What is the number "e" and where does it come from?

e (2.718281828...), also known as Euler's number, is a critically important number in mathematics. It forms the basis of the exponential function and the natural logarithm, and like π it crops up in innumerable places (even where you wouldn't expect it).

[@cheongth01]

No math teacher ever explained how the value of e is derived to me in all my years of schooling.... until now

[@Artistoh14]

69 likes...nice

[@quaffie]

school doesnt usually teach you that i learned it in a 'math for engineers' lecture

[@Lightwar49]

@@quaffie but to be fair you cant just throw of an transcendental number and expect to know what the hell it's supposed to mean

[@manwork6545]

Sorry but this is just an approximation of e only. Not e! This value doesn't exist unfortunately!

[@lovegarbage]

Probably because my maths teachers didn't know.

[@Iron-Bridge]

Society needs more teachers like this guy. Young, smart, relatable to youth and able to convey complex subjects in a simple way.

[@Avighna]

He's such a good teacher. I wish I had him as one of my teachers :(

[@stevekru6518]

Society in most of the US has decided teachers like him are needed only if they have an Education Degree (as opposed to a math or other STEM degree) and if he is a teachers union member.

[@thenuggywuggy8389]

I wish this was my math teacher, cause my math teacher makes us do these terrible projects focused on graphing, which we did for the entire year. Also she explains stuff in confusing ways and says we should have learned something we didn’t.

[@JitendraSingh-qd7jk]

and handsome too

[@DrakeRing]

Idk about the young part

[@natashalim3964]

Besides the accent, the way you know this is an Australian classroom is by how casually someone swears in front of the teacher

[@ryanshannon7703]

"HOLY SH!T!"

[@natashalim3964]

@Prashant Kumar it's not. try again.

[@roninnib6635]

@Prashant Kumar nope

[@Artistoh14]

timestamp?

[@marty7261]

@Prashant Kumar no he didn't

[@aplimsollpunk2738]

Still amazing 4 years later. Also, that class in the background sure is engaged. 4:36 "Shut up. Shut up." 4:31"Holy shit that was fun!" 7:57" Whooaa-

[@D1M1T]

2:30

[@tomdanub4231]

Lol

[@stachuvonokrutny7071]

😂😂😂😂😂

[@magmaplayz3745]

Great teacher stuck with fricks

[@olavigre8329]

Luigi at the end there😂

[@kevinkasp]

The single best way of explaining "e" by anyone, anywhere. And I believe this is how the number e was originally discovered. Truly excellent teaching. These students have no idea how genuinely lucky they are. Around the world literally a billion people have learned the number e and how to use it in calculus and other maths courses, and have been using it for years with still no clue how this mystical thing came about. These kids will have no fear of using it and will totally get it's significance and be able to teach it to anyone. Bravo Eddie Woo.

[@deanhuang6841]

I remember when I asked my Math TA why is the derivative of e^x still e^x? I was just asking for the answer, but she thought I was getting all philosophical so she spent 5 minutes explaining this concept hahaha. Now that I'm older and wiser, the simple explanation is what Eddie said: "The rate at which something grows/decays is proportional to itself". THAT'S why the derivative of e^x is itself...

[@yami_the_witch]

The way e was discovered is because of Calculus. Mathematicians wanted to find a function where it would be it's own derivative. So you have to solve the differential equation f(x) = f'(x), and out pops e if you do some complex mathematics. All of the rest are then discoveries afterwards.

[@spookynelly912]

@@yami_the_witch that is not at all how it was first discovered

[@zaczac3024]

Yes!

[@YuezhiTribe]

Exactly!

[@reetasingh1679]

This guy is just brilliant... I was speechless. He made maths so fun and interactive, something almost no teacher does. It's not all boring formulae and stuff, this guy actually involves the class and explains stuff extremely well. Hats off!

[@mdw159]

Mind blown..... I wonder my lectures 12 years ago like him.... :-)

[@danny1451]

Maybe our Aussie teachers need to take a leaf from his book, passion cost nothing!!

