The Best Writing on Mathematics 2012 by Mircea Pitici (PDF)

Description

The year’s finest writing on mathematics from around the worldThis annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2012 makes available to a wide audience many articles not easily found anywhere else–and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more.In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematician David Mumford and an introduction by the editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us–and where it is headed.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐After 8 years of outstanding work, Pitici has outdone himself in this wonderful edition. The stated objective of this series is to collect the best “lay accessible” articles in one place. In doing so, Mircea has to balance pure and applied, too specific vs. too general, and similar to “science” collections, balance the applications themselves between the obvious ones in physics with the less obvious in biology, photography and even dance! In addition, it’s now a tradition to include a little philosophy and education too.Topic summary:Foreward and Intro: MUST reads as AWESOME surveys of the “state of the field” in late 2012– cutting edge topics you’ll find collected nowhere else like octonions, perverse sheaves, monster groups and inaccessible cardinals! Also as usual– EVERY author included has a tone of fun and genuine humility, like Mumford, who says “The distinction between mathematics and physics is blurred and that between pure and applied is unknown.” When you’re just about satiated after the breadth and depth of the intro, Pitici then gives “brief reviews” of 92 additional books that he loved but didn’t use– a mind blowing collection that will totally exhaust your Amazon budget for the year.Content: Why math works (Livio!); Discovery or Invention?; Unplanned Impacts; N Dimensions; Primes; String Theory; Photography; Dance; The “sound” of a theorem; Origami Tessalations; The path from HS Calc to University Analysis (worth the price of the entire volume for our future in STEM); Teaching (5 more articles); History of math vs. science; De Morgan; Routing/traveling salesman problems; Cycloids/Bernoulli; Cantor; Philosophy; Infinite logic and finally: mating and dating: the math of the wedding game!What fun, yes? WAY worth the price here alone, but then wonderfully augmented with notes, articles that were NOT included, and the aforementioned list of top new book choices in numerous state of the art areas. I’ve hungrily looked forward to each edition, and have to say that this latest anthology has the most consistent quality of them all. This edition also continues the “creep” of including more and more formulas that aren’t really “lay” oriented– but with hard work a determined lay reader can “get” them. The topics go beyond undergrad, but the math doesn’t. And the facts and analogies are truly beautiful and wonder inspiring. Perhaps Pitici’s greatest contribution as an editor IS his love of beauty and wonder– it informs every choice with those most precious of take aways– inspiration and astonishment at where we’re at, and where we’re going. A little dose of this given all the “bad” news we see all day can’t hurt!!

⭐I despised the class I needed this book for bc we only needed it for 30 min of one class, other that it seems like an okay book

⭐A very useful book for math-teachers, both for the youngest and the mature students. The discussions about “why? and what for?” can be lifted above the usual level where “like and like not” own the arena. Also interesting for philosophical oriented teachers withlimited experience in the subject as such. (Probably most mathematicians live in peace with the fact that they don’t know it all.)Have been in the business for 45 years and liked the challenges and the “news” I also find in the book.

⭐The Best Writing on Mathematics 2012Mircea Pitici, Editor “All of us mathematicians have discovered a sad truth about our passion: It is pretty hard to tell anyone outside our field what you get excited about!” is the opening sentence of the forward to Pitici’s book. The claim that the author has stepped up to the plate with a terrific collection of answers to this query is well deserved.Surprisingly informal, some contributions are more thought process than strict logic. Leaving accolades to other reviewers here are some departures from expected mathematical discipline:Mario Livio, an astrophysicist:* Livio “posits” that both invention and discovery play a crucial role in why math works so well. Perhaps, but he goes on to state “Although eliminating the dichotomy between invention and discovery does not fully explain the unreasonable effectiveness of mathematics, the problem is so profound that even a partial step toward solving it is progress.” It is not clear that this explains anything at all or why it is a “partial step”.* “Issac Newton formulated calculus largely for the purpose of capturing motion and change, breaking them up into infinitesimally small frame-by-frame sequences. Of course, such active inventions are effective; the tools are, after all, made to order.” Why “of course”?* “Is mathematics invented or discovered? And what gives mathematics its explanatory and predictive powers? I believe that we know the answer to the first question: Mathematics is an intricate fusion of inventions and discoveries.” Well, he is free to “believe” anything. He goes on: “I truly do not know the answers, except to note that perhaps in a universe without these properties, complexity and life would have never emerged, and we would not be here to ask the question.” Oh, dear!Timothy Gowers, a Royal Society Research Professor at the University of Cambridge awarded the Fields Medal:* “If mathematics is discovered then it would appear there is something out there that mathematicians are discovering …”* “… one must be clear what it means to say that some piece of mathematics has been discovered, and then one must explain, using that meaning, why a Platonist conclusion follows. I do not myself believe that this program can be carried out, …” Belief again!* “… it is often said that Newton and Leibniz independently invented calculus. I planned to include this example, when quite by coincidence, on the day I am writing this paragraph, there was a radio program about their priority dispute, and the word “invented” was indeed used”. So what?* “If you type the phrases “complex numbers were invented” and “complex numbers were discovered” into Google, you get approximately the same number of hits (between 4,500 and 5,000 in both cases), so there appears to be no clear answer. But this too is a useful piece of data.” Useful or useless?* “I claimed earlier that the formula for the quadratic was discovered, and when I try out the phrase “the invention of the formula for the quadratic,” I find I do not like it, …”. What does this prove?* “If they could refer to the monster group at all, then does this not imply that it existed?” If only!Ian Hacking from the College de France, Paris:* “Mathematics is the only specialist branch of human knowledge that has consistently obsessed many dead great men in the Western philosophical canon.” “Only” is a bold claim even if the “dead great men” were alive.* “”Experiencing mathematics” in no way implies the possession of philosophical gifts – perhaps the opposite.” Why does it imply either?* “I now suggest that the reasons why there is philosophy of mathematics divide roughly in two. The experience of proof figures in both, but in different ways. For convenience I label one Ancient and the other Enlightenment.” For convenience and for bias?* In discussion Hacking quotes Jean-Pierre Changeux and tells us “he is a neurobiologist with access to the cognitive sciences”. Oh dear, how can we possibly argue against him?* “I think that what Changeux says is wrong – “mathematical objects exist materially in the brain” – but what he means is right. He means that the structures Connes so admires are by-products of our genetic envelope (a phrase I got from Changeux himself, but which he seems not to use in print).” And best left out of print!* “Starting with the idea that “to be is to be the value of a variable” … This is an interesting debate, but only to philosophers …Yet it has never moved a mathematician or a member of the republic of letters, outside the narrow confines of academic philosophy, to budge in favor of Platonism.” “Only to philosophers”? “Never”? Never, ever?* “Logical necessity, as we know it, is an invention of the modern era, derived from concepts of medieval Islam and Christendom, and harking back to very different notions in Aristotle. Of course, it ties in with the Ancient astonishment with proof, for we seem to prove things that must be true, cannot be otherwise. And how can this be?” “Of course”? And mathematicians often prove things to be true unexpectedly, things we thought otherwise.Malcolm Cameron6 October 2013

⭐I’m sorry to report that this book should not be purchased for the Kindle. It’s well-written and diverse, but the equations do not scale up and down when one scales the fonts, and they are inevitably too gray, too faint, and too small to be read. I’m looking forward to reading the book in hard copy. (I should point out that I have one of the old, black and white, non back-lit Kindles. Your mileage may vary.)

⭐If you like to read mathematics and are wondering what others are doing this is a good read. I have the last few years worth and will continue to get them as long as they pursue their current level of quality.

⭐Book was as described, and delivery was fast.

⭐Apart from the quality articles presented, the bibliography containing references (some annotated) to all the material the author reviewed in assembling this collection is astounding; it is worth buying just for that. A marvellous source for delving more into subjects of particular interest.

⭐Great!

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