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MathPrinceps's profile
Laurens Gunnarsen
Laurens Gunnarsen
Laurens Gunnarsen
@MathPrinceps

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Laurens Gunnarsen

@MathPrinceps

Mathematical physicist and mentor to mathematically talented youth. Talent is that which bridges the gap between what can be taught and what must be learned.

Joined June 2012

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    1. John Carlos Baez‏ @johncarlosbaez 6 Jul 2018
      • Report Tweet
      • Report NetzDG Violation

      Randomly pick two points on the unit sphere... in n-dimensional space, just to show off. What's their distance, on average? If n = 4, @gregeganSF showed it's 64/(15 pi). I predict that as n gets big, it approaches sqrt(2). What about the humble n = 2, 3 cases?pic.twitter.com/Wkb8ruuaFa

      4 replies 24 retweets 58 likes
    2. D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i‏ @sigfpe 6 Jul 2018
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      Replying to @johncarlosbaez @gregeganSF

      If p(s)=s²√(4-s²)/π then the even moments are the Catalan numbers. I.e. E[s²ⁿ] = C(n+1)

      3 replies 0 retweets 12 likes
    3. John Carlos Baez‏ @johncarlosbaez 6 Jul 2018
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      Replying to @sigfpe @gregeganSF

      Zounds, Dan - that book has brainwashed you! One has to ask: do we get some other funky series of integers if instead of the unit sphere in 4d we use a sphere in some other dimension? Or is this just a 4d thing?

      3 replies 0 retweets 5 likes
    4. D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i‏ @sigfpe 6 Jul 2018
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      Replying to @johncarlosbaez @gregeganSF

      I can understand why people are into conspiracy theories. The fun thing about mathematics is that the conspiracies often turn out to be provable. No time to work on this problem now though - bread to bake!

      1 reply 0 retweets 5 likes
    5. John Carlos Baez‏ @johncarlosbaez 7 Jul 2018
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      Replying to @sigfpe @gregeganSF

      Monstrous Moonshine is one of the biggest conspiracies: you're humbly computing coefficients of a function that classifies elliptic curves and they turn out to be dimensions of reps of a simple group with 8 x 10^53 elements. Nobody's gotten to the bottom of this one!

      2 replies 1 retweet 13 likes
    6. Timothy Gowers‏ @wtgowers 10 May 2019
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      Replying to @johncarlosbaez @sigfpe @gregeganSF

      I thought Richard Borcherds and others got to the bottom of it in the 1990s. What’s left to do?

      3 replies 0 retweets 6 likes
    7. John Carlos Baez‏ @johncarlosbaez 10 May 2019
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      Replying to @wtgowers @sigfpe @gregeganSF

      Borcherds hacked out a proof of Monstrous Moonshine that requires lots of complicated calculations that mysteriously work out - a "verification" rather than an "explanation". See the very high-level sketch on Wikipedia to sense the ugliness! https://en.wikipedia.org/wiki/Monstrous_moonshine#Borcherds'_proof …

      1 reply 0 retweets 6 likes
    8. John Carlos Baez‏ @johncarlosbaez 10 May 2019
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      Replying to @johncarlosbaez @wtgowers and

      "These relations are strong enough that one only needs to check that the first seven terms agree with the functions given by Conway and Norton." That doesn't count as *understanding* Monstrous Moonshine - that's just checking that it's true. This stuff should be *beautiful*!

      1 reply 0 retweets 5 likes
      Laurens Gunnarsen‏ @MathPrinceps 11 May 2019
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      Replying to @johncarlosbaez @wtgowers and

      And yet it is far from clear that any essential progress in this direction has been made since Borcherds bulled his way to this first solution. As Erdos said, "Problems worthy of attack prove their worth by fighting back."

      9:31 AM - 11 May 2019
      • 3 Likes
      • Waldemar Puszkarz John Carlos Baez D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i
      0 replies 0 retweets 3 likes

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