I wanted a book on why the universe seems to be explicable in terms of math at a deeper philosophical level. Instead I got a decent history of physicsI wanted a book on why the universe seems to be explicable in terms of math at a deeper philosophical level. Instead I got a decent history of physics that covers some familiar ground (the birth of relativity and quantum mechanics) and some unfamiliar ground (recent mathematical advances in gauge theory), with the combination of capsule biographies and light explanations that are not enough to fully explain.
What made the book a little more than that was the overarching narrative about the different styles of physics, experimental, theoreticians responding to experiments, and theoreticians who treat mathematical beauty as an end unto itself. Graham Farmelo argues that Einstein and Dirac were exemplars of this last approach and their modern heirs are string theorists who are working entirely unmoored from experiments or even commonsense reality, but Farmelo is still betting on them because of the mathematical beauty of their approach. Over the course of the story, Farmelo describes a period of falling out between math and physics and how they came back together again that I had not previously been aware of.
This book is much too short to accomplish it's goal--which is to explain Andrew Wiles proof of Fermat's Last Theorem and to ground that explanation inThis book is much too short to accomplish it's goal--which is to explain Andrew Wiles proof of Fermat's Last Theorem and to ground that explanation in the history of mathematics. Simon Singh's Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem does a much better job but even that falls short. In contrast to Singh's explications that really try to explain the concepts, Amir Aczel presents more of a capsule series of biographies of the many mathematicians over the last several centuries whose work converged in the proof of Fermat's Last Theorem. He tries to explain some concepts with words and figures but the explanations themselves are too elliptical. The individual pieces of the book are interesting and often entertaining enough. And the argument that you need to understand all of mathematics to understand the proof of Fermat's Last Theorem is also driven home with overwhelming force. But I was hoping for something more....more
I have been captivated by Alan Turing’s story ever since I saw Derek Jacobi perform it in Breaking the Code. The Imitation Game movie almost ruined itI have been captivated by Alan Turing’s story ever since I saw Derek Jacobi perform it in Breaking the Code. The Imitation Game movie almost ruined it. But this book does not share much more than a subject and a title, it is much better.
I really like the Jim Ottaviani scientific biographies in graphic novel format ostensibly aimed at YA readers (Feynman, Hawking, and Primates: The Fearless Science of Jane Goodall, Dian Fossey, and Biruté Galdikas) and this one was no exception. This was probably a higher ratio of life to works than the others with Jim Ottaviani making less effort to explain Alan Turing’s major contributions and doing more to showcase his life. But it is quite a life.
I say ostensibly YA because all of the biographies are relatively sophisticated in a variety of ways: flashbacks, imaginary scenes, someone narrating interspersed with the stories, somewhat complicated themes that do not whitewash some of the more sordid personal details, and most importantly a lot of attempt to explain the science....more
A fantastic book about calculus. A blend of the history of the development of calculus, its applications, and intuitive explanations of its power fillA fantastic book about calculus. A blend of the history of the development of calculus, its applications, and intuitive explanations of its power filled with nicely intuitive explanations that will either provide a refresher or a different way of understanding what you have already learned.
Steven Strogatz proceeds in (sort of) chronological order, defining calculus not as what you learn in school but any technique that breaks things apart into infinitesimal pieces and puts them back together again in order to solve problems. Rather than describing an immaculate conception of calculus by Leibniz and Newton, Strogatz starts with Archimedes, shows several geometric applications, and even spends a lot of time on Descartes and Fermat before even getting to what we consider calculus today. In all of these he shows how a combination of abstract ideas but also in many cases practical problems led to the development of calculus.
The chronological order is interrupted (in a good way) by Strogatz’s many descriptions of the applications of calculus to different practical problems, most of which are in the analytically relevant chapter. These include GPS, AIDS drugs, rocketry, and more. In all of these cases Strogatz shows his pedigree as an applied mathematician, going into significant but highly readable detail about the models and discoveries underlying these areas.
Overall, the book is very nicely written and highly recommended....more
This was a long, strange trip through the statistical analysis of causation. Judea Pearl writes beautifully and in an almost grandiose manner, dubbingThis was a long, strange trip through the statistical analysis of causation. Judea Pearl writes beautifully and in an almost grandiose manner, dubbing himself a Whig historian of the science of causation--how it was forgotten by statistical analysis that put correlation at the pinnacle of analysis, how it was rediscovered later, and in particular the importance of structural models that combine an understanding of the world with the data--but do not just let the data speak for itself. The book combines a history of science with a number of specific examples (e.g., do cigarettes cause cancer or does an algebra program in Chicago increase math knowledge) along with some of the mathematics of his method. But mostly Pearl's method centers around writing causal diagrams with arrows that allow you to identify blockers, cofounders, and the like. The arrows and terminology was not familiar to me from econometrics but many of the conclusions and techniques were (e.g., RCTs, multiple regression and instrumental variables).