[@ayandamtolo8312]

actually teachers like these are really costly because they are rare and usually they are really qualified thus they find it easy to explaim

[@ankurrai8677]

NO OFFENCE INTENDED. Actually he is teaching in such a way so that even the weak minds(about +97℅ of the human population) which might be considered as good by those +97℅ people but the truth is that by this way mathematics (in the known sphere of humans) won't evolve and that's what is happening we have not told about any new discovery (in this field ) since 3 to 5 decades

[@ankurrai8677]

NO OFFENCE INTENDED. Actually he is teaching in such a way so that even the weak minds(about +97℅ of the human population) which might be considered as good by those +97℅ people but the truth is that by this way mathematics (in the known sphere of humans) won't evolve and that's what is happening we have not told about any new discovery (in this field ) since 3 to 5 decades

[@dejanaleksic904]

I love how he explained everything in only 8 minutes, my teacher was talking about this for 3 and a half hours, and nobody understood the formula, we all just memorized it... Congratulations!

[@arsive02]

Atleast your teacher had taught you about this unlike my teacher.

[@suly4346]

@@arsive02 at least you had a teacher.

[@MikaelS5]

atleast you have a life

[@azqswx90]

@@MikaelS5 at least you have a.. Oh damn it I think you won that battle

[@chunchunmaru]

yeah dude, it's so hard to memorize e^x

[@TheMrMonk11]

Dude, I'm a secondary teacher (in my second year now), you are literally my inspiration. You're now my reference point for how good a teacher I can be.

[@user-lc6jq1hi1r]

If you wanna be a good teacher; just take the following as a rule: Let the students interact with you & the subject in class, and let them witness how beautiful whatever subject you're teaching is. And afterall don't be too boring yourself, have a good sense of humor. Wish you luck with your fourth year!

[@Raysnature]

@@user-lc6jq1hi1r'll also say watch how he holds discipline in the class too. Not apparent in this video but in others he does have to call students to account and he is brilliant IMHO at that too.

[@user-lc6jq1hi1r]

@@Raysnature exactly, something ive also noticed lately

[@tristramgordon8252]

Just apply the maths you are teaching to a real world situation, job done. Everyone is interested.

[@keramidasnicolas2079]

Mark, you certainly are a good teacher, too, because you recognise and try to imitate a good teacher. Good luck.

[@Destruction320]

The students who are lucky enough to be taught by teachers like this one will find it easier to live in this world. Too bad there are very few teachers like him.

[@stevekru6518]

Yes, too bad, but in most of the US it is not coincidence. State licensure requirements, supported by unions, mandate college degrees in education. As a general rule, talented math students will not put up with simplistic education courses. As a well known writer explained, when visiting colleges he saw STEM majors working on problem sets, while the education majors were cutting letters using safety scissors on poster board.

[@veramae4098]

They go into better paying jobs, and where they don't have to deal with constant student harassment.

[@arnesaknussemm2427]

@@veramae4098 and constant pointless beaucracy

[@ahmedalhomaide4416]

That's why KZbin is here!😁

[@ge_song5]

people like this should be famous, they actually make a difference in our life.

[@virajnagpure]

Totally agreed. Meanwhile, other KZbinrs who call themselves influencers or "content creators" don't know the difference between content and garbage!

[@slayin1496]

​@@virajnagpure because those content creators provide entertainment which may not serve as much utility but increase happiness instead which is arguably just as important. An unhappy individual is generally less productive and their ability to learn and perform goes down. Not saying a youtuber is more important than this guy by any means, just that they're not innately useless, I don't know where i'd be without some of the "content creators" I watch. Big fan of Eddie wu though lol he was at my mum's uni graduation and filmed a miniseries at my school, his videos helped me through my HSC and definitely contributed to my grades

[@ProSquidGaming]

He is

[@aidanivesdavis]

Passionate teacher:) Well done! Way to engage the class.

[@NuisanceMan]

+Aidan Davis Cool teach, cool class.

[@JohnyAngelo]

+Aidan Davis Well, hes young.

