This is the third Selecta of publications of Elliott Lieb, the first two
being Stabil- ity of Matter: From Atoms to Stars, edited by Walter
Thirring, and Inequalities, edited by Michael Loss and Mary Beth Ruskai.
A companion fourth Selecta on Statistical Mechanics is also edited by
us. Elliott Lieb has been a pioneer of the discipline of mathematical
physics as it is nowadays understood and continues to lead several of
its most active directions today. For the first part of this selecta we
have made a selection of Lieb's works on Condensed Matter Physics. The
impact of Lieb's work in mathematical con- densed matter physics is
unrivaled. It is fair to say that if one were to name a founding father
of the field, Elliott Lieb would be the only candidate to claim this
singular position. While in related fields, such as Statistical
Mechanics and Atomic Physics, many key problems are readily formulated
in unambiguous mathematical form, this is less so in Condensed Matter
Physics, where some say that rigor is "probably impossible and certainly
unnecessary". By carefully select- ing the most important questions and
formulating them as well-defined mathemat- ical problems, and then
solving a good number of them, Lieb has demonstrated the quoted opinion
to be erroneous on both counts. What is true, however, is that many of
these problems turn out to be very hard. It is not unusual that they
take a decade (even several decades) to solve.
