# Irrational Exuberance

Tomorrow is Pi Day, and a very special one writes I.I.I. chief actuary Jim Lynch.

For one second the date and time will represent pi’s first 10 digits (3/14/15 9:26:53), a moment both trivial and mnemonic.

Pi is an important number in insurance, as any actuary who has reflected on the matter will tell you.

Actuaries grapple with the mathematical discipline known as statistics, the heart of which is the normal distribution. The normal distribution is famous for its bell-curve shape, but relevant on March 14 is that the number pi appears in the formula for the normal distribution:

If I may be a bit hyperbolic, the mathematical foundation of insurance balances upon the number pi.

Pi is famously irrational, its digital expression neither ending nor repeating, but it is not the only irrational number in the normal equation. There’s the square root of 2 (1.414213562 . . .). There’s also the number e (2.71828 . . .), which you might remember if you studied logarithms in precalculus, but probably not.

So irrational numbers play an important role in insurance as elsewhere. Some, like pi, help us understand the world better. Others, like the irrationally small percentage of homeowners who purchase flood insurance, are less honorable, and the I.I.I. notes them in this infographic.