[@johnthe3rd383]

Aidan Davis I was first

[@andrewcbuensalida]

Is there even a class? Or were the students' voices dubbed in to make you think he's teaching a class ;)

[@mrlordsaif5708]

@@andrewcbuensalida ok

[@musictest9999]

i could watch this guy teach maths all day

[@matiascabral1502]

Nataly RAW he's got a KZbin channel for a reason...

[@bonsaiplant6731]

what do you think I'm doing right now?

[@__skillz]

Math*

[@lordmomstealer]

Hi

[@lordmomstealer]

919 subscribeer without any vedio hats off to you

[@mturker100]

I had a teacher like this for my first Calculus course in high school. She was brilliant and engaging and taught us the reasons behind doing things... instead of just "do them because I say so". To this day she is the reason I enjoy mathematics and get excited about learning new facets of the science. I credit her with my SAT Math jumping over 100 points inside of a single semester. The right teacher is something you just can't put a price on. Bravo, man!

[@cdmcfall]

Learning the logic is critical. Kudos to your teacher.

[@alpineclimb4081]

Einstein's right when he said, "If you can't explain it simply, you don't understand it well enough". Some people cover how shallow their understanding is by throwing jargons in class.

[@othmanouahabi4250]

You notice how Einstein's is becoming Jesus exponentially?

[@tombirkland]

I love watching this teacher's lectures. And while I am not much of a mathematician, this was both crystal clear and mind blowing. So cool.

[@zeddash]

5:10 whoever said 365.25 - I like you

[@Ynoxxx]

+FinnShack Leapyear?

[@zeddash]

Ynox Yeah, average year length

[@ubererhs2898]

well 365.25 isnt exactly correct either. a year is about 365.2425 days

[@zeddash]

UbererSK Close enough for a quick answer;

[@MmMmMonsterkill1]

+Fin Koya 365.2422, that's what i memorized xD

[@chocolatechocochoco]

hey, who's your math teacher ? -It's Eddie yeah but Eddie who ? -yes ... anyways great teacher

[@arlo4639]

did you just...?

[@ledues3336]

chocolatechocochoco ahahah

[@swarnaprakash549]

chocolatechocochoco no, woo

[@CesarAHaro]

Mildly racist. Wildly funny!

[@user-bp9tp3fr6q]

Who?

[@Krystaltho]

I'm in my differential equations class and I never knew where e came from. I wish my teachers in high school taught me this.

[@MusicILike-cy4et]

Drake Aure Read the chapter on exponential functions in Spivak, Calculus. It gives a rigorous definition. Then read from a complex analysis that extends e to complex numbers and reveals a relationship between pi, e, the pure imaginary number i, 1, and 0.

[@jmiquelmb]

There are some videos on youtube that help you visualize and better understand Euler's identity [e^(pi*i)+1=0], if they are of your interest

[@JensenPlaysMC]

you were studying calculis before you were taught what e was?

[@alessandrosala5272]

Me too, I'm in 12th grade, we are doing limits and functions analysis and I ALWAYS wondered where that number came from, I asked my teacher but she couldn't explain. You can also find it in physics like in capacitors formulas etc, very very interesting and odd number

[@jasonchandler2754]

@@JensenPlaysMC He said he was using it in diff equations before he knew where it came from, not before he knew about it.

[@vgernyc]

Eddie: "It's a number that exists in reality just like Pi does." Student: Surprised Pikachu Face

[@manwork6545]

Unfortunately that's not true. I'm sorry but these numbers doesn't exist!

[@lovegarbage]

He said that because he doesn't really know either.

[@CircuitrinosOfficial]

@@manwork6545 Yes it does, it's how radioactive material decays.

[@scarmackd1498]

@@manwork6545 define what you mean by not existing. I can measure my weight, say, to the nearest 100th of a pound. However, my exact weight is an irrational number that's decimal places stretches on to infinity, just like pi or e. Does that mean that the exact value of my weight doesn't exist?

[@kotzenderkeks61]

@@scarmackd1498 yes

[@essp4922]

I remember learning that pesky limit as a formula and always wondering why it was e. This is eye-opening. I suppose this is what a mathematical epiphany feels like; it's an incredible feeling!!

[@Prashik_ft11]

4:36 Some guy: it's 2.2...... Girl:Shut up!!

