Structure and Randomness: pages from year one of a mathematical blogShare this page
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.
Table of Contents
Graduate students and research mathematicians interested in broad exposure to mathematical topics, particularly in analysis.
Tao does a fine job of providing new insights into old ideas, building intuition about why results come out the way they do, exploring why certain problems are at once interesting and hard, and explaining tricks. ...Tao has a book, and a blog, that mathematicians will definitely want to read, either on their screens or on dead trees, and it will be of interest to mathematically sophisticated readers coming from physics, statistics, economics, computer science and doubtless other disciplines. In Structure and Randomness we have a fascinating glimpse into the mind of one of the best mathematicians working today.
-- Cosma Shalizi, American Scientist