The Hardy-Littlewood Circle Method is amazing. We’re learning about how to get asymptotic formulae for the Waring problem. It’s a shame that there is no (known) asymptotic bound or for the number of representations of n as the sum of two squares. That would tell us a lot about prime numbers (or at least those congruent to 1(mod 4)). We may also get to see the proof of Vinogradov’s Theorem (also known as the Weak Goldbach Conjecture, which is no longer a conjecture).

I wonder if it’s necessary to do differential calculus with lines. What happens if instead of fixing a point and moving another point closer, we fix a point and move two points on opposite sides closer to get a quadratic? Will that parabola have any interesting properties? I might play around with it some time.

Kevin makes me feel like a slacker. He’s taking nine classes, and I’m only taking seven at most depending on how taking is defined.


About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.
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5 Responses to

  1. eternalfight says:

    Nine classes? What kind of classes are these?

    • Simon says:

      I think at least six of them are math classes, and at least four of them are graduate classes. But then, he’s a third-year student.

      • eternalfight says:

        How is that possible?
        Especially the graduate courses. Everything I’ve ever read says to only take a few courses and focus on those in depth (greater depth than demanded of undergraduate courses) — is this guy a machine or something?

  2. Anonymous says:

    And who is Kevin? 🙂

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