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 non-rigorous 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, as an outgrowth of
his own website at UCLA. This book is based on a selection of
articles from the first year of that blog. These articles discuss a
wide range of mathematics and its applications, ranging from
expository articles on quantum mechanics, Einstein's equation
$E=mc^2$, or compressed sensing, to open problems in
analysis, combinatorics, geometry, number theory, and algebra, to
lecture series on random matrices, Fourier analysis, or the dichotomy
between structure and randomness that is present in many subfields of
mathematics, to more philosophical discussions on such topics as the
interplay between finitary and infinitary in analysis. Some selected
commentary from readers of the blog has also been included at the end
of each article. While the articles vary widely in subject matter and
level, they should be broadly accessible to readers with a general
graduate mathematics background; the focus in many articles is on the
“big picture” and on informal discussion, with technical
details largely being left to the referenced literature.
Readership
Graduate students and research mathematicians interested in
broad exposure to mathematical topics, particularly in
analysis.