In some cases Pearl claimed a greater profundity than I was able to follow, for example I could understand the Bayesian interpretation of his argument but he claimed there was a bigger one. In other cases he claimed that his diagrams opened up entirely new paths to solving causal questions and understanding the results of statistical analysis. In all of these cases I confess that I mapped them into my previous understanding rather than expanding, changing, evolving my previous understanding--and am unsure if this represents my limited understanding of his book or his overclaiming about his ideas, many of which were well understood and implemented in econometrics before.
The last chapter on AI, free will, explicability, and correlation vs. causation in big data was quite interesting but a bit of a departure from the rest of the book.
Overall, would recommend this to economists or others who are very interested in statistical analysis, it takes some effort at times (nothing like a textbook, which would be the best way to assess the novelty of some of the ideas), but amply rewards it....more
The best portrait of what it means to do research--especially abstract mathematical research--that I have ever read. It might even top G.H. Hardy's A The best portrait of what it means to do research--especially abstract mathematical research--that I have ever read. It might even top G.H. Hardy's A Mathematician's Apology.
Cédric Villani does not tell but instead shows. Specifically, through a combination of diary entries, reprinted emails, and other material, he shows the almost daily process of collaboration that over the period of about a year led from a rough idea to a published paper. The progress depends on his own curiosity, his talks with colleagues--whether it is someone down the hall who notices a link in an equation on his whiteboard or the brutal comments he gets from seminars and referees. And his progress depends on lots and lots of work, dead ends, and returning to basics in new areas.
I say that Villani shows but not tells because he makes no attempt at all to simplify any of the complex mathematical language and even includes pages and pages of equations. There is no expectation that the reader will come close to following these (in fact, he writes that even mathematicians outside of his speciality would not follow most of it). But that is not the point. The book does not leave you thinking that you understand mathematics in general or even the theorem that he spends 250 pages discussing--I still have only a faint idea of what it is about and an even fainter idea of how it was proven. But the book does leave you with a much better understanding of how math is done.
The book also has a certain poetry to it, highlighted by the fact that it is literally interspersed with the occasional poem or discussion of the manga or Neil Gaiman that Villani is reading. But even these interludes are as much about how the mind can and can't switch between topics as it is about the topic Villani is switching to....more
I don't regret being baited and switched into reading this book. And I have only myself to blame for being baited and switched. I expected the book t I don't regret being baited and switched into reading this book. And I have only myself to blame for being baited and switched. I expected the book to be more about Ramanujan but instead it was mostly a memoir of a mathematician named Ken Ono. But the fulcrum of the book is Ramanujan. Ono was brought up by Japanese immigrant "tiger parents" who pressured him into being a mathematician. He rebelled to the point of dropping out of high school. But then he found a letter that Ramanujan's widow sent to his father thanking her for a donation to build a statue of him and that set his mind off--with a lag--so that he found himself constantly coming back to Ramanujan, both his life and his specific, unproved ideas. The book includes a 50 page mini-biography of Ramanujan and an appendix that attempts to explain some of his specific ideas. What makes the memoir so interesting is that it is not about a top mathematician but instead about someone struggling to join the profession and contribute and about the struggles, semi-failures, and semi-successes that go with it. My disappointment was that, other than the appendix, it attempts to cover very little of the substance of Ono or Ramanujan.
And if you are looking for a biography of Ramanujan, The Man Who Knew Infinity is one of the best scientific biographies ever written about an amazing and glorious and tragic life and mind....more
The Signal and the Noise was a really great read. It's one of those books that lets you annoy your friends by tediously repeating facts, many of whichThe Signal and the Noise was a really great read. It's one of those books that lets you annoy your friends by tediously repeating facts, many of which they already have picked up from reading the book, reading reviews, or other tedious friends. Like when the Weather Channel says it is a 30% chance of rain it rains 30% of the time, but that when it says a 10% chance of rain it really means a 3% chance of rain (they would rather people be pleasantly surprised). Or that earthquakes are unpredictable. Or that minor league baseballs players are difficult to predict and give a good advantage to very good scouts, while in the majors it is different. Or that a particularly great professional sports better will win 56 percent of the time. Or other examples drawn from the areas Nate focuses on: political predictions, elections, the macroeconomy, financial markets, epidemics, earthquakes, terrorism, baseball, chess, and poker.
There is a deeper and more important set of lessons in the book to anyone that has not been sufficiently exposed to Bayesian methods. None of that was new to me, but it is still interesting to read and should be mandatory reading for anyone who has not been exposed to it before.
