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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. Laurens Gunnarsen‏ @MathPrinceps 29 Jul 2016
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      Replying to @MathPrinceps @MrGrahamMoore

      Which means that, if you are not yourself an expert, you must force your expert advisers to earn their fees by teaching you.

      1 reply 0 retweets 0 likes
    2. Laurens Gunnarsen‏ @MathPrinceps 29 Jul 2016
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      Replying to @MathPrinceps @MrGrahamMoore

      Not just by supplying accurate jargon, but by actually teaching you at least one clear example of genuine genius thinking.

      1 reply 0 retweets 0 likes
    3. Laurens Gunnarsen‏ @MathPrinceps 29 Jul 2016
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      Replying to @MathPrinceps @MrGrahamMoore

      Which is a very considerable challenge, even for an expert. Because, alas, pedagogy is an art of little interest to experts.

      1 reply 0 retweets 0 likes
    4. Laurens Gunnarsen‏ @MathPrinceps 29 Jul 2016
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      Replying to @MathPrinceps @MrGrahamMoore

      But it's possible. Here's a beautiful and transparent illustration of your doctrine, drawn from the early career of Ramanujan

      1 reply 0 retweets 0 likes
    5. Laurens Gunnarsen‏ @MathPrinceps 29 Jul 2016
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      Replying to @MathPrinceps @MrGrahamMoore

      Ramanujan observed that 9 = 1 + 2x4 16 = 1 + 3x5 25 = 1 + 4x6, and that 3 = sqrt(9) 4 = sqrt(16) 5 = sqrt(25), etc, etc.

      1 reply 0 retweets 0 likes
    6. Laurens Gunnarsen‏ @MathPrinceps 29 Jul 2016
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      Replying to @MathPrinceps @MrGrahamMoore

      These observations were not new to him, of course. His genius was to see what they actually meant. To fashion them into art.

      1 reply 0 retweets 0 likes
    7. Laurens Gunnarsen‏ @MathPrinceps 29 Jul 2016
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      Replying to @MathPrinceps @MrGrahamMoore

      Ramanujan saw that these mundane facts fit together in a dazzling way. He saw that 3 = sqrt(1 + 2x4) is just a first step.

      1 reply 0 retweets 0 likes
    8. Laurens Gunnarsen‏ @MathPrinceps 29 Jul 2016
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      Replying to @MathPrinceps @MrGrahamMoore

      It has infinitely many counterparts, 4 = sqrt(1 + 3x5) 5 = sqrt(1 + 4x6) 6 = sqrt(1 + 5x7) which nest like Russian dolls.

      1 reply 0 retweets 0 likes
    9. Laurens Gunnarsen‏ @MathPrinceps 29 Jul 2016
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      Replying to @MathPrinceps @MrGrahamMoore

      So that 3 = sqrt(1 + 2x4) = sqrt(1 + 2xsqrt(1 + 3x5)) = sqrt(1 + 2xsqrt(1 + 3xsqrt(1 + 4x6))) = ... , etc., ad infinitum.

      1 reply 0 retweets 0 likes
    10. Laurens Gunnarsen‏ @MathPrinceps 29 Jul 2016
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      Replying to @MathPrinceps @MrGrahamMoore

      This is 3 as an infinitely long string of nested square roots -- a novel mathematical beast, when Ramanujan encountered it.

      1 reply 0 retweets 0 likes
      Laurens Gunnarsen‏ @MathPrinceps 29 Jul 2016
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      Replying to @MathPrinceps @MrGrahamMoore

      Like one of Holmes' deductions, no one else was able to put these pieces together. Ramanujan alone recognized 3 in this form.

      11:03 AM - 29 Jul 2016
      1 reply 0 retweets 0 likes
        1. Laurens Gunnarsen‏ @MathPrinceps 29 Jul 2016
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          Replying to @MathPrinceps @MrGrahamMoore

          This is a humble yet authentic picture of how his mind worked - a genuine example of his genius that can fit into a film.

          0 replies 0 retweets 0 likes
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