[@GR0907]

😂😂😂

[@spyrex3988]

Nah dood i bet that's a Rachel

[@asknorway]

And they wonder why math isn't popular..

[@tylermerlin8320]

I almost shouted 225 at my phone. It's fun

[@Phantom_Kraken]

Every math class has “that student”

[@DukeLaCrosse20]

eMail is the growth of the number of mail messages I have after a year of spam.

[@zelalem9249]

lol

[@--_9623]

What do you mean

[@rngsus4002]

That doesn't even make sense

[@VishalKhemnar360]

yes, if you keep replying to them...

[@aarifarafi4712]

Lol

[@alfonshomac]

"you and your feeble units of measurement!"

[@saimnaqvi7169]

Physicists feel attacked

[@POW710]

👌

[@keramidasnicolas2079]

@@saimnaqvi7169 They are.

[@keramidasnicolas2079]

Such a line !

[@anushkasaha8858]

😂

[@CosmopolitanXMan]

Great explanation. Just want to add that the key principle here is *compound interests* and letting _the interests generated earlier to produce higher results_ , e.g. generate interest after one semester rather than one year, generate monthly instead of semesterly, etc. This allows the principal itself to grow as the base for the next interest calculation. E.g. after 1 semester 50% (0.5) interest generates a result of (principal 1 + interest 50%) and then this result combined immediately generates a new interest; "the clock starts ticking" immediately the next day after one semester, no need to wait until one year (read: increasing the value of n). This compound interests on smaller timeframes (increased n) are resulting in dynamic base values, therefore the growth becomes *exponential: the growth is given on previous growth* .

[@nitinraj5372]

He teaches his student the most basic thing which are never taught in a school and school make student an intelligent donkey..... Huge respect for him

[@1BrknHrtdRomeo]

I'm not completely hating on my high school experience...but Goddammit, I wouldn't have been such a math delinquent if I had someone like you for a teacher! Your teaching method is utterly brilliant and engaging. All teachers should be like this.

[@matiascabral1502]

JayGatzVFXsk8r pay close attention, this method is extremely dependant on the students' intrinsic motivation rather than only the teacher... if done right, the results are far greater than the regular methods though.

[@tldoesntlikebread]

True in that it not only depends on the teacher but the students. My education system is like it begins to turn people into worker drones so the curiosity that could arise in maths classes barely exists. I wish I had passionate teachers

[@areejimranahmed7042]

I already teacher like him

[@faithlesshound5621]

@@matiascabral1502 You're right, this method might not work at 3 pm on a Friday afternoon.

[@matiascabral1502]

@@faithlesshound5621 Indeed, once the subject loses priority status, that's it.

[@HanSolo-dh4rn]

This guy is actually a really great teacher, actually shows some enthusiasm in his work.

[@McVidsAndTutorials]

he seems very enthusiastic. He is an awesome teacher.

[@avi12]

This is why KZbin is an amazing platform - allows teachers like this one to teach in such a fun and engaging way

[@aleefbilal6211]

I just don't have words. Beautifully explained. I just watched 8 mint video and didn't even got bored, that how amazingly it is taught. May ALLAH bless him and me with this type of teaching method. Ameen.

[@jalwerdt85]

This lecture was absolutely engaging. You have an amazing talent. Thank you!

[@CarlosEduardo-xv3vi]

Sir Eddie Woo, you're just a amazing teacher. I'm brazilian and the professors here don't even get close to your foot. I just want to thank you for the amazing classes or part of it that you upload here on KZbin, I really enjoy them. Keep the excelent work you do, your students are so lucky. I hope someday I can watch one of your classes! Sorry about my English, I'm a little bit rusty.

[@vinayseth1114]

Wow- the best explanation I've come across- wish you were there to teach me in school! :D. Thanks a ton ! :)

[@lidarman2]

Eddie, I have a graduate degree in physics but I still enjoy your videos because you have an insight I have never experienced in all my years of education and experience.

