e (Euler's Number) - Numberphile

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Dr James Grime discusses "e" - the famed Euler's Number.
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[@HalcyonSerenade]

"Don't put that in the video" _Puts that in the video_

[@anonyKinetic]

they had ONE job

[@LUBAProduktion]

absolute M A D L A D

[@Peter_1986]

+HalcyonSerenade Kinda reminds me of that scene in Monty Python And The Holy Grail, where King Arthur got annoyed by a scene and then ran in front of the camera and screamed "Cut that out! Cut that out!".

[@elemenopi9239]

r/madlads

[@aayushkashyap1365]

Savage

[@Albeit_Jordan]

Teacher: In what year did the defeat of the Spanish Armada occur? Me: Euler or Gauss.

[@hammerth1421]

e's decimal expansion is random, so the likelyhood of finding a four integer sequence in it that coincides with the year of the attack by the Spanish Armada is equal to 1.

[@chanderule605]

@@hammerth1421 WRONG There's no proof of e being a normal number So, unless you prove that or find the year itself, you can't say that

[@hammerth1421]

@@chanderule605 Even though e is not a normal number, it's digits are still random. While you can't find any sequence of any length in it, you are pretty much guaranteed to find every four digit sequence, also the year of the Spanish Armada.

[@chanderule605]

@@hammerth1421 There's no proof of that other than "it's kinda likely" And I dont think it's proven to be random either

[@AnHebrewChild]

HammerTh its digits are not random. Now I'll have to wait and see if you reply with what I expect you'll reply with.

[@Gunbudder]

Math is just all about who can pronounce Euler the most correct

[@someonespadre]

The football team at one of my hometown high schools was the “Oilers.”

[@skillybiskuit12]

I have a tattoo of Euler’s identity and just now found out it’s pronounced “Oy-ler”

[@zyronebiglang-awa6871]

the edmonton hockey team is called the oilers (don't even ask me about hockey alr)

[@PMT17]

Germans: You dare challenge us mortals

[@ninjafish3755]

@@PMT17 fax

[@cyclingcycles7953]

I can't believe Euler predicted the meme.

[@terrariaman8454]

no he didn't

[@randomstuff6821]

@@terrariaman8454 wooosh

[@tipstyx1867]

Terraria Man r/woooosh

[@DormitionOrDominion]

@@tipstyx1867 r/ihavereddit

[@theshuman100]

You fool. The man made the oldest shitpost

[@Desiqnify]

e

[@Iscannon]

No one cares

[@Desiqnify]

Sari Masu yea haha I look in subscriptions and was uploaded 3 second ago :D

[@max19970]

e

[@Hepad_]

