There are many bits and pieces of folklore in mathematics that are
passed down from advisor to student, or from collaborator to
collaborator, but which are too fuzzy and nonrigorous to be discussed
in the formal literature. Traditionally, it was a matter of luck and
location as to who learned such “folklore
mathematics”. But today, such bits and pieces can be
communicated effectively and efficiently via the semiformal medium of
research blogging. This book grew from such a blog.
In 2007 Terry Tao began a mathematical blog to cover a variety of
topics, ranging from his own research and other recent developments in
mathematics, to lecture notes for his classes, to nontechnical puzzles
and expository articles. The first two years of the blog have already
been published by the American Mathematical Society. The posts from
the third year are being published in two volumes. This second volume
contains a broad selection of mathematical expositions and
self-contained technical notes in many areas of mathematics, such as
logic, mathematical physics, combinatorics, number theory, statistics,
theoretical computer science, and group theory. Tao has an
extraordinary ability to explain deep results to his audience, which
has made his blog quite popular. Some examples of this facility in
the present book are the tale of two students and a multiple-choice
exam being used to explain the $P = NP$ conjecture and a
discussion of "no self-defeating object" arguments that starts from a
schoolyard number game and ends with results in logic, game theory,
and theoretical physics.
The first volume consists of a second course in real analysis,
together with related material from the blog, and it can be read
independently.
Readership
Undergraduates, graduate students, and research mathematicians
interested in all areas of mathematics.
