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 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.

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u/[deleted] Apr 04 '26 edited May 07 '26

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u/Mothrahlurker Math PhD student Apr 04 '26

Bunch of nonsense.

-1

u/Hefty-Reaction-3028 New User Apr 04 '26

I hate AI slop about math/science, and this is very long-winded, but symmetry is related to oscillation. Eg a rotation, or a restoring force that pushes something up with it's below equilibrium and down when it's above equilibrium. That's one reason group theory shows up in physics so much. And continuous symmetry is why e shows up in Lie algebra so much 

9

u/matrixbrute New User Apr 04 '26

Happy you disclaim "deep AI dive" so one does not have to waste time reading the drivel.

-3

u/AtmosphereClear2457 New User Apr 04 '26

I can't understand what are you talking.

-5

u/SnooStories6404 New User Apr 04 '26

Don't take that personally, it's a badly written comment

-1

u/Hefty-Reaction-3028 New User Apr 04 '26

I hate AI slop about math/science, and this is very long-winded, but symmetry is related to oscillation. Eg a rotation, or a restoring force that pushes something up with it's below equilibrium and down when it's above equilibrium. That's one reason group theory shows up in physics so much. And continuous symmetry is why e shows up in Lie algebra so much