2.718281828459045235360287471352662497757247093699959574966967627724076630353 547594571382178525166427427466391932003059921817413596629043572900334295260 595630738132328627943490763233829880753195251019011573834187930702154089149 934884167509244761460668082264800168477411853742345442437107539077744992069 551702761838606261331384583000752044933826560297606737113200709328709127443 747047230696977209310141692836819025515108657463772111252389784425056953696 770785449969967946864454905987931636889230098793127736178215424999229576351 482208269895193668033182528869398496465105820939239829488793320362509443117 301238197068416140397019837679320683282376464804295311802328782509819455815 301756717361332069811250996181881593041690351598888519345807273866738589422 879228499892086805825749279610484198444363463244968487560233624827041978623 209002160990235304369941849146314093431738143640546253152096183690888707016 768396424378140592714563549061303107208510383750510115747704171898610687396 965521267154688957035035402123407849819334321068170121005627880235193033224 745015853904730419957777093503660416997329725088687696640355570716226844716 256079882651787134195124665201030592123667719432527867539855894489697096409 754591856956380236370162112047742722836489613422516445078182442352948636372 141740238893441247963574370263755294448337998016125492278509257782562092622 648326277933386566481627725164019105900491644998289315056604725802778631864 155195653244258698294695930801915298721172556347546396447910145904090586298 496791287406870504895858671747985466775757320568128845920541334053922000113 786300945560688166740016984205580403363795376452030402432256613527836951177 883863874439662532249850654995886234281899707733276171783928034946501434558 897071942586398772754710962953741521115136835062752602326484728703920764310 059584116612054529703023647254929666938115137322753645098889031360205724817 658511806303644281231496550704751025446501172721155519486685080036853228183 152196003735625279449515828418829478761085263981395599006737648292244375287 184624578036192981971399147564488262603903381441823262515097482798777996437 308997038886778227138360577297882412561190717663946507063304527954661855096 666185664709711344474016070462621568071748187784437143698821855967095910259 686200235371858874856965220005031173439207321139080329363447972735595527734 907178379342163701205005451326383544000186323991490705479778056697853358048 966906295119432473099587655236812859041383241160722602998330535370876138939 639177957454016137223618789365260538155841587186925538606164779834025435128 439612946035291332594279490433729908573158029095863138268329147711639633709 240031689458636060645845925126994655724839186564209752685082307544254599376 917041977780085362730941710163434907696423722294352366125572508814779223151 974778060569672538017180776360346245927877846585065605078084421152969752189 087401966090665180351650179250461950136658543663271254963990854914420001457 476081930221206602433009641270489439039717719518069908699860663658323227870 937650226014929101151717763594460202324930028040186772391028809786660565118 326004368850881715723866984224220102495055188169480322100251542649463981287 367765892768816359831247788652014117411091360116499507662907794364600585194 199856016264790761532103872755712699251827568798930276176114616254935649590 379804583818232336861201624373656984670378585330527583333793990752166069238 053369887956513728559388349989470741618155012539706464817194670834819721448 889879067650379590366967249499254527903372963616265897603949857674139735944 102374432970935547798262961459144293645142861715858733974679189757121195618 738578364475844842355558105002561149239151889309946342841393608038309166281 881150371528496705974162562823609216807515017772538740256425347087908913729 172282861151591568372524163077225440633787593105982676094420326192428531701 878177296023541306067213604600038966109364709514141718577701418060644363681 546444005331608778314317444081194942297559931401188868331483280270655383300 469329011574414756313999722170380461709289457909627166226074071874997535921 275608441473782330327033016823719364800217328573493594756433412994302485023 573221459784328264142168487872167336701061509424345698440187331281010794512 722373788612605816566805371439612788873252737389039289050686532413806279602 593038772769778379286840932536588073398845721874602100531148335132385004782 716937621800490479559795929059165547050577751430817511269898518840871856402 603530558373783242292418562564425502267215598027401261797192804713960068916 382866527700975276706977703643926022437284184088325184877047263844037953016 690546593746161932384036389313136432713768884102681121989127522305625675625 470172508634976536728860596675274086862740791285657699631378975303466061666 980421826772456053066077389962421834085988207186468262321508028828635974683 965435885668550377313129658797581050121491620765676995065971534476347032085 321560367482860837865680307306265763346977429563464371670939719306087696349 532884683361303882943104080029687386911706666614680001512114344225602387447 432525076938707777519329994213727721125884360871583483562696166198057252661 220679754062106208064988291845439530152998209250300549825704339055357016865 312052649561485724925738620691740369521353373253166634546658859728665945113 644137033139367211856955395210845840724432383558606310680696492485123263269 951460359603729725319836842336390463213671011619282171115028280160448805880

[@DNXTMaster]

Liwo Jima you forgot a couple digits

[@edu2076]

December 31st 2019, 3:52 AM GMT 2.718.281 (e million) views :)

[@aakaasha6123]

Wow

[@WindowsXP_YT]

What about e^e?

[@HenryTheTodd]

Today on February 71st,1828, 1:82 e'clock

[@tanojiro]

01/01/2020 15:45pm.

[@Galgani333]

@@HenryTheTodd hahahahahah

[@AcmeRacing]

My Business Calculus professor at the University of Southern Maine was a big Euler fan. All of the classrooms Mainville used had a bit of graffiti; the Euler number, its square and its cube (all written out to five or six places) were written above the blackboard in magic marker. Since we used natural logs in the class, it was like an authorized cheat sheet during exams.

[@trixylizard6970]

"Everybody knows this anyway. If you don't, now you do."

[@mshrm.]

not knowing the values of it to a few decimal points is crazy anyway😭 or just using a calculator but i presume it was a non calculator paper

[@YTSunnys]

Main Theme - e

[@2cflame]

Main Theme - e

[@fooglesplays4560]

Main Theme - e

[@benjaminan1183]

YTSunny Main Theme - e

[@infernocop1009]

Main Theme - e

[@Dre-ip8np]

Main Theme - e

[@Zahlenteufel1]

1:29 Said no-one ever...

