e is golden.

[@MyEpitt]

I'm always amazed when somebody discovers something this obscure. Why would anybody ever think to look for this?

[@MasterChakra7]

It's the same old answer for Maths and Physics : cocaine

[@donach9]

​@@MasterChakra7amphetamine, I reckon

[@plislegalineu3005]

@@donach9 Walter Weiss, the competitor of Leonard Euler

[@logician1234]

What a crossover

[@BikeArea]

How far fetched can an identity be? Michael: Yes.

[@looney1023]

I love e. My favorite is this stochastic definition: Let X_i ~ Uniform(0,1) for integers i. If N = min { n | X_1+X_2+...+X_n > 1 }, then E[N] = e. In words, if you repeatedly draw uniform random numbers between 0 and 1 and keep a running total of the sum, then on average, it will take e draws for the sum to exceed 1.

[@Rócherz]

Unrelated, but the video made me realize this: If Φ = (1+√5)/2> 1 is the positive root of x² -x -1 = 0, then Φ² = Φ +1, so that 1 = Φ² -Φ = Φ(Φ-1), but then, 1 = 1/Φ(Φ-1) = 1/Φ² × 1/(1-1/Φ). Since Φ > 1, we have 0 < 1/Φ < 1, thus *1 = 1/Φ² +1/Φ³ +1/Φ⁴ +1/Φ⁵ +1/Φ⁶ +…*

[@cycklist]

I love the magical tapping on the board.

[@johntse5770]

U reli LOVE using Dominated Convergence Theorem to switch the order of summation and integration in proving summation identities. u've already shot a video on when Feynman's trick doesn't work. When will u shoot a video when this Theorem doesn't work? 🤩🤩

[@gm-123-0]

10:04 is this wizardry?

[@ilyafoskin]

Michael is the math teacher at Hogwarts

[@donach9]

I love the magic knock

[@DanielGomes-sw2fd]

8:30 The terms are all positive so you can always exchange the two summations.

[@wesleydeng71]

Interesting. You could plug in other values than 1/ψ. For example, for x=1/2 one gets e^0.5 = replacing ψ with 2 in RHS.

[@ingobojak5666]

Thanks for that! Indeed, for any 0

[@sunritpal1037]

What the hell is up with that amazing thumbnail 😳

[@mikecaetano]

Sweet! Decomposition of unity meets up with friends...

[@goodplacetostop2973]

16:50

[@debussy_69]

Haven't checked out Michael in a while, glad you're still here

[@aarong2374]

Didn't realize R. Schneider is in the band "the Apples in Stereo!"

[@CM63_France]

Hi, I suppose you mean : "our favorit identity involving e", but also some way : "defining" e . So mine is : lim_{n->infty} (1 + 1/n)^n . But if you mean only "involving", my prefered indentity is e^ix = cos x + i sin x .

[@2manypeople1]

There is a yt-video titled "Unveiling Connections between Mathematical Constants: The Conservative Matrix Field". That would be a nice topic in this context.

[@Anonymous-zp4hb]

Damn, that's beautiful.

[@minwithoutintroduction]

رائع جدا كالعادة. الطريق شاقة و الوصول ممتع

[@d-nize]

Why should numbertheoretical functions like these two (especially my(n)) combined with an geometric (classic sense, ratio of certain lengths) defined number be in any relation to a trancendental number? This is mathemaGics. :D Would be nice to see following scenario. Use this expression as a Definition for exp(1). Extend the definition to exp(x) for real x and assuming exp(ix) = cos(x)+isin(x) find similar expressions for sin(x) and cos(x).

[@hcgreier6037]

Woouh! That's hard to grasp, but very nice!🤣

[@ceebongo]

What. In. The. Actual. Phi.

[@wenkoibital4779]

e is everywhere /\ e is golden ---> means : gold is everywhere.😀

[@Alan-zf2tt]

Amazing - it has a poetic beauty all of its own. And I suppose it emphasizes: all of math is really a human construct or does it? 🙂

[@abdoshaat3304]

This topic under what branch in mathematics

[@synaestheziac]

Almost e hundred thousand subs!

[@gp-ht7ug]

Very interesting identity! I am a simple man and my favorite identity is Euler’s identity e=cosθ+isinθ

[@lucid_]

Thats e^(iθ) but yeah i see your point

[@ruffifuffler8711]

? Something about pincers and prongs ?

[@ahmedgg8867]

Nice

[@charleyhoward4594]

too abstract ....

[@mariochavez3834]

Indeed m8 But you can't deny the coolness of this identity

[@michaelgolub2019]

It seems that there was a mistyping in #\delta$ definition: $\mu e0$ is to be replaced by $\mu e1$.