[@joshuamichaelrico7365]

“Bro what did I miss out while I was gone?” “Yeah we started a new unit, and…” “And? What.” “It’s complicated”

[@timothysantama4102]

A fun yet intelligent teacher always brings any sort of materials into comfort to embrace the students' thought

[@letoiiatreides2466]

You are an excellent teacher!

[@davidkuitunen6684]

This guy needs to start working for khanacademy.org Thumbs up if you agree.

[@irockrock44]

I vote for Khalid as well from betterexplained.com

[@collin9143]

I think khan academy should be working for Eddie instead

[@veretxnerd983]

Lol ok

[@timothykimari8154]

@@collin9143 true

[@johncanes5686]

@@zeidkazi3402 you misunderstood. He's not forcing eddie. He's just suggesting he should work for Khan academy because he would greatly benefit everyone's education

[@al3ksejkramaric]

at the end someone's mind was blown "woooaaah" ^^

[@kleps6463]

Lol that was most hilarious part of the video for me as well.

[@crookeddesk]

Had to scroll too far down to find this lmao

[@hans_____]

waAaAaA

[@gordonwalter4293]

Eddie's enthusiasm is great but his examples are crisp and clear to a degree that makes him truly a fantastic University physics teacher.

[@panchitomontero9051]

There's something about this math instructor that makes complex number concepts easy to understand. I'm getting back to learning all that I didn't in the past. Kudos to the instructor!

[@KaranPatel-nu7fp]

I am Engineering Graduate . and All i can say is , I wanted you badly while those mathematics classes that i had during my childhood !! Still , It's never too late. Starting my Education once again ! Thanks a lot .

[@andyxaero5396]

you sir are an amazing teacher ! .... respect

[@NothingMaster]

Great Teacher!He gave them the best intuitive answer possible.

[@franciskm4144]

Excellent, I taught 40 years, now I realised how easy it is to prove the value of e

[@alfonsomiraglies6093]

This teacher is AMAZING. Love him

[@neetishraj]

Everyday I am having my eureka moments just because I watch your videos, and I am a computer science graduate with good background in mathematics. I studied all my life to pass the exams, I feel so terrible right now. I ended up being a well trained student and not well educated. Looks to me like I ll be going back to my books and I will read them with fresh perspective with a free and broad mind and asking why this why that at every point. Thank You Mr. Eddie Woo, I am so glad you got selected in worlds top 10 best teachers for 2018

[@kiyokhanna5896]

u iit?

[@Greg-iu6ys]

How my life, school reality, and my feelings towards math would be different if i met more people like yourself during my educational path. What you doing is just amazing.

[@reazrahman1850]

Unfortunately this guys video will only get few hundred thousands views, while perhaps it's most amazing, useful and beautiful video ever for ones knowledge.

[@patrickpettyjr.2487]

While stupid bullshit gets millions of views...

[@marktr2731]

As of right now, it is about "e" million, so.....exponential growth my friend

[@cinedeconfinamiento6148]

I quit math when I was 14 due to a bad teacher and chose a branch of studies that didn’t include math because of that. One of the greatest regrets of my life. I so wish I had a teacher anywhere near Eddie. Superb didactics! His pupils have a treasure in him

[@UbiMortus]

I can't believe I am 39 and watching this, getting entertained AND getting more educated at the same time. Kudos.

[@BPsen1]

I really enjoy this kind of videos. I do love maths because, back in the years, I had a teacher who gave me this passion. If all the teachers could be like Eddie , I think students wouldn't see maths as a boring thing anymore

[@kieran.stafford]

Brilliant Eddie. You are a born communicator.

[@brendonbarratt7551]

That was so brilliant. Building up the concept from simple beginnings.

[@akshitahuja5279]

My father is a great mathematics teacher but He is on another level. Just love to listen the concepts and still feel like a kid after even completing the graduation. Love from India

[@ericgelders]

Inspirational, authentic and unfazed in the face of funny remarks - brilliant teacher!

[@TitoSilversax]

I didn't want this video to end...

[@semiawesomatic6064]

"You and your feeble units of measure" new favorite qoute.

