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fermatslibrary's profile
Fermat's Library
Fermat's Library
Fermat's Library
@fermatslibrary

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Fermat's Library

@fermatslibrary

A platform for illuminating academic papers. We publish an annotated paper every week. Our chrome extension for arXiv: https://fermatslibrary.com/librarian 

fermatslibrary.com
Joined September 2015

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    Fermat's Library‏ @fermatslibrary 13 Apr 2018
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    This identity is called the Sophomore's dream - in contrast to the name "Freshman's dream" which is given to the incorrect identity (x+y)ⁿ=xⁿ+yⁿ, this one has a similar too-good-to-be-true feel, but is true!pic.twitter.com/mshBfdqmiU

    6:00 AM - 13 Apr 2018
    • 724 Retweets
    • 2,480 Likes
    • Pascal Kwanten Davecorteso LatePotato Looking for a Developer Position to help you ゆきと Esther Rishiraj against the dying of the light Spanish Chiropractors Nieto de Zeus
    17 replies 724 retweets 2,480 likes
      1. New conversation
      2. plutoo‏ @qlutoo 13 Apr 2018
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        Replying to @fermatslibrary

        proof?

        3 replies 1 retweet 10 likes
      3. Théootz‏ @Totzenberger 13 Apr 2018
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        Replying to @qlutoo @fermatslibrary

        :)pic.twitter.com/pt59XfGXcZ

        1 reply 16 retweets 111 likes
      4. 1 more reply
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      2. Viktor Blåsjö‏ @viktorblasjo 13 Apr 2018
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        Replying to @fermatslibrary

        The x^x form of the identity (also given at https://en.wikipedia.org/wiki/Sophomore%27s_dream …) is the historically primary one, and arguably more natural. Johann Bernoulli presents it (and not the x^-x form) in his letter to Leibniz of May 1694.

        1 reply 0 retweets 5 likes
      3. Viktor Blåsjö‏ @viktorblasjo 13 Apr 2018
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        Replying to @viktorblasjo @fermatslibrary

        The reason for preferring the less natural x^-x form seems to be that it makes the sum easier to write in sigma notation — a pedantic modern obsession not shared by anyone in the 17th century. Bernoulli simply wrote out the first five terms, so to him there was no problem.

        0 replies 1 retweet 3 likes
      4. End of conversation
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      2. Erik Postma‏ @postmath 13 Apr 2018
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        Replying to @fermatslibrary

        I've heard of that freshman's dream mostly in the context of Z/nZ, in which case it's actually true.

        1 reply 0 retweets 0 likes
      3. Scoffing Mathematician  🏳️‍🌈 🇪🇺‏ @BarbaraFantechi 13 Apr 2018
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        Replying to @postmath @fermatslibrary

        "I've heard of that freshman's dream mostly in the context of Z/nZ, in which case it's actually true." If n is prime.

        0 replies 0 retweets 5 likes
      4. End of conversation
      1. asis kumar dasgupta‏ @d_u_l_u 13 Apr 2018
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        Replying to @fermatslibrary

        Beautiful!!!....

        0 replies 0 retweets 1 like
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      2. Sadiq T. Yakasai‏ @sadiqtyakasai 13 Apr 2018
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        Replying to @fermatslibrary

        Again, in English please?!

        1 reply 0 retweets 1 like
      3. maryam z‏ @mamanurayn 14 Apr 2018
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        Replying to @sadiqtyakasai @fermatslibrary

        pic.twitter.com/77Q9KmnGBm

        0 replies 0 retweets 0 likes
      4. End of conversation

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