[@GameNOWRoom]

xD

[@NickBLeaveIt]

Zahlenteufel1 I mean, maybe in sarcasm...

[@TheYvesL]

That was hillarious, I'm dying lol

[@alvarogoogle]

Republican$ and Democrat$ in Congress say that all-the-time...

[@unreal-the-ethan]

No, _everyone_ said this... in a sarcastic manner.

[@user-AADZ]

Wow SiIvagunner

[@RadeonVega64]

yea

[@MrDaraghkinch]

Pride x humility = "I would not have called it g, I would have hoped that someone else would have called it g and I would have accepted that."

[@ganges6661]

Please don't ever stop making maths videos. I truly appreciate your explanation (history and reasoning). Love your work and truly admire what you are doing.

[@arthurthekyogre9155]

If they stop making math videos they would stop making videos, the channel is numberphile

[@granvillebarraclough8846]

BA in Maths I presume.

[@slowpoke8641]

eeeeeeeeeeeeeeeeeeeeeeeeeeeeee

[@albertobernal2537]

@@granvillebarraclough8846 Why though? because at day 1 MA he'd be bound to be sick of it already or have moved on to another area of studies altogether? hehehe :D Sorry, I had to reply, even 2 years late :P I love the videos as well, gotta say.

[@rexlongfellow]

8:58 when they say Infinity War is the most ambitious crossover in history

[@WillsOW4]

What?

[@sticks9757]

I don't get it

[@goat6354]

Lol

[@78anurag]

@@sticks9757 e , π and i(√-1 if you don't know) are the most iconic constants (except i) in Math. So in this equation they powered e to the power of π multiplied by i and added them with 1 which is equal to 0 (bizzare actually. How e, π and i are really complex numbers in math somehow combine into making a simple number which is -1) So in summary all the iconic constants(except i) in 1 equation.

[@sticks9757]

@@78anurag That's literally not what I asked

[@10thdoctor15]

It is a beautiful equation. I had it on my birthday cake when I was 18.

[@XavierAzumangaDaioh]

this is E-silly that fun E haha High Qualit-E ripper siivagunner, cause of the E-vent

[@ColeMoir]

uh huh

[@Alexizhereee]

GHOST AND PALS FAN?! Rare find!!

[@XavierAzumangaDaioh]

yep@@Alexizhereee

[@Alexizhereee]

@@XavierAzumangaDaioh Eyyy bro whats ur fav ghost song lemmie guess distortionist. Frl frl.

[@XavierAzumangaDaioh]

yes, ong no cap fr fr no joke@@Alexizhereee

[@JS_SN_UQAU]

best title - 10/10

[@vladimirshitov2160]

2.7182818284/2.7182818284

[@Hennal_]

i r8 e/e

[@JarodJL]

e/π

[@kaptencgp]

A solid 5/7.

[@mattchandler2387]

If you graph x^y=y^x, you get two simultaneous graphs. One is x=y, and the other is some variation of y=1/x. They cross at the co-ordinate (e,e)

[@ur_mom_is_so_fat]

Nice

[@adamkotter6174]

I tried to eyeball what the y=1/x -like function might be, and the closest I can seem to get is y=((e-1)^2)/(x-1) + 1. It matches the asymptotic behavior of x^y = y^x and passes through (e,e), but it doesn't perfectly match. The true function has something to do with the fact that ln(x)/x has two different x values that give the same y value for any positive y less than about 0.368, but for the life of me I can't figure it out.

[@davidiv4915]

@@adamkotter6174similarly the graphs a^x and loga(x) intersect at coordinates (e,e) when a = e^1/e not really sure why that is but it’s neat.

[@ChordettesFan325]

@@adamkotter6174 that "about 0.368" number is actually 1/e. I don't know why though.

[@ChordettesFan325]

@@davidiv4915 it's pretty satisfying if you sub in x=e to both equations. a^x = (e^(1/e))^e = e^(e^e) = e^1 = e loga(x) = log(e^(1/e))(e) = e (because of the line above)

[@illinoisdarkskystarparty2812]

Thank you! There are lots of discussions of e on KZbin, but this is by far the most lucid I have seen. I learned calculus 55 years ago, never used it in real life (I became a soldier and later a lawyer) and am returning to re-learn it at my own pace. This video has been a tremendous help in my understanding of this important concept.

