Where does “e” come from?

I’m Ali Alqaraghuli, a postdoctoral fellow working on terahertz space communication.

I make videos to train and inspire the next generation of engineers. If you want to help me, share this video with a friend who might be interested in engineering.

The opinions in this video are my own and do not represent NASA or any other organization.

[kasratabrizi]

I remember in high school when i asked the math teacher where this e came from he looked at me as if I asked a stupid question and just said: "this is a constant and you shouldn't be focussed on that to much. Just now that it is there so we can use it for whatever concept we want to explain". It is amazing how many teachers crush the curiosity of a student and how many students end up not reaching their full potential because of the educational system. It is sad. Anyways, I am very happy that you explained this in simple terms and I finally understand this now.

[ishani-]

I'm a high school senior and I've liked the idea of being an engineer for quite some time but this last year has been very difficult personally.
Then, a couple days ago I came across a few of your videos and my passion for engineering was reignited.
No kidding. You literally came as a godsend.
The knowledge you share and the way you share it is amazing! Thank you so so much for what you do!! ❤

[robharwood]

I love how you tied the *motivation* for finding e into this 'mystery' of having derivative/slope of 2^x being less than 2^x, whereas deriv/slope of 3^x is bigger than 3^x -- and then *drawing* this on the board. Very intuitive that there should be someplace in between where the deriv/slope is equal to the original curve.

[Delan]

Great video Dr. Ali . Can you do Euler’s formulas next time . Thank you

[davido]

You've been one of the most underrated youtubers for engineering students for a long time. I am glad this video format is working well for you

[arclight]

The reason most people hate maths is because these concepts and the reasons behind them are not as intuitive as other subjects like physics as chemistry. Any subject can be enjoyed when you have a good grasp of what you're studying and why it's happening. Only if maths was taught the way this man teaches, students would love maths. Thank you.

[jh_esports]

We got Ilkay Gündogan explaining math in a Real Madrid jersey before GTA6

[exo-]

isaac from kenya, i likes your intuition Ali on every topic it's refreshing to hear you talk on the most neglected yet essential things to understand in engineering, much love here

[BAKERSTSIR]

At first, I wondered what was too hard for my teachers that made them not explain this to us, but then I realised that it's not because it's simple; you're just a good teacher who can build the way to reach the point.
Thank you.

[macebio]

I do love the way you manage to explain things. Only those who really understand things can explain them so clearly.
Chapeu

[MrBartuzi]

Those explanation videos are amazing. You truly have a gift when it comes to teaching.

[Dharma_kuppala]

“Wow, this is the most unique and clear explanation of exponential numbers I’ve ever seen on YouTube! You made it so easy to understand. Please make more videos like this—your teaching style is amazing!”❤

[mohsinshawkat]

الاستاذ علي القرغولي: شكرا للمرة الثانية. هذه واحدة من المفاهيم العويصة في الرياضيات التي نجحتم في توضيحها وتقديمها بشكل رائع. اللوغاريتم الطبيعي مفهوم عظيم وضروري ان يكون واضحا لكل مهندس ورياضي وفيزياوي. السلاسة والوضوح من صفات الطريقة التي تقدم بها. تحياتي وتقديري.

[ingiford]

Actually, I like the geometric version of showing where logs comes.

There is a set of curves that have a fairly unique property: Area under the curve from a to b is the same as the area under the curve from c * a to b / c; where a, b, c are positive reals. This set of curves are y=k/x for some positive k.

If you take k to be 1 (a natural number to pick) and the area going from 1 to e; the area is exactly 1

[promerops]

This is quite the clearest and the best explanation of e that I have come across in all my 75 years. Thank you!

[Gruuvin]

YES! FOURIER TRANSFORM IS A GREAT NEXT VIDEO!
I just found you. Double E here, an old guy who likes math. I've never seen e explained this way, and I'm ready for more insight on Fourier and Laplace. Another good follow up video for this one is to show how nature has selected e as the most natural exponential.

[omoleyeamuleru-marshall]

May you be BLESSED! As this was a frustration throughout my entire grade school career... And I searched the Internet for hours and just gave up in frustration, leading to chug and plug execution without learning. My only criticism is you didn't do this a few years earlier... May this video be passed long and wide. Thank you so much! This is like a salv on a long festering mathematical wound.

[VasanRailkutumbam]

Please make more theoritical videos, I loved your explanation for e

[Dev-lmfx]

Thank you ! You’re very inspiring and your videos are very cool !!!

[nihilisticnirvana]

your stuff is so interesting to watch! I'm in my gap year after high school rn and your videos keep me connected to math on my year off. nice! keep making videos