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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 3 Oct 2019
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      Replying to @BarbaraFantechi

      It's bizarre to say that you can be a great mathematician "even if you calculate a lot." Most great mathematicians have been extremely avid calculators. Even Riemann, generally thought a paragon of geometric insight, calculated maniacally; his nachlass is full of calculations.

      1 reply 0 retweets 1 like
    2. RCA88‏ @rca619700 3 Oct 2019
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      Replying to @MathPrinceps @BarbaraFantechi

      For the curious non mathematicians.. what does “to calculate” or “not calculate” mean/infer?

      1 reply 0 retweets 2 likes
    3. Scoffing Mathematician  🏳️‍🌈 🇪🇺‏ @BarbaraFantechi 3 Oct 2019
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      Replying to @rca619700 @MathPrinceps

      This is an extremely good point! Most mathematicians calculate, but in very different senses of the word. I know very few who, like Don does, enjoy doing computations involving integers with dozens of digits. Most of us , myself included, wouldn't be able to.

      1 reply 0 retweets 3 likes
    4. Laurens Gunnarsen‏ @MathPrinceps 3 Oct 2019
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      Replying to @BarbaraFantechi @rca619700

      Calculation is a form of play. It observes certain rules, like those of tennis, and may be deadly serious. But it need not have a precisely defined goal; one does not always play "to win." Sometimes one just goes out and whacks the ball around, for the sheer fun of it.

      1 reply 0 retweets 1 like
    5. Laurens Gunnarsen‏ @MathPrinceps 3 Oct 2019
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      Replying to @MathPrinceps @BarbaraFantechi @rca619700

      Even when whacking the ball around for the sheer fun of it, though, one still tries to avoid hitting the ball into the net, or outside the lines. And in this sense calculation is always constrained and structured, even if its purpose is not always perfectly clear.

      1 reply 0 retweets 1 like
    6. Laurens Gunnarsen‏ @MathPrinceps 3 Oct 2019
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      Replying to @MathPrinceps @BarbaraFantechi @rca619700

      Often the play seems magically to organize itself, in some strange and surprising way. As one fiddles around, obeying the rules of calculation, one often starts to feel as though the rules themselves are somehow pushing one in a certain direction. As though they subtly bias play.

      1 reply 0 retweets 1 like
    7. Laurens Gunnarsen‏ @MathPrinceps 3 Oct 2019
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      Replying to @MathPrinceps @BarbaraFantechi @rca619700

      The great thing about calculation is that one can do it even when one is stuck and frustrated -- which, for most mathematicians, is the usual state of affairs. Calculation can then be a form of active meditation. It keeps the mind turning, often in the right general direction.

      1 reply 0 retweets 3 likes
    8. Laurens Gunnarsen‏ @MathPrinceps 3 Oct 2019
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      Replying to @MathPrinceps @BarbaraFantechi @rca619700

      And when calculation leads to this feeling that the rules of the game itself are somehow biasing play in a certain way, rewarding some choices and punishing others, then the activity takes on a tantalizing fascination. One struggles to hear the subtle guidance it is offering.

      1 reply 0 retweets 1 like
    9. Laurens Gunnarsen‏ @MathPrinceps 3 Oct 2019
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      Replying to @MathPrinceps @BarbaraFantechi @rca619700

      According to the eminent mathematician-historian Jeremy Gray, "[Gauss] himself said that many of his best discoveries were made at the end of lengthy calculations, and much of his work on elliptic functions moves in a sea of formulae with an uncanny sense of direction."

      1 reply 0 retweets 2 likes
    10. Laurens Gunnarsen‏ @MathPrinceps 3 Oct 2019
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      Replying to @MathPrinceps @BarbaraFantechi @rca619700

      Gray adds that many great mathematicians had an almost eerie knack of thinking in formulae. "One is struck as often by the technical power of great mathematicians as by their profundity. Nonetheless, some mathematicians have the ability more than others."

      1 reply 0 retweets 1 like
      Laurens Gunnarsen‏ @MathPrinceps 3 Oct 2019
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      Replying to @MathPrinceps @BarbaraFantechi @rca619700

      Gray cites Euler, Gauss, and Kummer as paragons of raw technical power -- as master calculators whose profound insights were rooted in extensive play of just the sort I've been describing. (Klein and Poincare, though, he acknowledges were noticeably less virtuosic in this way.)

      12:55 PM - 3 Oct 2019
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      • RCA88 Valeria dePaiva
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        2. Laurens Gunnarsen‏ @MathPrinceps 3 Oct 2019
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          Replying to @MathPrinceps @BarbaraFantechi @rca619700

          Among contemporary mathematicians, Don Zaiger has long seemed to me perhaps the most temperamentally similar to Euler. For him, calculation is a delight and an indispensable source of inspiration. (Atiyah says this was also true of Zagier's great adviser, Friedrich Hirzebruch.)

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        3. RCA88‏ @rca619700 4 Oct 2019
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          Replying to @MathPrinceps @BarbaraFantechi

          Thank you! I am more in the neuro science realm, but there are intersections .. Years ago Edward DeBono coined the term/process “lateral thinking” as a way of developing non-linear innovation (paraphrase “digging lots of holes, instead of one hole deeper”) ..

          1 reply 0 retweets 1 like
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