[@rajeshpandey2198]

Your story is interesting

[@justanotherguy469]

Is not it such a treat? It is analogous to discovering classical music later on in life, when you were once exposed to it as a child, but strayed from it to listen to contemporary music in the interim.

[@le_dr3677]

Euler was such a fit guy He worked everything out

[@MohaMMaDiN55]

I remembered when I first watched this video. It was like 2 years ago and I barely understand what’s going on. Now I watched it again after the previous 2 years and I found myself turned super focused. I understood everything Thanks for your explanation

[@ChiefVS]

I can relate... I was 13 when I watched it... Now I'm 16 and I understand this lol. This is what I study loool

[@MrInsideEye]

One might say you had continuous interest

[@kuj2887]

@@MrInsideEye Underrated comment.

[@mariomario-ih6mn]

You said the same thing on the Cardano's formula video

[@keithwilson6060]

I’ve recommended Numberphile to various young students having trouble with maths. It is an excellent motivator for cultivating an interest in maths.

[@martinshoosterman]

Whats this, A Numberphile video, about a real number!? I never thought id see the day.

[@thomassynths]

It also happens to be a complex number.

[@martinshoosterman]

Thomas Eding um, no it isnt.

[@thomassynths]

Complex numbers encompass the reals. It is complex with imaginary part = 0.

[@JustPingo]

Thomas Eding e is totally on the complex plane.

[@michaelbauers8800]

All real numbers are in the set of complex numbers. If that seems odd, just consider also that all integers are in the set of reals...etc.

[@subaduck]

I'm a complete mathematical moron, and yet I've always been fascinated by higher level maths. The idea of calculus, even geometry is just amazing. I've never in my life found anybody who could get me through a college level algebra course. I get close, but have never been able to finish it. I feel as though I've always sat outside the sun, watching other people achieve and understand this. I'm a sort of "Flowers For Algernon" guy. In any case, this is really interesting.

[@tsjoencinema]

Five minutes in to math and chill and he gives you this look 5:18

[@stezenast5878]

e^(i*pi) = -1 is very useful in electrical engineering phasor notation and complex impedance. It essentially allows equations that would need calculus to solve to be easily solved algebraically.

[@The_Aleph_Null]

The complete Euler formula tho for every angle, not just the Euler identity everyone knows

[@pentachronic]

You can thank Laplace and Fourier for that too!

[@poisonpotato1]

It’s also used in Controls engineering, and vibrations

[@Jeff_Lichtman]

Also useful in digital signal processing.

[@spyrex3988]

It's also used in computer science for writing various algorithms and making them efficient wrt complexity

[@clumsyjester459]

e^(i*pi)+1=0 not only brings together the most important constants, but also the basic arithmetic operations addition, multiplication and exponentiation.

[@Xerxes1337]

And is the most tatooed formula among maths nerds.

[@johndododoe1411]

Yet it works only because of some semi arbitrary definitions, such as the extension of powers of e along the imaginary axis.

[@PC_Simo]

@Clumsy Jester Exactly 👌🏻🎯😌.

[@Arkhs]

I've been trying to understand the relevance of this for days, but you made it so damn simple to understand. Truly the best channel for maths content.

[@Stargazer93]

I legitimately believe this will help when I try to do a college calculus class again. No one bothers to explain what’s going on with new material. When you understand why you use symbols and how, it makes it easier to solve things. Thank you.

[@vseve9397]

what is up with all these clickbait titles

[@nejx8711]

VSeve I know right, they didn't even put the thumbnail in the video. Fockin clickbaiters😂😂😂

[@ApplicationBot]

VSeve they need more arrows and circles

[@drew.k2385]

How is it clickbait? The video is about... e.

[@ApplicationBot]

Andrew anon its an ironic comment

[@nejx8711]

ApplicationBot Technically, since he obviously knew what he was talking about, it wasn't ironic, it was just a joke.

[@bitchassmoththing]

i love siivagunner

[@ErZi-uo7fm]

8:58 Biggest crossover in history.

[@HHHHHH-kj1dg]

Heckk yea

[@huggalove]

love your videos, also the happiness you obviously have from talking about the math! i enjoy numbers immeasurably, part of my job, and these videos are so pleasing!

[@natroful]

this content is timeless thanks for all the enthusiasm and clarity

[@aaronleperspicace1704]

"Euler, he works everything out!" Well does he work out?

