $(\mathrm{TransitionProbability}_{ij})$, this expresses the important fact that once we have formulated our problem in terms of matrices, it is perfectly safe to forget where the problem came from originally — in fact, remembering what the matrix “really” describes might only be unnecessary psychological baggage that prevents us from applying all linear-algebraic tools at our disposal.