You may have come across “e,” Euler’s number, in math if you’ve learned about half-life, exponential functions, or compound interest. But where does this irrational number come from? Why is it important? 

First, if you graph the expression (1+ 1/x)^x, there will be a point where the curve flattens out, called an asymptote: 

The value on the y-axis where the curve flattens is about 2.718, or “e.” 

Those who have come across e^x in algebra might realize that the slope of an e^x graph at any point is also e^x, as is the area under its curve! 

Despite being named after Leonhard Euler, two others are also credited for the discovery of this extraordinary number: John Napier and Jacob Bernoulli. 

Napier was on the hunt for a shortcut to solving exponential math, and he ended up using the number “e” in his list of logarithms (operations used to solve exponentials) without “discovering” the number. 

Bernoulli was studying financial problems related to compound interest (when money exponentially increases every so often). He found that his sequences were approaching the number 2.718… consistently. This actually comes from the equation we graphed earlier, as compound interest follows a very similar format and therefore has the same asymptote as (1+1/x)^x. 

Then, finally, in 1731, Euler proved “e” was irrational and gave it its name! 

You may have heard the equation e^(iπ) + 1 = 0. This is another fundamental use of Euler’s number, as it can connect the imaginary world (i) and the real world! 

All in all, Euler’s number is phenomenal and likely the most important constant in nature, as it deals with growth and decay. It’s impossible to study math and not run into Euler’s number, be it in finance, probability, derivative/integrals, or logarithms.