  [X] Close this message.  (Editor's Note: Bucknell's Web site
is featuring some of the University's newest teacher-scholars.
They are among the new faculty members highlighted in the Fall
2007 edition of Bucknell World.)  The next time you make a
secure online purchase, thank number theory. This little-
understood branch of mathematics guides the cryptography that
keeps your credit card information secret.  In talking to
assistant professors of mathematics Sharon Garthwaite and Nathan
Ryan, one senses they are grateful for this application, because
it helps them to justify their field to non-mathematicians.
However, for them, the pure intellectual beauty of the theory,
and not potential applications, drives their research.  Modular
forms Both professors work with modular forms, which Ryan
explains not by describing what they are, but how they ave been
used. A famous mathematical puzzle, Fermat’s Last Conjecture,
had stumped mathematicians since the 1600s: Why does the
equation xn + yn = zn have no non-zero in