The most beautiful equation in math, explained visually [Euler’s Formula]

Comments · 1.4K

• RO

  @rowan985 · 2 years ago

  i wish math in highschool was taught in tandem with its history and utilizations

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• PE

  @pendragon7600 · 2 years ago

  You pretty much determined the course of my life. You released the imaginary numbers are real series when I was 14 and uninterested in math. That series kicked off my passion for mathematics and I'm now pursuing a PhD in complex analysis and algebraic geometry. My thesis focuses on modular forms. Seeing this video was like a flashback to where it all started. Eternally grateful to you and for the wonderful exposition you produce. I'll buy the book someday (PhD students have no money lol).

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• YO

  @Yotam1703 · 2 years ago

  Your complex numbers series was my introduction to higher math education! It’s a pleasure to see you continue it.

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• MA

  @manuelcastellanos122 · 2 years ago

  I'm from Dominican Republic and let's say math isn't much of a thing here. I initially watched your complex numbers series graduating from high school, and I knew a spark started there. Now I'm about to present my thesis for my MSc in Applied Mathematics and it is so rewarding to look back where it all started. Looking forward to get your book!

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• SL

  @sloppycee · 2 years ago

  Euler's motivating example and insight that the i's should cancel; so log(-1) should have an I somewhere is such important knowledge. I hated how they taught math with no context or motivation. This is great!

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• KA

  @Kazner0h · 2 years ago

  That final visualization is really stunning. It always amazes me how much a graphical representation can help make a complex subject feel intuitive.

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• SK

  @skfineshriber · 2 years ago

  After studying engineering mathematics I gained an enormous respect for mathematicians such as Euler. Here I was, struggling like hell to understand their equations and transformations, while realizing these people had the insight and intellect to INVENT these mathematics. It was awe inspiring.

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• AB

  @abpdev · 2 years ago

  I envy younger people who are just getting into math/science because they are starting of surrounded by such amazing free content to explain difficult concepts!<br>I had a hard time understanding this equation in my first and second year. It just seem so odd and counterintuitive. <br>It became one of those truths that I accepted because the textbook said so. <br><br>The manner in which you presented it here just makes so much sense! The intro, the papers/conversations from the authors, notes, diagram... WELL DONE AND THANK YOU!

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• FY

  @fyu1945 · 2 years ago

  <a href="https://www.youtube.com/watch?v=f8CXG7dS-D0&amp;t=573">9:33</a> You define a conjugate as &quot;flipping the sign of the imaginary component&quot; but what you&apos;re doing here is not flipping the sign of the imaginary component, but flipping the sign of the exponent, which happens to be imaginary. Of course in reality it amounts to the same thing, but that&apos;s what we&apos;re trying to prove! We don&apos;t know yet if 2^(-bi) is the conjugate, so we can&apos;t use this fact to prove the magnitude of our number is 1.

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• FL

  @FlyingJetpack1 · 1 year ago

  One of the things I hated about math in highschool was how the teacher handwaved my question when I asked &quot;why&quot; when an equation was simply given to us as some form of universal truth that I need to memorize. In a single video you managed to write off a list of reasonings for a dozen or so questions that kept bugging me in my childhood. If only teaching in school could&apos;ve been even a fraction of this approach of teaching...

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• JO

  @JohnMartinIT · 2 years ago

  The statement that &quot;many of the equations and graphs we spend our time with are just shadows of a more elegant, powerful and higher-dimensional mathematics&quot; reminds me of Plato&apos;s analogy of the cave, which I&apos;m sure you appreciate has some interesting implications. Maybe that&apos;s why you say imaginary numbers are real; indeed, they may be more real than the more tangible shadows we deal with in this mundane world.

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• MY

  @Mytubecleaner · 2 years ago

  <a href="https://www.youtube.com/watch?v=f8CXG7dS-D0&amp;t=900">15:00</a> wow, that was an enlightement moment for me

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