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EmilyGorcenski's profile
Emily G
Emily G
Emily G
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@EmilyGorcenski

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Emily GVerified account

@EmilyGorcenski

Lead Data Scientist, activist, survivor. Was actually assaulted by an actual right-wing terrorist. Opinions belong only to me, especially the bad ones. she/they

Deep Space Nine
emilygorcenski.com
Joined June 2013

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    1. Emily G‏Verified account @EmilyGorcenski Apr 6

      You don't necessarily start from the top and go to the bottom. Good proofs will do some really clever things like set up a good one-two punch. The Galois proof I talked about earlier is like this.

      1 reply 0 retweets 7 likes
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    2. Emily G‏Verified account @EmilyGorcenski Apr 6

      Galois proof is done in two major steps: first, we establish that a polynomial is solvable by radicals if and only if its splitting field has a solvable Galois group. This is not easy by any means.

      3 replies 0 retweets 9 likes
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    3. Emily G‏Verified account @EmilyGorcenski Apr 6

      "If and only if" is a bidirectional implication. We have to prove both directions: 1. solvable by radicals implies the splitting field has a solvable Galois group; 2. the splitting field having a solvable Galois group implies solvability by radicals.

      1 reply 0 retweets 8 likes
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    4. Emily G‏Verified account @EmilyGorcenski Apr 6

      But once we do that we set up the coup de grace: now we only need to compute the Galois group for a quintic polynomial (not so hard) and then show it is not solvable. This is probably not easy to follow if you don't know these terms. That's ok.

      1 reply 0 retweets 8 likes
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    5. Emily G‏Verified account @EmilyGorcenski Apr 6

      What's elegant about this is it avoids a tremendous amount of tedium by doing a lot of overhead work first. We establish that the problem we care about looks like this other thing. Once we do that, the rest falls like dominoes.

      2 replies 0 retweets 11 likes
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    6. Emily G‏Verified account @EmilyGorcenski Apr 6

      A good proof is like a good chef cooking a complex meal. It's chaos and complexity and drama! And then, all of a sudden, everything comes together at the end. It can be hard to understand what they're doing at first... but them BAM.

      2 replies 1 retweet 12 likes
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    7. Emily G‏Verified account @EmilyGorcenski Apr 6

      Have you ever seen that clip of Susan Boyle at Britain's Got Talent? It's a trainwreck at first. She's dowdy, and old. She's out of her element. "I Dreamed a Dream?". Simon's making fun of her. She is mumbling her words... And then she sings.https://www.youtube.com/watch?v=RxPZh4AnWyk …

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    8. Emily G‏Verified account @EmilyGorcenski Apr 6

      That is what a perfect proof feels like.

      3 replies 0 retweets 10 likes
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    9. Emily G‏Verified account @EmilyGorcenski Apr 6

      Becoming good at math means being able to identify the setup work that needs to take place. This is not a special skill. Much like any professional, if you become good at something you know how to get started, whether it's starting a software project or a new patient record or

      1 reply 0 retweets 10 likes
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    10. Emily G‏Verified account @EmilyGorcenski Apr 6

      But great mathematicians can see multiple steps into the future in this process, to intuit connections that are not obvious. Throughout my math undergrad, I viewed math as a mostly mechanical, procedural process. Which made sense for my discipline (scientific computing).

      1 reply 0 retweets 9 likes
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      Emily G‏Verified account @EmilyGorcenski Apr 6

      But as I shifted more into formal analysis I began to finally understand proof. It took a mental maturity well-beyond my undergrad years to get there. It really took me until my late-20s. And I'm still learning that process.

      12:15 PM - 6 Apr 2018
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      • Laurent Gⓐtt⓪ Jame sTruitt 📜 Luis Bruno                                       . Sam Squires Rongeur 。.*.(っ ᐛ )っ 🔪 ($_$)ノ🎩 Pathologically Eclectic Rachel Lindsey Peter Barfuss 𒀱 Hetti Von Grell
      2 replies 0 retweets 12 likes
        1. Emily G‏Verified account @EmilyGorcenski Apr 6

          When I took Real Analysis at RPI I finished with a C, partly because it was my last semester and once I got a passing grade I stopped going. When I re-took the class at UVa, I had much more maturity and a finer grasp of proof-based math and got an A+.

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        2. Jalane "Smash the Fash" Schmidt  👩🏾‍🏫 🇨🇺‏ @Jalane_Schmidt Apr 6
          Replying to @EmilyGorcenski

          Some top mathemeticians do ground-breaking work early, though, yes? (Not said dismissively of your own learning process.) I was always jealous of my math PhD colleagues, whose dissertations were often short papers where they worked out theorems. So different than humanities!

          2 replies 0 retweets 0 likes
        3. Emily G‏Verified account @EmilyGorcenski Apr 6
          Replying to @Jalane_Schmidt

          This is a common myth that is largely a product of western academic structures. But it is true that math PhDs can be (much) shorter.

          0 replies 0 retweets 1 like
        4. End of conversation

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