The Best Writing on Mathematics, 2013 eBook Ý The

5 thoughts on “The Best Writing on Mathematics, 2013

  1. Bojan Tunguz Bojan Tunguz says:

    I’ve always been fond of Mathematics and as a theoretical Physicist have taken a fair number of Math courses in college and grad school However since getting out of grad school my exposure to the Math world has been rather cursory to nonexistent That’s why I was really excited to come across this volume of interesting and insightful essays on various Math topics The nature of topics covered in this volume is very diverse It ranges from insights into the pure contemporary abstract mathematics to the applied Math of early scientific instruments Mathematics touches almost every aspect of scientific cultural and even artistic life and the selection of topics in this book reflects the protean nature of this metadiscipline Most of the essays are written in an accessible and easy to follow style and this book ought to be readable by the widest imaginable audience For a book on Mathematics there are surprisingly few euations and numbers This collection will especially appeal to readers who appreciate the cultural pedagogical and historical aspects of Mathematics One thing that I wish is that this collection contained articles on recent research and development in Mathematics Like many sciences Mathematics has become too complex and fragmented even for most of its practitioners A collection of essays that is aimed at an advanced layperson explaining what is exciting about the recent mathematical research would probably have a lot of appeal to a wide audience Another thing that I didn’t like about this collection is that there were two or three essays that I found completely rambling Their authors seemed to relish a pseudo intellectual discourse and tried to come across as very philosophical and intellectually profound Instead those essays felt really trite and vacuous Fortunately that kind of writing was in a distinct minority and did not really detract from the enjoyment of this volume However I would still expect a book that claims to be the “best” collection of mathematical writing to be completely void of such inanities

  2. Charles Daney Charles Daney says:

    Mircea Pitici the editor of this collection as well as three previous volumes in this series and additional volumes each succeeding year is a mathematical educator who is deeply interested in mathematical communication to professional audiences and to the general public source My review of the preceding volume for 2012 is herePitici states in the Acknowledgments of the 2012 volume The Best Writing on Mathematics 2012 that the responsibility for the eventual shortcomings in the final result is solely mine The writings selected as the best of the year do represent a variety of kinds of writing about mathematics such as non technical expositions of theoretical mathematical topics opinions about the teaching of mathematics essays on the history or philosophy of mathematics biographies of important mathematicians and descriptions of interesting real world applications of mathematicsProspective readers of these anthologies should realize that the selection is mainly the opinion of the editor alone who is not himself a working mathematician It's unclear how much reliance has been placed on the opinions of other reviewers Conseuently characterizing the selections as the best writings is a bit of a stretch Readers may find that many perhaps a majority of the selections don't address whatever interests them most about mathematics In particular readers will probably be disappointed if they mainly want to read about actual mathematics with euations and some technical details Most of the selected articles deal instead with peripheral matters such as mentioned above If your interest is in suchlike things you may be satisfiedThe very first volume in the series The Best Writing on Mathematics 2010 placed the selected writings in reasonable categories But in the next volume The Best Writing on Mathematics 2011 the editor states I gave up the thematic organization adopted in the first volume since some of the texts are not easy to categorize and some of the themes would have been represented by only one or a very few pieces This should alert a prospective reader to not feel that much has been missed if many of the selections are merely skimmed or skipped entirely based on the reader's particular interestsAs a consolation prize for the inevitable shortcomings of the selection process the editor thoughtfully provides in the Introduction a substantial list of Other Notable Writings These are all books 65 in this volume This alone helps justify the price of the anthology If you have any interest in math at all you should find in this list a few things worth your time and which provide much depth than a short article possibly could As a further sweetener the editor includes at the end of the volume a fairly extensive list of articles that were considered for selection this year but that did not make it into the book because of various constraints mostly related to the space available andor to issues of copyright As far as space is concerned it should be noted that this 2013 volume having only about 250 pages is the shortest of the series thus far by as much as over 150 pages in some cases Judging only from the titles it appears that 15 or so of the items in this list might have been much better choices for the present volume than most of the actual choicesAll that said I'll mention which of the 20 articles seemed best to me In first place hands down is Terry Tao's article on the surprising universality of a few simple mathematical laws that emerge out of situations of apparent great complexity Tao is one of the leading contemporary theoretical mathematicians a Fields Medal winner an expert in many branches of mathematics and a skilled expositor so anything he writes for a general audience is almost certain to be top notch In this case the laws he writes about include the law of large numbers the central limit theorem Benford's law and Zipf's law All of these deal with statistical distributions of various sorts of things one might not expect to exhibit the regularity that in fact exists This is much like statistical mechanics in physics where fairly simple mathematical laws turn out to describe the aggregate behavior of very large numbers of particles each of which individually has highly random behavior One common example from physics is random matrix models Whenever there is a collection of a large number N of things like particles one can form an N×N matrix out of numbers such as correlation distance or relative velocity relating any pair of things There sometimes appear to be simple laws that apply to the eigenvalues of such matrices In particular in the theory of prime numbers which is one of Tao's main interests the Riemann zeta function is a famous and very important object The Riemann Hypothesis deals with how the zeroes of this complex valued function are distributed The hypothesis is still unproven and is considered by many to be the most important unsolved problem in mathematics because the distribution of the function's zeroes is strongly related to how the prime numbers themselves are distributed Many number theorists suspect that a random matrix based on zeroes of the Riemann zeta function may provide a way to attack the Riemann Hypothesis The 2012 collection in this series has an excellent but short article by Tao on the general topic of Structure and Randomness in the Prime NumbersThere are several other articles in this collection dealing with probability and statistics Topics covered include randomness history and mistakes of calculating gambling odds and a rather terrible article on whether probability is relevant to valuing financial derivatives not the mathematical kind There's little depth to these articles but they may be of interest if probability is your thingIn second place for uality among the articles in the collection under discussion is Ian Stewart's Fearful Symmetry Stewart like Tao is a master mathematical expositor He wrote the Mathematical Recreations column for Scientific American from 1991 to 2001 has about 35 books on mathematical topics published for general readers and has authored or co authored 5 math textbooks Stewart's article in the present volume deals with how approximate symmetries arise in most multicellular plants and animals Symmetry is an extremely important concept in mathematics as well as in physics art etc and Stewart has written entire books on the subject e g Fearful Symmetry Why Beauty is Truth A History of Symmetry Symmetry A Very Short Introduction The present article actually says little in general about symmetry but it does explain somewhat the biological origins of symmetry as perspicaciously suggested by Alan Turing but having nothing to do with Turing machinesMy choice for third place among the articles is Machines of the Infinite by John Pavlus a seasoned science writer It's about the P vs NP problem which is the top unsolved problem of theoretical computer science and also one of the outstanding unsolved problems of mathematics Unfortunately there are few specific technical details such as what the classes P and NP actually are This vagueness will probably leave most readers unclear as to what the problem is and why it's so interesting and importantIn fourth place is An abc Proof Too Tough Even for Mathematicians by journalist Kevin Hartnett The abc conjecture was proposed only in 1985 but is of such generality that Fermat's Last Theorem finally proven only in 1995 is just a corollary as are at least three other proven but very deep results The exact statement of the conjecture is a little complicated though it doesn't involve any advanced math However the statement isn't uite as intuitive as FLT so most non mathematicians might wonder WTF is that about The article doesn't go much further than saying it's about a tight relationship between additive and multiplicative properties of ordinary integers What does make it especially interesting though is that in 2012 the reclusive but respected Japanese mathematician Shinichi Mochizuki claimed to have a proof based on some extremely highly abstract mathematics he developed which hardly any other specialists feel they understand yet haven't found to contain any obvious errorsAs for the remaining 16 articles in the collection yawn

