July 15, 2008
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Elliptic comment:
My comment on a discussion of elliptic curves and modular forms at Secret Blogging Seminar, about 10 PM tonight:
How does this affect popularized discussions of the Taniyama-Shimura
conjecture– for instance, Ivars Peterson’s, in “Curving Beyond Fermat,”
November 1999– which claim, for instance, that “Elliptic curves and
modular forms are mathematically so different that mathematicians
initially [in the 1950's, the early days of the conjecture] couldn’t
believe that the two are related.”?Update of about 10:45 PM tonight:
A reply by the author of the discussion, Scott Carnahan:
I don’t think anyone doubted that there is a connection between
elliptic curves and modular forms on the level I described above.
However, the Taniyama-Shimura conjecture refers to a more advanced idea
about a deeper connection.Carnahan then gives a one-paragraph summary, definitely not popularized, of the deeper connection.
