We may be celebrating Pi Day here at io9, but we would be irrational to deny that there’s more to mathematical interestingness than simply dividing an object’s circumference by its diameter. Here are seven numbers we love as much as pi.

#### 1. 1

1 may be the loneliest number, but it’s the littlest number that could — the first non-zero integer that displays remarkable properties of self-reliance. Aside from being the first whole number, it is its own square, cube, and factorial. It’s also very stubborn; when you raise 1 to any power — even a number as high as a googolplex (1 followed by 10 to the 100th power, or 10^(10^100)) — you still get 1. It's the first and second number in the Fibonacci sequence. It is neither a composite number, nor a prime number (mathematicians rejected this idea because it complicates fundamental theorems of arithmetic). It is, however, a unit (like -1). And it’s the only positive number that’s divisible by exactly one positive number.

#### 2. *i*

Any number that doesn’t actually exist, but is still useful, has to be considered cool. Also called the **imaginary unit**, *i* is the square root of -1 (*i*2 = -1). This number cannot exist because no number multiplied by itself can equal a negative number.

At first, **imaginary numbers** were considered useless (an imaginary number is a number that, when squared, gives a negative result; e.g. *5i* = -25). But by the Enlightenment Era, thinkers began to demonstrate its value in math and geometry, including Leonhard Euler, Carl Gauss, and Caspar Wessel (who used it when working with complex planes). They’re useful in that they can be used to find the square root of a real negative number.

Today, *i* is used in signal processing, control theory, electromagnetism, fluid dynamics, quantum mechanics, cartography, and vibration analysis. The figure *j* is often substituted in these fields, which is used to represent the electric field current. The imaginary number also appears in several formulas, including the Euler Identity.

As an aside, Isaac Asimov’s short story “The Imaginary” (1942) featured the eccentric psychologist Tan Porus who explained the behavior of a mysterious species of squid by using imaginary numbers in the equations which describe its psychology.

#### 3. Graham's Number

Simply put, this is the largest useful (i.e. non-arbitrary) number known to mathematicians. But it’s an *astoundingly* large number. Named after Ronald Graham, it’s the upper bound to a certain question that involves Ramsey Theory (a branch of math that studies the conditions under which order must appear). Consequently, it’s the biggest number used for a serious mathematical proof.