e is transcendental

In this video, I give a very clever (albeit non-intuitive) proof that e is transcendental, that is that e cannot be a zero of a polynomial with rational coefficients. This proof is originally due to Hurwitz, and involves nothing more than elementary calculus. Enjoy! Also it’s my 31st birthday today!!! Go prime numbers!

[@drpeyam]

Thank you for the birthday wishes, you made a sweet day even sweeter ❤️

[@blackpenredpen]

You are in your prime now!!

[@mcfloh55]

Even a Mersenne prime. And as binary number five ones in a row: IIIII. That's really a big thing. :-D

[@PuzzleQodec]

And a huge prime, too, much bigger than 13!

[@renzalightning6008]

Happy Birthday Dr Payem!! your age is now the missing number in the sequence!! 1, 2, 4, 8, 16, __, (special sequence) All the best!!

[@bernardz2002]

That 3blue1brown reference? :D

[@renzalightning6008]

If it is, happy coincidence XD

[@plaustrarius]

Happy Birthday Dr. Peyam!!! Thank you for the upload, amazingly easy to follow! Enjoy your prime birthday! 29, 31, 37, and 41 are some of my favorites! 41 is my favorite "prime generator" under the polynomial p(n) = n^2 + n + k where you let k = 41, you get a string of primes from p(0) all the way to p(39), and then p(40) = 41^2!

[@chdfnh]

Happy birthday, Dr. Peyam. I think that all of us appreciate the time, work, and passion that you put in these videos. Thank you so much!

[@mihaiciorobitca5287]

U are 31 ys old ,31 is 11th prime nr,11 is 5th prime nr ,5 is 3th prime nr ,3 is 2nd prime nr and 2 is also prime ;))) U born in 1987 ,300 th prime nr and don't forget ! "e is transcendental !"

[@drpeyam]

Mihai Ciorobitca That is amazing, I’m gonna steal this from you 😄

[@mihaiciorobitca5287]

Dr. Peyam's Show all right !

[@nouretaoufik]

just waw

[@mcfloh55]

Herzlichen Glückwunsch und alles Gute zum Geburtstag. :-)))

[@duncanw9901]

Love these long format videos! Can't wait till after I take Lin. Alg. to rewatch those you did. Also, it's weird how I always get math tutoring ads on yours, flammy's, and BPRP's videos. Like lmao I'm watching a 50 minute video on proving a number to be non-algebraic and I need a tutor for algebra 1. NJ google :).

[@redvel5042]

Amazing proof! Also amazingly accessible! And of course, happy birthday, Payem.

[@leonardromano1491]

Happy Birthday, Doctor Peyam! I am not the person that has requested this video a year ago, but I have waited for this video my entire life! Thank you for making these amazing videos!

[@dgrandlapinblanc]

Merci Dr Peyam's ! Belle démonstration que je vais revoir encore et bon anniversaire ! À bientôt !

[@cleverking2003]

A great video on a birthday of a great man! Happy birthday, Dr Peyam!

[@alejandrogarridogouro388]

Happy birthday!! Dr. Peyman. You are a good mathematician. Thank you so much for your videos. You are the best.

[@GRosa]

Herzlichen Glückwunsch zum Geburtstag! / Tavalodetoon mobarak! 🎉

[@gadxxxx]

Whatever that means, I think I agree.

[@Albkiller22]

Happy birthday dr peyam and a lot more year's of teaching!!!

[@tyultim99]

Happy birthday Dr. Peyam!!! Really great video, and thanks so much for always posting excellent math videos!!!

[@MrBoubource]

You are actually making a present on your birthday

[@finweman]

You've made 30 other birthday specials? Impressive! Thanks for all the cool stuff.

[@timurpryadilin8830]

Wow, very impressing! Happy birthday, Dr Peyam !

[@faith3174]

happy 31st birthday! i hope you have an amazing day :)

[@maxweinstein1537]

Wow. It's amazing how e's properties are only really used in the beginning. Happy Birthday, יום הולדת שמח, and all that jazz.

[@drpeyam]

Amazing, isn’t it? I was surprised as well!

[@jaybihola606]

Happy Birthday Dr. Peyam! Love your videos!

[@masterbuilder271]

Happy Birthday! Thanks for all the great videos :)

[@maximilianmueller4707]

Happy birthday for the best math teacher

[@nouretaoufik]

looking for another great video in ur next prime birthay

[@dw2843]

Happy birthday! Thanks for these great videos.