[@sagetarus1]

Him: "How about every minute" Me: **breaks out in a song about love**

[@JohnMushitu]

I finally understand what Euler was going for. Thank you

[@jatinbhatia4954]

Hello! I love your teaching style! I am an Engineering Post Graduate, I don't watch your videos to learn the concept but to witness the sheer brilliance of how you deliver the concept and i am always left wondering how much effort goes in preparing for each lecture. keep up the good work sir.

[@lolaplolap1]

By using formula, A= P(1+r)^n If P=1. // $1 in the bank A=(1+r)^n Bank calculates by minutes in a year. r= 1/the time period so r=1/(365x24x60) n=time period. so, A=(1+(1/(365x24x60))^(365x24x60) = e^1 = 2.71828

[@lolaplolap1]

It's something. *jumps up meme

[@jbel7510]

1:10 "the larger a population gets, the faster it can grow" - watching this amidst 2020 coronavirus pandemic 😂

[@glennkim1020]

"you and your feeble units of measurement!"

[@vanshbharadwaj9829]

@@antonpap5540 Shut you mortal, you and your feeble units of measurement does matter

[@quaffie]

watching this in the first world amidst feminism

[@soerika2964]

watching "things decay when they decay in relation to their own size"

[@joemarshall4226]

The larger a lie is, the faster it will grow.

[@dolphin8773]

4:31 "holy shit" :D

[@theeligator8728]

i can not thank you enough, but really you are the best teacher. Mostly teachers here are trying to prove students that they are dumb but look at this awesome teacher who proves e instead of downgrading his students thank you man thank you again...

[@packtech]

Why exactly didn't I have a Maths Teacher like this when I was in School. This guy is an inspiration, a BORN Teacher. You can feel the Passion he has and it is infectious. I would have gone to his Classes on my Death Bed no problem.

[@captainvice69]

I wish you were my maths teacher.

[@youtubegoogle4163]

Please please please explain the 'e' in complex numbers. I just want the easy proof of e^(ix) = cos(x) + i sin(x)

[@ezzaddin9351]

very easy proof

[@youtubegoogle4163]

@@ezzaddin9351 Please provide the link to the proof video. It would be a great help !

[@ezzaddin9351]

@@youtubegoogle4163 I was joking, Im pretty sure there is no "easy" real proof for this that doesn't involve bunch of infinite series and calculus. But if you are okay with that here are a couple videos proving it kzbin.info/www/bejne/rWGXlZuraLGChaM , kzbin.info/www/bejne/kKm8gHitgpuKmM0 , kzbin.info/www/bejne/hGS7qZ1qrbOdf9E , Good luck with your mathematical endeavors!

[@youtubegoogle4163]

@@ezzaddin9351 The third video gave me a really really easy proof ! kzbin.info/www/bejne/hGS7qZ1qrbOdf9E A Great thanks to you bro ! I don't know why, but It is really hard to find things like this on KZbin. It required me around 3 years to get to some great Engineering KZbin Channels.

[@ToadSmasher]

This is the kind of man i want to be when i’m an adult.

[@JohnVanderbeck]

I always appreciate when someone explains where these numbers come from, unlike when I was a stupid where they just told you numbers and told you to memorize them. Like it didn't matter what it was or where it came from just memorize it!

[@fiercegamer7732]

I didnt have much intrest in math but now I watch his video and go to school and ask those questions to my teachers, at one point they were frustrated at my instant growth in asking of so much questions but its sometimes fun flexing your knowledge on your fellas. Thanks for giving me the knowledge now maths is my A+ grade subject!

[@seyamrahman1002]

Title: what is the number ‘e’ Me: I thought ‘e’ was a letter

[@goununo]

Thanks!!!! You made me smile at math e little more.

[@thethakuri]

e = lim n -> INF (1 + 1/n)^n

[@Herosmurf]

+thethakuri that inf should be a sup as it's increasing

[@vaughanbbrean71]

Just found e on my calculator and wondered why it has the value 2.718......... You explained beautifully and I am inspired to recap what I once new and move on EXCELLENT thanks!!!

[@arctown]

He solves problems which I was never bothered in my life.

[@Volvoman90]

6:46 - That infinity symbol was glorious.