[@ximalas]

He's having a break now. Stay tuned for the next iteration of the Universe.

[@adtoes]

Does he even lift bro

[@Raptorman0909]

He skipped everything but head day ... wait, that sounded kind of dirty!

[@johnbyron1077]

@@Raptorman0909 It did didn't it?

[@scratch7996]

@@Raptorman0909Calling it brain day would work

[@arazemijo9674]

This is my new favorite channel; it's so well-explained, interesting and fun even when dealing with complex topics, and yet somehow really adorable and nerdy at the same time.

[@utkarshsaini5650]

Watch ted ed

[@johnbiluke8406]

It isn't nerdy.

[@jawadulkabir9120]

I think this is the first numberphile video I ever watched and I come back to rewatch it every once in a while. I just love it.

[@maskedmarvyl4774]

I would never have understood this concept if it wasn't for this video.

[@ChickenSuitGuy]

smooth e

[@PoopTVYTP]

309 likes and still no answers

[@sergiofls7623]

e

[@venkateshbabu5623]

Nice mix.

[@clippygoat]

And here we are, the letter e used to be a running jokes on siIva’s rips and now a lord farquaad meme. So siIva is now a normie meme?

[@iblesstherains]

*TASTE E*

[@owenlewis6546]

Lord Farquad wants to know your location.

[@AlphahawkA25]

Owen Lewis you mean Lord MARKquad

[@Yudhiprasada]

Markiplier wants to know your location.

[@lordfarquadfn9736]

uhh...

[@sadkat4499]

Lord Farquad *E*

[@OG_CK2018]

I can switch this between 2k likes and 2.1k likes imao

[@OwenDLC]

This is perhaps one of my favorite videos of all time. Thank you.

[@eqral]

This video just made me extremely excited about math. For the first time, i actually enjoyed learning this.

[@vicr123]

What a lovely title. Captures the essence of this video quite well. Fully encapsulates and proves the quote by the "not-so-well-known-outside-his-circles" Victor Tran, "A letter says an entire video!" :)

[@badmanjones179]

clik bait title

[@bigsmoke4357]

badman jones how tf is 'e' clickbait?

[@mb_2174]

Prediator X makes ya curious. "what the heck? its just an e?? gotta look at this" not enough to classify as clickbait though!

[@vicr123]

Merlin Brennt But this is a mathematical channel. As soon as I saw the title, I knew that they were going to do something with Euler's constant. :) But I suppose the logarithmic graph and James Grime on the thumbnail helped too :)

[@mb_2174]

Victor Tran oh you must be very smart!

[@picknikbasket]

Crikey Bluey, there was a flamin' Ozzie 10c piece in there!

[@numberphile]

+picknikbasket ;)

[@Creeestopher]

A U.S. dime, as well :)

[@sana-ow6vq]

?H$lllllaaA

[@jacksonstarky8288]

As this video approaches pi million views, it occurs to me that I would love for Numberphile to revisit Euler's other number -- gamma -- from a mathematician's perspective. I enjoyed Tony's video on the subject, but I would be very interested to learn more about the mathematical underpinnings of gamma, including its connection to the Gamma and zeta functions, and given that James has discussed Riemann before, he seems to be the logical choice for such a video. I've been waiting for 3Blue1Brown to do something on gamma tying in with their videos on Riemann and the prime number spirals too. Maybe because we know so little about it, but I find gamma to be a far more interesting number than either pi or e... which are still the second and third most interesting numbers, with the golden ratio coming in at #4.

[@Dr.S.MohammadM.Kashani]

I truly enjoyed the video with the passion and brilliant approach of explanation from James Grime! Thanks a lot!

[@antivanti]

e^iτ=1

[@ianhoward1518]

So much prettier

[@antivanti]

Yes. Much cleaner.

[@TheofilosMouratidis]

he wrote e^(i*Tau)=1

[@Neme112]

And if he misses zero in the formula, then: e^iτ=1+0

[@gogl0l386]

No he is correct. It is from Euler's formula which states that: e^ix= cos(x)+i*sin(x), where i^2=-1. If you plug in pi then the sin terms becomes zero and the cos term becomes -1 thus giving us the famous expression e^ipi=-1. But if you plug in tau (that is 2 times pi) then it's the same as pluging in 0 which means the sin term becomes zero and the cos term becomes 1, thus giving us the equally correct expression e^itau=1

[@dooki51]

Happy e day! (2/7/18)

[@agnomilted5206]

What about 27 January?

