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    I am not sure whether this belongs in Lobsters, on the other hand:

    I read this long time ago, and it’s still one of the most insightful analysis of human aspects of mathematics. Another classic is On proof and progress in mathematics. Both are highly recommended.

    My favorite quote from “On proof and progress” (this isn’t particularly cherry-picked; the entire article is like this):

    Parts of this proof I could communicate in two minutes to the topologists, but the analysts would need an hour lecture before they would begin to understand it. Similarly, there were some things that could be said in two minutes to the analysts that would take an hour before the topologists would begin to get it. And there were many other parts of the proof which should take two minutes in the abstract, but that none of the audience at the time had the mental infrastructure to get in less than an hour.

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      Have you ever read http://bentilly.blogspot.com/2010/08/analysis-vs-algebra-predicts-eating.html?

      Back when I was in grad school there was a department lunch with corn on the cob. Partway through the meal one of the analysts looked around the room and remarked, “That’s odd, all of the analysts are eating corn one way and the algebraists are eating corn another!” Everyone looked around. In fact everyone was eating the corn in one of two ways. One way was to munch over the length of the corn in a straight line, back up, turn slightly, and do another row across. Kind of like how an old typewriter goes. The other way was to go around in a spiral. All of the analysts were eating in spirals, and the algebraists in rows.

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        Is that quote meant as a joke or did the analysts really eat the corn differently? Genuinely would believe both answers :)

        EDIT: never mind, I read the article!

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          I must have, as it is familiar. Wow that article is now 10 years old.

          I wonder how algebra vs analysis interacts with Gowers’ theory vs proof method (“combinatorics”). To me both algebra and analysis seem predominantly theory-building fields, so I think two axes are orthogonal.

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        Here’s a good article by Michael Atiyah about trends in mathematics:

        Another famous “two cultures” paper, though one which is quite out of date if you ask most working statisticians: