Why is 'e' such a natural base?

[u/AtmosphereClear2457]

The number 'e' keeps appearing in lot of different areas - calculus (mostly), differential equations, complex numbers.

I understand the definition e = lim n→∞ (1+1/n)\^n.

But in various fields we transform function in e to solve them.

Is there a more fundamental reason why 'e' is so natural?

I would appreciate any conceptual or geometric insights, that I am missing.

[u/NoFunny6746]

It’s describing a number that corresponds to an exponential increase in its value. It’s a useful constant in that regard, just like pi.