A proof that e is irrational - Numberphile

Professor Ed Copeland shows a proof by Joseph "Voldemort" Fourier that e is irrational.
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Ed Copeland is a physics professor at the University of Nottingham.

NUMBERPHILE

Videos by Brady Haran

[OldQueer]

Proof by contradiction always feels like ending a story with "and then they woke up and it was all a dream"

[duff]

"R has to be positive because it's just a sum of positive terms."

Now that's rich coming from you lol

[paaaaaaaaq]

More professors and teachers should be like Ed. When you don't really know something at the moment just say "I don't really know".

[omgitsliamg]

"e is approximately 3"

Smells like ENGINEER in here

[pleaseenteraname]

"e^x is the only function that differentiated it gets back to itself"
Zero function: _angry analytical noises_

[jasonpatterson]

Why e is useful: When you are solving differential equations (which wind up describing an awful lot of things when you look carefully) you get lots of situations where a rate of change is related to the value of a thing. (ex: The rate of bunny births/deaths is related to how many bunnies there are.) When you find a solution, or even an approximation, for these sorts of things, e pops up all over the place. Compound interest, radioactive decay, population modeling, temperature change over time - all involve e.

[ruchirkadam]

This feels like an oldschool numberphile video :0

[zacharydenboer]

Love that it was pretty close to completely rigorous and had minimal hand waving

[arasmith]

"e" who shall not be named...

[Vodboi]

14:28 "We know that R has to be positive, because its a sum of positive terms". The irony of this being said by the same guy who did the "1+2+3+4+... = -1/12" video.

[lambdaprog]

The smiliest astrophysicist in the planet is back!

[Philoreason]

Camera man: Why is it important?
Mathematician: Wrong question!

[cariboubearmalachy]

All mathematicians shoukd write "ta-dah!" At the end of their proofs instead of QED.

[forthrightgambitia]

3:26 I am surprised he didn't say the obvious reason: that property lets us solve a whole bunch of differential equations that model physical and non-physical dynamics.

[enderwiggins]

Btw if anyone’s curious about how he got that series expansion e^x = 1 + x + 1/2x^2 + 1/3! x^3 ..., a really easy way to verify that this makes sense is to use the property that e^x = d/dx e^x. If you take a derivative of each of the terms in the infinite series, they all kind of “shuffle” down. 1 -> 0 so it disappears, x -> 1, 1/2x^2 -> x, etc!

(One of the reasons I think this expansion is so neat is it’s another visual way to see why e^(i pi) + 1 = 0

[aSpyIntheHaus]

Prof Ed's voice is just so calming. I'm pretty sure I transcended into some dimension of e just listening to this video.

[tetsi]

3:14 Brady is a brilliant interviewer. I love how he's able to ask "normal human" questions and how those are the ones that experts trip over and make them think. I bet Brady could have asked all kinds of very in depth detail questions about some obscure technicality and Prof Copeland would have had a quick answer but a simple "Why is that useful?" is not a thing that he has thought about :-D

[jellymop]

Man I love Ed. It’s a pleasant surprise every time he shows up

[lotoa]

"Why is that useful?"

To me it is very useful when solving differential equations, a lot of the methods for solving them involve e in some way. Since differential equations describe a lot things in nature, e becomes a really important function.

[ygalel]

4:53 The moment you understand the choice of thumbnail