  3. Wanda Wanda says:

    I was impressed by the breadth of these articles and appreciated how the technical detail was appropriate for each topic at hand ie not afraid to bust out formulae and a bit of light technical exposition For this reason I think my favourite articles of this collection were Bridges String Art and Bézier Curves and Slicing a Cone for Art and Science; in particular I thought that the discussion of Bézier curves in the context of architecture was fascinating and enjoyed the approach to coming up with a mathematical model for why the chords of the Jerusalem Chords bridge comprise a distinctly parabolic shapeWhy Mathematics What Mathematics and Math Anxiety were also pretty fantastic for their analysis of how math is taught at the lower levels and the impact that has on the areas of research given the most focus promoted through funding; there were echoes of this theme present in A Revolution in Mathematics where uinn gives an idea of how to reconcile education and research primarily through how we think about mathematics and how mathematics should be doneMy opinion of this collection was changed for the worse by the three final articles Errors of Probability in Historical Context The End of Probability and An abc Proof Too Tough Even for Mathematics there were small typographical errors in the first and it took some doing to follow their reasoning coming from someone with their MSc in computer science who is an amateur mathematician and has been exposed to this material in years gone by; the second was unreadable due to a lack of defining terms and incomprehensible expository style; the last was wholly unsatisfying due to being far too superficial and editorialIn short I highly recommend this collection and will be obtaining other entries in this series

  4. Charles Charles says:

    The phrase “best writing” in the title refers to the best expository writing nearly all of the content of all of the articles can be understood by the mathematically sophisticated high school student Many different areas are covered from mathematical history to probability the philosophy of mathematics and how to best teach it dealing with math anxiety to mathematics in the modern culture of 247 multimedia It is reasonable to say that any person that starts at page one and reads through to the end will find some essays fascinating and others somewhat boring However different people will find their sets of fascinating and boring to be different; such is the nature of the human mathematical animal My favorite essay was “High Fashion Meets Mathematics” by Kelly Delp It opens with the geometry of surfaces and describes how some unusual surfaces can fashionably be draped on a female body The real strength of this book is how it demonstrates the breadth of mathematics and how it permeates our very existence both in allowing us to understand nature and make things that conform to nature’s laws as well as how the human brain processes information Published in Journal of Recreational Mathematics reprinted with permission and this review appears on

  5. Alan Clark Alan Clark says:

    A wide range of subjects some about mathematics itself others about its history and applications and some are interesting than others They run the whole spectrum from easy to understand to heavy going

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The Best Writing on Mathematics, 2013 [EPUB] ✰ The Best Writing on Mathematics, 2013 By Mircea Pitici – This 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 M This annual anthology brings together the Writing on ePUB ↠ 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 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 The Best Epub / 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 Philip Davis offers a panoramic view of mathematics in contemporary society; Terence Tao discusses aspects of universal mathematical laws in complex systems; Ian Stewart explains how in mathematics Best Writing on PDF/EPUB ë everything arises out of nothing; Erin Maloney and Sian Beilock consider the mathematical anxiety experienced by many students and suggest effective remedies; Elie Ayache argues that exchange prices reached in open market transactions transcend the common notion of probability; and much much In addition to presenting the year's most memorable writings on mathematics this must have anthology includes a foreword by esteemed mathematical physicist Roger Penrose 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.