Ramanujan's favorite coincidence (it's not a coincidence)

Comments · 396

• NO

  @nodrogj1 · 6 months ago

  "Approximately in the set" is a war crime and I refuse to believe otherwise

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• TO

  @tomkerruish2982 · 6 months ago

  It's a Parker integer.

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• XS

  @xshortguy · 6 months ago

  I was tricked into watching a Pi approximation video.

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• AN

  @Anonymous-zp4hb · 6 months ago

  We need a new unicode character for the "appoximate membership" symbol

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• 11

  @11kravitzn · 6 months ago

  <a href="https://www.youtube.com/watch?v=NNmLocqtbgg&amp;t=1080">18:00</a> You swapped 613 for 163

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• O0

  @o0ss_st · 6 months ago

  “I guess we could abuse notation here”. Yes that was abuse <a href="https://www.youtube.com/watch?v=NNmLocqtbgg&amp;t=37">0:37</a>

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• MO

  @modulo_math · 6 months ago

  Previous 100 videos - let&apos;s do an undergraduate integral. <br><br>This video - let&apos;s cover an entire book on algebraic number theory and modular forms in 30 minutes 😂

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• OB

  @objective_psychology · 6 months ago

  RIP Ramanujan you would have loved Monstrous Moonshine

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• BR

  @BriceMarnier · 6 months ago

  196884 ? I think I see a Monster coming...

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• IN

  @InfiniteRegress · 6 months ago

  This is my favourite bit of maths! For those who want to get lost down a rabbit hole, it gets even crazier because of the &quot;moonshine&quot; connection to the largest sporadic simple group, the Monster, studied by Conway and proved to be more than a numerical coincidence by Richard Borcherds. <br><br>If I understand things properly (and I might not, so please fact check me), you can represent the roughly 8*10^53 (I like to say 8 &quot;monstrillion&quot;) elements of the Monster group as matrices meant to transform a space (while preserving a certain kind of symmetry of that space) in such a way that composing any two produces another one. There are 194 such irreducible spaces (A001379 on OEIS) where the first is trivially 1 dimensional, and then the second (the famous one) is 196883 dimensional. <br><br>In other words, the simplest way to construct the Monster group is as a set of 8 monstrillion 196883-by-196883 matrices that preserve a certain kind of symmetry of a 196883 dimensional space (related to the 196884 dimensional Griess algebra). One thing to note is that 196883 = 47*59*71, and if you factor that 8 monstrillion number, the largest 3 primes are 47, 59, and 71. As a sidenote, 71^2 = 5041, which is 1 more than the largest number known to have its sum of divisors exceed a certain value; and if 5040 truly is the largest (look up Robin&apos;s Theorem), then the Riemann Hypothesis is true! But I digress. <br><br>The number 163 shows up here again, too. I still do not fully understand the details, but the character table for the Monster is a 194-by-194 table that encodes the structure of the group and yields 194 functions that can be used to construct a space that turns out to be only 163 dimensional. <br><br><br>Anywho, like I said, this is a rabbit hole, one which leads to many others, so be prepared to get lost. Cheers!

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• AU

  @austin4768 · 6 months ago (edited)

  I knew that 163 is the largest Heegner number but TIL that 613 is the largest Heeger number.

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• KE

  @ke9tv · 6 months ago

  <a href="https://www.youtube.com/watch?v=NNmLocqtbgg&amp;t=1080">18:00</a> I&apos;m getting the hives looking at that 613.

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