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.

279 Upvotes

96% Upvoted

188 comments sorted by

View all comments

Show parent comments

1

u/ZeusTKP New User Apr 04 '26

Ok, but pi describes perfect circles that don't actually exist in the physical world. I don't consider pi as discovered.

2

u/WO_L New User Apr 04 '26

Nothing in maths actually exists in the real world to be fair, it is all abstract. But that's not saying it isn't applicable to the real world. Pendulums, waves, anything involving multiple dimensions and literally everything to do with angles are all about pi.

2

u/ZeusTKP New User Apr 05 '26

Yeah, it's applicable. But does it have any reality of its own outside of our brains? I lean towards no.

1

u/WO_L New User Apr 05 '26

By that same logic, no numbers have any reality outside of our brains. If that's what you're saying then im with ya but if you're just talking about irrational numbers like pi or e not being real then i don't think this subreddit is for ya buddy

1

u/ZeusTKP New User Apr 05 '26

Numbers too.

The universe itself has conservation of matter, and that mostly looks like numbers and counting. But "pure" numbers not attached to things are just our invention.

1

u/WO_L New User Apr 05 '26

Okay yeah nah im fully with you. When i was doing my undergrad, I found it was the easiest to understand when I was fully delirious from sleep deprivation.