[@Dude-cf8hb]

Woowowowowowowowowowowowowowowowowowoeowowowow

[@kiremitt]

I late. Waiting for 27/18/28

[@darkfrei2]

The next is 2718-2-8

[@ameeraallee539]

Oh my gosh... there can only be one e day a century🤤

[@patrick.1943]

2:07 'β, it's β!'

[@imveryangryitsnotbutter]

Real ones remember when this video was just titled 'e'.

[@devincory9695]

We're gonna talk about... EEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEE EEEEE EEEEE EEEEEEEEEEE EEEEEEEEEEE EEEEE EEEEE EEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEE

[@okokokx2934]

EEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEE EEEEEE EEEEEE EEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEE EEEEEE EEEEEE EEEEEEEEEEEEEEE EEEEEEEEEEEEEEE

[@seangrand3885]

. eeeeeee eeeeeeeeeee eeee eeeee eeeeeeeeeeeeeee eeee eeee eeee eeeee eeee eeeeeeeee

[@domjanabi6006]

E and e is not the same

[@seangrand3885]

domjanabi yeah, one is capital, the other is lowercase

[@blue9139]

EEEEEEEEEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEEEEEEEEE EEEEE EEEEE EEEEE EEEEE EEEEEEEEEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEEEEEEEEE EEEEE EEEEE EEEEE EEEEE EEEEEEEEEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEEEEEEEEE EEEEE EEEEE EEEEE EEEEE EEEEEEEEEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEEEEEEEEE EEEEE EEEEE EEEEE EEERE EEEEEEEEEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEEEEEEEEE VVV VVV VVV VVV VVV VVV VVV VVVVVV

[@jtveg]

The KZbin video with the shortest title?

[@ThatWarioGiant]

John Thimakis no vsauce holds that title with no title

[@all_time_Jelly_Fish]

John Thimakis yet it doesn't terminate

[@vyuni9220]

there's a vsauce3 video with an infinity symbol as the title... so no, not quite

[@shamilk4158]

e

[@clynaelle]

John Thimakis Vsauce also has a video with no title, its about nothingness

[@Triadii]

I love how everything comes together, especially in the end..

[@MsAmour2009]

Lovely lecture! thanks a lot for explaining it so well!

[@OriginalPiMan]

y = 0 gradient is 0, area under the graph is 0

[@muellernikolai8630]

lol that's actually true xD

[@danielglen410]

says person with a pony icon

[@gaouchos35]

Yeah but that function is boring and useless :(

[@Terminator5618]

Is this for e^x? Or all functions? Both don't work because n^x=0 is undefined except for n=0, and there are plenty of functions where the gradient at y=0 is not 0? or am I misinterpreting the idea? Haha

[@Terminator5618]

OriginalPiMan Nevermind, just got it. "f(x)->0". Mind you, this is kinda cheating seeing as the x value has no effect on the gradient anyway ;)

[@pablogriswold421]

Does saying "Don't put this in the video" ever work?

[@badmanjones179]

we will never know because there can never be recorded evidence, because that would mean putting it in the video

[@pablogriswold421]

badman jones Perhaps memoirs would recollect how a courteous editor obeyed the request?

[@revansithari2060]

Pablo Griswold you could put it in a separate video and thus you wouldn't be putting it in the video the person's telling you not to put it in

[@cykikvisage]

Why don't you ask Schrodinger?

[@badmanjones179]

Revan Sith'ari ahah imagine like a whole "dont put that in the video" compilation

[@grumpclips]

I can't listen to the intro without hearing the SiIvaGunner cover

[@simonbeasley989]

Great explanation. How have I never been taught this before, it took just 10 minutes and I totally get it.

[@aaronleperspicace1704]

"Wow thanks a lot, bank!" 😂😂😂🤭🤭

[@Flexy59]

1:29 "Wow, thanks a lot bank!" made me laugh more than it should have

[@genshinsbizzareadventures]

I knew i wasn't alone😂

[@alerdoballabani8322]

An absolute masterpiece, I have not seen a better explanation historical or logical before. Well done.

