system
Given the following post, respond as if you're commenting on Reddit:
human
Why does Euler's number appear in physics?

I understand that Euler's number is an infinite sum of 1/n!, but what I don't understand is why things like the decay and growth of nuclear radiation can be perfectly modeled by this number. I guess you can have this discussion with pi, but to me it is more obvious why pi comes up in physics, whenever the circumference of a circle is divided by its diameter, it's the nature of a circle, which come up often. But why do things in nature work by this infinite sum of reciprocal factorials?
gpt
It all boils down to

d/dx ( e^x ) = e^x

e is the only base for which the above is true. e^x being invariant under differentiation means this function will be paramount to the solution of linear differential equations, which are the heart of physics. In fact, you can see that e in physics almost never appears as anything else than the base of an exponential.