[@abstractcafe2352]

Happy birthday Dr. Peyam!

[@ImPresSiveXD]

Thank you so much and happy birthday! :D

[@mcmage5250]

Omgee my second fave math yt has a birthday and is turning prime number qwq fascinating

[@8dolev]

Happy birthday! Watched till the end - *Respect!*

[@oliverdixon4660]

At 10:33, shouldn't 0 < \theta_N < N, instead of 0 < \theta_N < 1?

[@danielfisher587]

At 50:31, do you need to invoke a triangle in equality to say the absolute value of the linear combination of the C's and epsilons is less than 1 follows from the absolute value of any epsilon being as small as you like? And happy birthday! At least _you_ can still count to your age on one hand.

[@sujothc2052]

Belated birthday wishes

[@harryhan31]

5 minutes before I'm a day late but Happy birthday Professor!! Thanks for being awesome :)

[@drpeyam]

Awwww, thanks so much!!!! 🙂🙂🙂

[@gadxxxx]

Happy birthday Doc. May I book a consultation please?

[@stevethecatcouch6532]

Happy birthday. The first 31 are the hardest.

[@vanilla3M]

I subscribe your channel because of this awesome video.

[@drpeyam]

Thank you!!! 🙂

[@PackSciences]

Joyeux anniversaire!

[@MrRyanroberson1]

What I wonder: x+x' = y+y', and other such functions, where x≠y. Are there any solutions? As I typed this I've tried exponential, probably disproves polynomial, and sinusoidals... None seem to work, every adjustment contradicts itself.

[@MrRyanroberson1]

Thinking back on it, I'm almost certain that if there are no solutions, then that implies that f(x)=x+x' is inversable, but that sounds like saying x(x+1) is inversable to a unique solution... Maybe not?

[@tezeralorisso4823]

I have a question, if p divides a and b but doesn't divide c So can we say that p can not divide a+b+c ?

[@drpeyam]

Yes of course, do it by contradiction and use c = a+b+c-a-b and you would find that p divides c

[@valatko]

Happy birthday

[@fountainovaphilosopher8112]

Well happy birthday!

[@shanmugasundaram9688]

This is Hermite's original proof.I do understand a contradiction arise in the equality of an integer to a fraction.In whatway does it tell our initial assumption that 'e' is algebraic is wrong.The final part of the proof is to be elobarated.

[@harikishan5690]

happy birthday Dr Peyam

[@drpeyam]

Thank you!!! And see you on Monday 😄

[@harikishan5690]

can't wait!

[@SmileyHuN]

Happy birthday sir!

[@adamcummings20]

Happy birthday

[@bandamkaromi]

Great. And happy birthday.

[@Absilicon]

Sorry I was late, happy birthday!

[@h4c_18]

Your birthday is 2 days after mine? Happy 31st birthday, Dr. (426880*sqrt(10005)/13591409)M ;). Our ages are a prime number xD.

[@elijahbelov209]

Is 42:00 a reference to blackpenredpen's Bell Curve video?

[@elijahbelov209]

Also happy birthday! Best wishes!

[@drpeyam]

Probably not, I recorded that video a couple of weeks ago :)

[@drpeyam]

And thank youuu!!!

[@wietse8987]

Happy bday man :))

[@japotillor]

Многая лета!

[@ЮрійЯрош-г8ь]

Happy birthday, sorry that I am a day late.

[@Zonnymaka]

Happy (belated) P-day!

[@drpeyam]

Thank you!!!

[@jonathangrey6354]

2:21 and the Chen lu

[@JPK314]

Thanks! You missed an edit you meant to make around 42 minutes

[@yuvalpaz3752]

FINALLY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! my god it took time :)

[@drpeyam]

Yuval Paz HAHAHA, I was wondering where your comment was 😂 For some reason YT thought it was spam

[@yuvalpaz3752]

Oh, good thing that you notices. Now days I don't watch all of your videos because of my condition(I need to be more focused on most of them) but seeing this one I knew I had to watch it. When I will get better I will also watch everything I missed ;)

[@funkycude57]

PEEEEEYYYYYYAAAAAAMMMMM

[@mauricepanero]

That was definitely non intuitive! Lost me big time.(

[@finweman]

You've made 30 other birthday specials? Impressive! Thanks for all the cool stuff.

[@eleazaralmazan4089]

Happy Birthday Dr. Peyam!

[@ManiFunctor]

Happy birthday Dr.Peyam!