[@elektronz123]

3:51 let’s just take a moment to appreciate his hard work

[@nickjohnson8495]

e is such an interesting number. I came up with the strangest function that approached e as x approached infinity. y = 1/((x^(x+1)/(x+1)^x) - ((x-1)^x/x^(x-1) It’s pretty cool. ex: (56^57 / 57^56) - (55^56 / 56^55) Take a reciprocal of this number and be amazed

[@aishwaryajangir2909]

great job!

[@blue9139]

What about this Y^D=Y So tell me What numbers the letters are ok

[@tuckersmith7991]

e shows up in very interesting places. x^y=y^x is an unusual graph that shows 2 lines, one linear and one curved, intersecting at the point (e,e). the graph of x^x also contains some e-related information; the minimum value for f(x) is at x=e^-1, or decimal 0.3678... so the lowest point in the graph of x^x is (e^-1,(e^-1)^e^-1)) or (0.3678,0.6922). It all has to do with exponential and logarithmic growth.

[@madhavgaur5412]

Nice work bro, I like these types of persons

[@anonsensename5101]

Just use (1 + 1/x)^x like normal people... Ok it's a joke, don't get offended

[@superscienceshow]

The relation and usefulness of e, I, and trigonometry melted my mind.

[@sydneydwoskin4950]

I've just starting considering this number extensively because of calculus one. This is wondrous. Thank you for the video

[@theatheistpaladin]

7:20 my mind just exploded... exponentially.

[@corruptio]

f(x)=0 also has that property... but not as useful.

[@GuyfromtheWAN]

Jay Chan isn't the gradient of X=0 infinity?

[@seansmolinski]

f(x) = 0 is not synonymous with x=0, but y=0. At any point on the function, the output (y) is equal to 0, the slope is 0, and the area under the curve is 0.

[@alhassanelsayed5861]

the amount of passion and love for math makes the points go straight to ur heart and brain

[@Torthrodhel]

That's fascinating especially the bit where the area = the value = the gradient.

[@LRosieB]

Thank you so much for this, I’m learning logarithms right now, and I couldn’t understand what the natural logarithm was about and wanted to know. This helps a lot!

[@Zodiacman16]

Your thumbnail is mine now.

[@TheEssem]

Makoren Why does your pic look so familiar

[@chhavigupta2802]

Essem because it's the same pic as in Ur identity card.

[@roshankulkarni1772]

Fantastic explanation, building it from the foundations! Thank you.

[@unternerdsbyalexandraelisa7550]

Thanks for this enthusiastic explanation! :) I find the use of e very useful in complex analysis, where we can write e^(it) instead of cos(t) + i sin(t).

[@StephenAnimations]

Which of those expressions would be easier to evaluate? I suppose I could plug in some dummy values and figure out myself but im lazy. Personally I think the latter expression but I like how the first expression is more compact.

[@psychoh13]

"Don't put that in the video" *puts it in the video* typical!

[@looijmansje]

We can not know how many times they actually say that, and it is actually not in the video. So you can't say if it is really typical.

[@psychoh13]

Koen Looijmans ಠ_ಠ

[@Skeleton-bs7zy]

I gave you 200

[@moosewhisker8072]

e^x is not the only function to have the same area, value, and gradient. f(x)=0 also has that property.

[@DavidBooercheese]

MOOSEWHISKER so does 2 * e^x :O

[@Zolhungaj]

That's true of all functrions on the form f(x) = ke^x, where k is a constant. Your is a special case where k = 0

[@W.M.-]

Chrischo1997 finally someone who knows what there on about

[@ericdunn9001]

That's trivial

[@zuzusuperfly8363]

+marche45 Here's how I think about your comment. Zero could be considered a trivial multi-variable function, with a well-defined gradient. That gradient is zero. If you say, "0 does not have a gradient", doesn't that mean you're implicitly saying that 'having the value zero' is the same thing as 'not having a value'? Little bit pedantic, but that's the spirit of this thread anyway.

[@innovbrain]

Thank you sooooo much. Your explanation was excellent and now I almost fully understand the use of Euler's number. 😊

[@nikolthomas2544]

"Euler, he works everything out." Nice to know he didn't skip leg day

[@lawnmower69]

I mostly like how passionate and excited he is while talking about this math's stuff

[@joseluisdiaz9627]

Thank you! :) I love this video; the passion that you transmit talking about numbers is incredible.

