e (Euler's Number) is seriously everywhere | The strange times it shows up and why it's so important

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Published 2019-05-15
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Timestamps/Extra Resources

2:42 - Derangements (en.wikipedia.org/wiki/Derangement)
3:11 - Optimal Stopping (en.wikipedia.org/wiki/Optimal_stopping)
5:25 - Infinite Tetration (en.wikipedia.org/wiki/Tetration)
6:25 - 1958 Putnam exam question (mks.mff.cuni.cz/kalva/putnam/putn58.html)
9:33 - Fourier Transform (GIF credit to 3blue1brown, check out his video on the FT here:    • But what is the Fourier Transform?  A...  )
10:56 - Gamma Function (en.wikipedia.org/wiki/Gamma_function)
12:53 - Casimir Effect Paper (arxiv.org/pdf/hep-th/9901011.pdf)
13:20 - Higher Dimensional Spheres (en.wikipedia.org/wiki/Volume_of_an_n-ball)

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All Comments (21)
  • Both English professors and Math professors agree that 'e' is everywhere.
  • @gubx42
    Imagine a bank that pays 100% interest per year, after a year you have... $0, because it's a scam.
  • @zoeymccann124
    e is everywhere, literally. even in the word everywhere four times
  • @Tiqerboy
    One of the first applications of 'e' I remember is in the case of radioactive decay because the rate of decay is proportional to the amount that is left.
  • @brookej0
    I feel like 'e' is some snippet of our universe's source code that we weren't supposed to discover and the developers must be really pissed off about it 😂
  • @malou5290
    d/dx(eˣ) = eˣ is mindblowing really
  • I'm an old geezer (56), and have a little envy about this and all of the YouTuber's who publish informative and captivating videos on mathematics, physics, etc. The scope of topics and their graphical representations are captivating and enlightening. Keep up the good work: it is influencing many lives for the better.
  • @bryan.flores
    Im starting to notice that numbers are everywhere in math🤯
  • @Porururidimu
    I don't understand a single thing but sounds cool
  • Not a physics or math student, I literally limped my way through school to end up slightly successful in banking, and you make me want to rediscover my passion for learning and make me feel like I could tackle quantitative finance. Thank you genuinely and I hope you continue to inspire others to reach higher.
  • @peybro
    2:24 when you get caught stealing cookies by your German grandmother
  • People don't become mathematicians or engineers because it is easy - quite the opposite. This is a great channel - might help people understand how much fun math and engineering really are. He makes many of these topics approachable by those new to the concepts (the viewer is along for the ride in learning in some cases), while also being really interesting to those who already have backgrounds.
  • @BangMaster96
    What i don't get is, how can people figure this out? I can do basic calculus, algebra, linear algebra, etc.., but then, i see things like from this video, and it just completely blows my mind. Like, how is an individual able to find out formulas for real world systems? For example, formulas for fluid dynamics, or circuit analysis, etc..What do they do that helps then derive these formulas? Again, look at Maxwell's equations, how did he come up with all those equations? What did he do that led to him deriving those equations? Also with fourier transform, how did he figure out what variables and equations to use? Math just goes out of my mind once i start learning many of the abstract concepts, there truly are some real geniuses on this planet, just the fact that those people can understand what an equation is doing, and how to derive those equations is beyond my scope of understanding.