I take some issue with the presentation of economics. Nate is completely right that macroeconomic forecasting has a terrible track record, and does not even appreciate how terrible its own record is. But he doesn't seem to recognize that there is a lot more to economics than macroeconomic forecasts. And, at least as much of the fault with those forecasts lies with the people demanding and using them as with the people providing them.
And I'm not quite as impressed with Nate's election forecasting--anyone relying just on public polls taken in the days before the election would have correctly picked 49 or 50 of the 50 states in both 2008 and 2012. Nate did not have any magic, but he did have much better perspective on the uncertainty in the forecasts and how to read/interpret the significance of movements well in advance of election day.
But those are quibbles, this book really deserves wide readership, probably starting with all of those who rushed out to buy it after the election and still have it sitting on their shelves....more
A Mathematician's Apology has been on my mental reading list for a long time and, like many titles on that mental list, I cannot understand how I didnA Mathematician's Apology has been on my mental reading list for a long time and, like many titles on that mental list, I cannot understand how I didn't read it before. The edition contains a 50 page Foreword by C.P. Snow followed by the 90 page book by Hardy (actually, adjusting for different font sizes, the two parts are probably about equal in length). I read the book first so that I could think about it on its own terms and the Foreword afterwords. Both of them are outstanding and I would recommend reading them in that same reverse order.
Hardy wrote A Mathematician's Apology in the twilight of his career when he no longer was a creative, productive mathematician--and one of the many apologies in the book is the very notion of writing about what mathematics rather than actually doing mathematics. He conveys an enormous love and wonder for the discipline, illustrates it with sketches of some proofs, reflects back on his own work and his partnerships with Ramanujan and Littlewood, and discusses the purpose or lack thereof for mathematics. The book itself beautifully conveys the creativity and beauty of mathematics and the process and drive that leads people to do it.
C.P. Snow's Foreword is a mini-biography of Hardy, the almost novelistic story of Snow's friendship with Hardy (which begins and ends with discussions of cricket, starting when they met in the dining hall at Cambridge and ending on Hardy's deathbed), and a critical appreciation of A Mathematician's Apology....more
Sharon McGrayne is a very good and engaging writer. She has an interesting story to tell about the last 250 years of Bayesian thinking, how the theorySharon McGrayne is a very good and engaging writer. She has an interesting story to tell about the last 250 years of Bayesian thinking, how the theory has developed, and its many applications including how to price insurance, how to aim artillery, how to break the Enigma code, who wrote The Federalist Papers, how to find Russian nuclear subs, how to estimate the probability of a shuttle disaster, when to do various cancer screenings, whether cigarette smoking is harmful, etc. She also has a great set of characters, a parade of statisticians who are more colorful than I could have imagined, from the pioneers of Bayes, Price and Laplace to most recent statisticians like Cornfield, Tukey and Mosteller.
But, the book is deeply flawed and disappointing because it does so little to actually explain Bayes Theorem, how it was applied, how it led to different confusions than frequentism, and how the two have recently been theoretically synthesized. Most of this is not very complicated, one knows a decent amount already, but it would be more interesting to understand hot it was applied. Instead, the book concentrates much more on personality and the more surface descriptions rather than dwelling deeper and working out at least a few examples in more detail, both more of the theory from first principals but also better understanding what data and calculations various of her protagonists were using. Absent that, the book is often literally superficial.
Still, the book has a lot of upside -- but given that there is not exactly a huge selection of books covering this ground (unlike, say, quantum mechanics) to have this as nearly the sole choice is disappointing....more
Fermat's Last Theorem begins with Pythagoras, goes through Fermat's positing of his theorem, the attempts by Euler and others to solve it, and culminaFermat's Last Theorem begins with Pythagoras, goes through Fermat's positing of his theorem, the attempts by Euler and others to solve it, and culminates with Andrew Wiles's solution. It is generally entertaining and has the occasional equation, with a few more in the Appendix. But most of the relatively light analytical machinery in the book is devoted to ancillary problems or general illustrations, Singh does not even go beyond an extremely superficial description of the main feature of Fermat's proof in the case of n=4. Instead a lot of the space is filled with detours that are often found in these sorts of books, from the role of women in French mathematics in the 19th Century to the puzzle fad in the early 20th Century. In that way this book fell short of Singh's Big Bang which felt more focused and a little more thorough in trying to describe how scientists discovered what they did about the big bang....more
A really fantastic book. I appreciated a biography that had a lot of equations. But even without the equations not only was Ramanujan a wonderfully drA really fantastic book. I appreciated a biography that had a lot of equations. But even without the equations not only was Ramanujan a wonderfully drawn portrait but it also really conveyed collaboration and the very interesting story of Hardy as well....more
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