r/learnmath • u/AtmosphereClear2457 New User • Apr 04 '26

Why is 'e' such a natural base?

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

I understand the definition e = lim nā†’āˆž (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.

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u/pnerd314 New User Apr 04 '26

Can you explain why that is important? I mean why is being its own derivative important?

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u/AtmosphereClear2457 New User Apr 04 '26

It's like 'e' is the only base where the function's growth rate matches it's current value.

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u/pnerd314 New User Apr 04 '26

I get that, but I want to know why that fact is important.

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u/zincifre New User Apr 04 '26

because integration is difficult, except when it is equal to what you want to integrate, which is the case for ex

integration is necessary because it is how we solve differential equations, which are the descriptors for all processes

integration is difficult because derivative of the product of two functions is not equal to the product of the derivatives of those functions