Which mathematical constant is the limit of (1 + 1/n)^n?

e, about 2.71828, and the limit is literally a banking question. Jacob Bernoulli asked in 1683 what happens to compound interest as you compound more often - annually doubles your money at 100 per cent, monthly does slightly better, daily better still - and found the improvement converges rather than running away. It converges on e.

Its defining property is that the function e to the x is its own derivative: the rate of change equals the current value. Anything whose growth or decay is proportional to how much there is - populations, radioactive decay, a cooling cup of coffee, charge draining from a capacitor - is therefore described by e, which is why it appears in fields with no obvious connection to each other.

It is irrational and transcendental, meaning it is not the solution to any polynomial with whole-number coefficients - proved by Hermite in 1873, and much harder to establish than irrationality. Euler gave it the letter, probably not for his own name, and also produced the identity linking e, i, pi, 1 and 0 in a single line, which regularly wins polls for the most beautiful equation in mathematics.