(Disclaimer: I worked in derivatives on Wall Street for several years, though this book is more focused on stat arb, not my area.)

This book reminded...more(Disclaimer: I worked in derivatives on Wall Street for several years, though this book is more focused on stat arb, not my area.)

This book reminded me of When Genius Failed, not only in content matter but in style. This isn't a great thing, as I thought both books were hampered by some corny dramatics. In both cases the authors picked an inherently exciting topic; let the excitement tell itself and spend your energy telling us things we don't know rather than trying to inject more adrenaline into it. I'd rather the author kill every silly poker anecdote, every reference to the megalomania of Griffin and Asness, and instead talk some more about the basic principles of stat arb or convert arb, basic quant formulas and relative pricing approaches, I'm not expecting a textbook but when I read something I want it to walk away with as many new insights as possible.

The weirdest thing is the author's insistence on returning to the contrived theme of "The Truth," which far as I can tell simply refers to the ability to consistently beat the market, making it sound like Street quants were strange acolytes who thought of their work in reverent, near-religious terms. I've never met anyone who actually thinks like this; most quants or quantitative thinkers tended to think about their work with some scientific dispassion. Arguably that was actually the problem, because they were either too inflexible about violations of their assumptions (or failed to communicate the importance of flexibility to others), but I guess that didn't make as exciting of a story?

Style over substance, occasional insights clumsily wiped out by an unnecessary compulsion towards excitement. (less)

One of my pet peeves is the belief that "creative" people are those who study the humanities and that "analytical" types (as if "analytical" must some...moreOne of my pet peeves is the belief that "creative" people are those who study the humanities and that "analytical" types (as if "analytical" must somehow stand in opposition to creativity) are those who study sciences and mathematics. Perhaps this belief stems from a mathematics education grounded in rote, memorization, and dull exercises. The Mathematical Experience is about mathematics, but takes a much more philosophical tone, exploring the concept of proof and truth, the history of math, and the process of discovery/invention of new ideas and theorems. I enjoyed it very much.

The book takes the form of several essays, averaging a few pages long each. I particularly enjoyed:

- "Unorthodoxies," about crank ideas but also the possibility of valuable ideas appearing to be cranks at first. "The doors of the mathematical past are often rusted. If an inner chamber is difficult of access, it does not necessarily mean there is treasure to be found therein."

- The chapter on the Chinese Remainder Theorem, a really fantastic survey of the same idea as seen through different mathematical lenses over history.

- "Nonstandard Analysis" was a thought-provoking essay about the history of the infinitesimal dx - like most present-day people I had learned it as expressed in terms of limits (the Weierstrassian "reformation," as it were) but had no idea of the infinitesimal's controversial use in other proofs. Challenges the concept of rigor, as practically useful results were "proved" in non-rigorous ways; of what use, and how much use, is rigor, and what is the role of intuition? (This was a far better exploration of the topic than the chapter devoted explicitly to intuition.)

- The essays towards the end hammer a little over-long on the distinctions between Platonism (mathematics is universal, immutable truth "out there" that we discover), constructivism (we invent mathematics, and objects must be constructed for their existence to be proved), and formalism (math is just a set of rule manipulations that does not encompass philosophical questions). But I did find the initial discussion of it to be very interesting.

- The two computer-oriented essays, "Mathematical Models, Computers, and Platonism," and "Why Should I Believe a Computer?" I think it would be wonderful if a mathematician with writing talents would update this book with more about how computers have influenced the development of mathematics. (less)

A nondescript biography of Isaac Newton that nearly exemplifies what I'd consider to be an average book. There's no particular focus on one aspect of...moreA nondescript biography of Isaac Newton that nearly exemplifies what I'd consider to be an average book. There's no particular focus on one aspect of his life or another; it's a fairly straightforward treatment, almost like a long Wikipedia article, with many tidbits brought up here and there but no particular facet explored too deeply.

This is not in and of itself a problem but I think that if a writer wants to take this approach, he has to do a really good job of grabbing the reader by the collar and making his subject compelling. I don't think Gleick does this consistently. Occasionally promising items, such as his adversarial relationships with Hooke and Leibniz, his tendency towards secretiveness to the point of ciphering his findings in his correspondences, or his internal struggles with the doctrine of the Trinity, are too often briefly discussed and put aside. If you're going to take this approach, you need to make every anecdote and every remark memorable, lest you fall into a laundry-list pattern.