[@mathssucker]

I grew up in sciences being inspire by this kind of Channel, learning more daily! Now I started mine to, thanks for the inspiration!!

[@RSLT]

Great Job! Well explained!!! Thanks for the excellent and cool explanations.

[@ShinySwalot]

Could you please make a video on all relations between e and pi? Because there are so many weird ones

[@ShinySwalot]

*****​ That's pretty neat! I'm a physics student btw

[@ShinySwalot]

And there's a reason for that too?

[@ShinySwalot]

A great mathematical reason of course ;) Might there also be a relation like pi^i*e perhaps?

[@ShinySwalot]

I wish I had such beautiful dreams... But e and pi are some weird numbers indeed. And the fact that they are related in so many ways is even stranger!

[@edhorsh2695]

e and pi broke up, pi was cheating on e with i, log saw them

[@fatinahmad6591]

شكرا جزيلا على هذا الشرح المبسط واشكر كل من قام بالترجمة ...اتمنى المزيد 🌺🌷

[@Ultimate2T22]

e is also used for log or Ln bases like e^ln(2) or log based e.

[@LawatheMEid]

The history of discovery those constants is amazing, thanks.

[@videopostrrr]

guys im just starting to expand my maths knowledge after an undergrad in politics and a post grad computer science (focussed on ontology) These videos are amazingly helpful for letting me continue to expand and combine my knowledge of disciplines, so big heartfelt thank you for posting such useful and accessible content.

[@OktatOnline]

I haven't been to a STEM university course (yet) but I think this video, plus 3Blue1Brown's video about e covers as much as a newbie to this topic could possibly want to know! Thanks for this great content

[@salacommander2674]

My biggest problem with math is that it drives me crazy to just plug numbers into formulas without knowing the significance of that number and why it needs to be in said formula. e has been driving me crazy for a while now and none of the explanations I'd gotten satisfied me until seeing this, so thank you.

[@gnomechild4459]

I really need to clean my monitor. It seemed especially Grimey during this video.

[@Pining_for_the_fjords]

He seemed high in this video, like he'd just done an e.

[@Ostebrix]

pi minus e is 0.42... meaning of life confirmed

[@liljefe3016]

StupidNedFlander that's what those '...' mean.

[@mrlabon123]

I wanted to like this comment but didn't because it has 42 likes.

[@norielsylvire4097]

Ostebrix s and so what, 0.42.. is log5?? no I dont know what is 0.42

[@heheheiamasupahstarchimera631]

StupidNedFlander It's called rounding

[@funkygecko]

two numbers being irrational doesnt guarantee that their sum will be irrational too. You may be correct in this specific case but your explanation isn't correct

[@wonderbucket1242]

Great video. This guys has a gift for teaching.

[@monikas4379]

Thanks You saved my life

[@william.darrigo]

I always understood e using limits in Calculus however this is a great, practical view that should be taught in class. Great video!

[@bauxsedai1495]

Now that is a proper title! 😊

[@ezioauditore7636]

I love this channel so much.

[@Udhaya.K]

Beautiful video! I now have a neat idea of what Euler's constant. Nearly at the end of the video, you mentioned that if we don't use Euler's constant we will have nasty ratios introduced into the equation, which will make it more complicated. Can you pl. show one such example? The lecture will be complete with that. And again, thanks a ton for this video!

[@Justin-tp1mx]

If you're taking the integral or derivative of an exponential function like 2^x, you would have to divide or multiply by the natural logarithm of 2. with e^x, ln(e) is one so dividing or multiplying by it doesn't need to be written.

[@xrisku]

this is why you pay your mortgage every 2 weeks, and make one extra payment a year, and a 30yr mtg = ~15 yrs. the interest kills you.

[@bluetiger2002]

xrisku yet with inflation that changes

[@R3lay0]

It's still calculated p.a.

[@JG-tt4sz]

Many banks simply hold the partial payment until the complete monthly payment is received.

[@carultch]

I don't think a bank gives you any credit for paying multiple times within the month.

[@lyuchang5665]

value = gradient = area.... OMG! I have used e for many years, first time noticing this amazing thing!! Thank you for the tutorial!

[@nathans8744]

Fantastic explanation, thank you so much

[@herculesmachado3008]

Congratulações. Excelent work: Dr. James Grime has the hability to be clear in teaching.

[@julioandresarriagarangel7183]

Such a beautiful and simple explanation, thank you!