[@anthonysilva5312]

This is my second favourite lesson.... with Newton’s law of cooling being my first. Too bad many non-math administration would dismiss this as “too lecture-like”.

[@chandramouliraula6263]

I wish you were my math teacher in school.

[@ishqdekhadakwasla3200]

I am from India and very happy to see the method of teaching . I really change the opinion about not mathematics is tough

[@nosir1479]

These videos will be a life saver for A Level Further Maths. He deserves some sort of award

[@RyanJensenEE]

I want to be as good a lecturer as this guy. It is going to take some practice to get there.

[@hereonly2comment]

I laughed way too hard when he said “this is interesting” because it is literally interest-ing

[@MarekDz60]

Exactly. Interesting but not correct :) :)

[@imveryaverageatpayday58q9]

whoever made the subtitles had a stroke, cuz they are nowhere close to what he says at certain parts of the video

[@rajnirani7772]

Sir you are amazing. No one ever explained to me the real meaning of e ever. I wish to be in ur class one day.

[@mikeriesco6174]

I'm 60, an engineer, learned about e decades ago. But never REALLY learned it, like this. Mind completely, totally blown.

[@markostepic8584]

4:30 holy shit XD Just like Captain America would say: Language! :P

[@nenokhan2041]

See that in 4:41 someone said shut up two times after that person said holy shit! XD!!!!!!!!!!

[@seventynine9885]

4:37, *Some one coughs* Me: Why are you not worried?

[@chrisc.4144]

It simply blows my mind that mathematics and nature are basically two sides of the same coin. It’s freaky.

[@MappingFreak]

Maths was created to explain nature

[@AK47_414]

Maths was created from nature

[@dcamron46]

You can tell these young kids are super under appreciative and inexperienced to know how valuable this guy’s instruction is. It’s really funny and makes the video even more enjoyable 😂

[@jimmoriarty6964]

Not only did I learn the concept of exponential growth, I also learned how parasitic banks are. Kudos

[@dozog]

This may appear very clear now, until they realise that banks do not effectively give you 'e' dollars at the end of the year if your savings account has an interest rate of 100%. They still give you 2 dollars.

[@Healthwannabe7556]

Nobody: Subtitles: what distinguishes the E cigarettes even it's as fast is that this is going to get ever faster... 1:39

[@riendXkolya]

This one is even better --> 4:49 "It's not bad sex with 10% plus right for Rita here"

[@MrMohneesh]

after so many years now I know what e is!!

[@DanyaJeyJey]

I still don't get it =(

[@frederickong1391]

Love the lesson. Correction: banks do not actually pay continuously compounding interest. It accrues daily, but does not compound within an interest period.

[@carultch]

They calculate the compounding daily. They apply it to your total balance every month. The end result is as if they compounded the interest daily. You just don't have the balance available accounting for the compounding until the next calendar month begins.

[@frederickong1391]

@@carultch I spent 13 years in interest rate derivatives, and all the interest rate instruments I dealt with did not COMPOUND interest on a daily basis. Typically, interest amounts were calculated as: Notional * interest rate * Day Count Fraction. The only time you'd go with daily compounding would be with overnight instruments (e.g. OIS) - were you referring to these? Continuous compounding is even more RARELY used in practice, even if John Hull suggests otherwise.

[@Domab.]

I thought this was such a good and clear explanation that I was able to show it to a young friend of mine, (below 10 years old) and they understood your explanation

[@snuffeldjuret]

Hm, I was expecting pre-euler stuff when talking about where e comes from :).

[@andrewsebayjf]

Spectacular Speech, Bravo sir, Bravo.

[@BubbaYoga]

Superb presentation. *WooTube

[@vincentschmitt392]

solve the differential equation f'=f and f(0)=1. Answer is x mapto exp(x). And we let exp(1) = e. From this one gets everything and in particular exp(x+y) = exp(x)*exp(y), a group morphism that reveals fundamental for stats, Fourier/Laplace theory, etc...

[@sneharajpoot8377]

Thank you sir for this explaining. Your teaching techniques are so good that I'm addicted to your videos. Wish I can meet you one day.