If I were Gleick, I would have focused around a really interesting idea that (like too many other things) he only mentions briefly, which is John Maynard Keynes's quotation that "Newton was not the first of the age of reason.... He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago." This is a great central theme - not merely Newton as the bridge between magic and science, but Newton himself belonging clearly on the ancients' side of that bridge. Subjects like Newton's intense religious struggles, his practice of alchemy, and the incipient disentanglement between philosophical metaphysics and modern physics would branch nicely from this idea. Perhaps this biography has already been written by someone prior to Gleick, but if it hasn't, it unfortunately wasn't written by him either. (less)

Richard Feynman, in addition to being one of the most important physicists of the 20th century, was also a colorful guy, intellectually curious, admir...moreRichard Feynman, in addition to being one of the most important physicists of the 20th century, was also a colorful guy, intellectually curious, admirably forthright, and cheerfully dorky. This book is a collection of his reminiscences, in chronological order, covering the span of his life from his youth to his older years.

Feynman serves as a humorous narrator to his own anecdotes, although with some tendency to ramble. His unquenchable interest in learning and teaching, his willingness to keep an open and prejudice-free mind, and his fondness for being a sort of honest prankster lead him into a lot of funny situations. A very enjoyable read, mostly great stories with a few lesser ones that Feynman still gets you through with a few laughs and winks. (less)

There are famous math problems that are easy to explain but difficult to solve, such as the four-color map problem or Goldbach's Conjecture; the Riema...moreThere are famous math problems that are easy to explain but difficult to solve, such as the four-color map problem or Goldbach's Conjecture; the Riemann Hypothesis is unfortunately not such a problem. Prime Obsession is author John Derbyshire's attempt to explain the RH in simple terms and to illustrate its place and importance in the history of mathematics. It's not an easy task, and I think what Derbyshire has written is suited for a relatively narrow audience of people: those who took some analysis or at least calculus in school but who didn't go on to enough pure maths to have already learned about the RH.

I fall under this category. The book did succeed in explaining the RH to me. But I do not think it imparted an adequate appreciation of why it is such an important problem. Some of the other results in the book, such as Euler's theorem (the "Golden Key") or the existence of Littlewood inversions, seemed to me to be more interesting or elegant. In particular, I do not know except in brief passing reference what mathematics would depend on the RH, and I do not know what the ramifications of a disproof would be. Towards the end Derbyshire goes very quickly through newer, complicated physics-based advances regarding the RH, leaving little possibility for deep understanding; I would have gotten rid of this section in favor of deeper coverage of the RH's consequences, even if this meant that we wouldn't be covering math newer than the 1930s.

Nevertheless I generally enjoyed the book. But then again I fall in the narrow audience mentioned above. If you are more mathematically advanced than I am, you may find this book entertaining but too basic. If you are less so, you may not even understand the RH properly at all, which is supposed to be the main purpose of the book. Rather than communicating the intuition and big picture, Derbyshire sometimes takes more of a procedural, step-by-step approach which he "babies" a bit to help along laypeople. This does help get the casual reader from point A to point B but is not going to leave a framework of true understanding in the reader's mind.

The odd chapters are more strictly mathematical and the even chapters are more historical. The history chapters for the most part can be digested and enjoyed by anyone, so even for relative math-phobes, half of this book will be pretty readable. Derbyshire does a very good job here of depicting the real people behind the theorems, not only with regard to their personalities but how their lives fit into the greater context of world history. I found the discussion of the great mathematicians' patrons to be particularly good. (less)

Before reading this, I'd heard it often described as a book discussing the similarities between music, art, and math. I've since found that to be a fa...moreBefore reading this, I'd heard it often described as a book discussing the similarities between music, art, and math. I've since found that to be a fairly incomplete (!) description; it's really more about the theme of self-reference and how it is manifested in those three disciplines as well as other areas, such as biology and artificial intelligence. The latter is particularly important, as Hofstader's "greater idea" here is that the concept of self-reference goes a long way towards the idea of consciousness and uniting the concepts of free will and determinism.

The book alternates between chapters that directly discuss self-reference like a "normal" book and short fictional dialogues between characters Achilles, the Tortoise, and some other friends (including, at one point, the author himself). The dialogues are slam-bang amazing, constituting some of the most delightful and witty writing that I have ever had the pleasure of reading. The rest of the book, its "meat," is still excellent, although I think it could have been shortened. Occasionally Hofstader stretches too much to draw his links between his disparate subjects. But there is a lot of terrifically fertile intellectual ground to tread upon here. (You might even say that the grounds are excellent!)

The size of the book and the fact that it directly uses formalized mathematics (although with as gentle a touch as possible for the general audience) may make this a daunting book to read. I recommend it for everyone though, particularly those without pre-existing backgrounds in logic/CS/math, as its ideas are too important, and its presentation too well-done, to pass it by. (less)