Wow, thanks so much. My 12 year old son, having mastered pi, has been asking me to explain e. Of course it’s made me realize how little I understood it back in math class. This is a totally graspable explanation, which I can now share with him. You rock.
This has been really useful for me! Thanks very much for your time in making this and the rest of the site.
“e” has always been a tricky subject for me…after going through this material I am starting to wonder why it was so difficult in the first place, it’s all so clear now!
Hey Kalid–
I had a minor aha moment when I realized that simple growth could be viewed as compound growth compounded only once. Not a big deal, but insight sometimes comes in increments.
Gratefully yours,
–Tim
fantastic job bro, u helped me a lot explaining one biggest questions in my mind,please keep your work going and are you from india?
I’d suggest you’ve maybe missed something right at the beginning. Although you use the word ‘compound’ in your opening paragraphs, I don’t think you have emphasised enough that e is the signature of a process whose rate is determined by the process itself; it’s that feeding-back that is the key. Not sure that I put that terribly well myself, but anyway for me the clearest example is the flow of water out of a full barrel with a hole at the bottom. The distance the jet spurts out is dependant upon the pressure, but the pressure is contantly decreasing because of the jet. Similarly in electronics the voltage across a charged capacitor discharging through a resistor; e is inolved because as the cap discharges, the voltage decreases so there is less electrical pressure behind the discharge. Sure that is implicit in the rest of your explanation, but for me the aha moment about e was just this feeding-back quality, and I think it’d be even better if this was up front.
thanks Kalid! it was great!
This is genius! What i’ve been trying to work out for a week now in one page. Thank you so much; you should teach 
thannnks
I was not satisfied with this artcle. I also read most of the comments. I remain unsatisfied. Here is why. This is not intuition. This is scence. Intuition means feeling. If the transcendental number “e” is from God, then how can I feel the meaning of this?
Khalid, I commend your efforts but you & the commentators have merely rehashed what I am already well aware of.Therer is neither deep insight nor intuitition on this page. Interestingly there was no mention of the gamma function, Sterling’s formula or the relationship to permutations. I felt nothing in the end.
Nice way writing . completely understandable
Thank you so much! I am in a college calc class and had never got to the point were I understood e. I knew how to work it, but it never made sence were it came from. you explained it in an excelently simplisitc fashion! The biggest thing is that I never had understood e is 100% and it’s what you do to it that changes it. I just knew if u had e you went by what power it was at.
Wow I am in 7th grade and I understood that, and no they do not teach e in middle school I just wanted to know what e was
Awesome description that was really simple thanks
WOW kalid really gr8
Actually I was doing a project on the topic e .
And this article was useful
But the thing is I just want something new about it .
So could you please help??
I was searching for an integer approximation for e (like 22/7 for pi).
once again thank you for the article
@Jeff: Thanks, really glad it came in handy. There’s a bit on interest rates here: http://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/
Robin A, Yes your assessment is probably accurate. Yet I am not dogmatic. Here is my take on this. Permutation means rearrangement which implies change and (possibly) growth. Growth is built upon passion which is the excess of desire over will. Passion multiplied by drive equals knowledge( drive is defined as desire fixated to will). Putting all of this together, we conclude that the number “e” is derived from primal passion in the monad.
Thanks Kalid, for explaining the practical use of e in an easy understandable fashion, I’m passed 50, math was useless, dry stuff brought to me by uninterested teachers.
Your type of explaining gives me the courage to have a go at understanding the world of math in a proper way.
Marc
Finally I have an intuition! Thanks!
Greetz from Switzerland
This is so great Kalid thanks. I went through engineering school never really understanding what the number e really meant. I mean, I know how and when to use it but I didn’t know where it came from. It gave me a feeling of euphoria truly understanding what it means. And that at an age of 31. The world should have more teachers like you
@Gautama’s friend: Awesome, glad it helped :).