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The Mind of the Mathematician

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R and mathematical ability and the impact of autism personality disorders and mood disordersThese topics together with a succinct analysis of some of the great mathematical personalities of the past three centuries combine to form an eclectic and fascinating blend of story and scientific inuiry. There are two parts to this book The first is about psycho

Free read ë PDF, eBook or Kindle ePUB · Michael Fitzgerald

What makes mathematicians tick How do their minds process formulas and concepts that for most of the rest of the world’s population remain mysterious and beyond comprehension Is there a connection between mathematical creativity and mental illnessIn The Mind of the Mathematician international. The book is a welcome attempt to use insights from psychol

Michael Fitzgerald · 6 Free read

Ly famous mathematician Ioan James and accomplished psychiatrist Michael Fitzgerald look at the complex world of mathematics and the mind Together they explore the behavior and personality traits that tend to fit the profile of a mathematician They discuss mathematics and the arts savants gende. This book concerns mathematicians' behaviors and personali

  • Hardcover
  • 196
  • The Mind of the Mathematician
  • Michael Fitzgerald
  • English
  • 03 May 2018
  • 9780801885877

5 thoughts on “The Mind of the Mathematician

  1. says:

    The book is a welcome attempt to use insights from psychology and related fields together with biographical examples to explain how the minds of outstanding mathematicians work in order to come up with important mathematical breakthroughs The first author Michael Fitzgerald is a psychoanalyst and professor of psychiatry The second author Ioan James is a mathematician who's been an important contributor in the fields of geometry and topology There's a lot of good information in their book but it still falls somewhat short of illuminating the central uestionsHere are three of the key uestions 1 How did the minds of exceptional mathematicians like Gauss Poincaré and Hilbert function in order to produce their extraordinary results? 2 Were there specific mental methods techniues habits or practices these people used? 3 Are there specific and identifiable positive or negative psychological traits or biographical details that these historical masters have in common?The book offers some answers to each of these uestions In a scant 160 pages the authors don't seriously attempt to provide new or better answers beyond what has been discussed among mathematicians for hundreds of years without a lot of definitive conclusions But the book does provide a decent survey of some of the proposed answersThe first part of the book which is not uite half by page count and may have been written mostly by Fitzgerald is a tour of the literature that deals with three topics 1 the nature of mathematics as a discipline and the milieu in which research mathematicians operate; 2 the nature of mathematical ability and the specific skills it comprises; 3 the dynamics of mathematical creation how creativity in mathematics has both similarities and differences with creativity in other pursuits such as art music and literature Numerous entire books have been written on each of these topics The discussion in this book occupies all of 60 pages so it's necessarily a very compressed and selective summaryThe second part of the book which was probably written mostly by James offers very brief biographical summaries of 20 historically outstanding mathematicians That works out to an average of about 5 pages per person The subjects are highly exceptional individuals who worked mostly between 1750 and 1950 and whose lives for the most part were far varied and eventful than average So the material presented on each can hardly scratch the surface of personal lives that are uniue than 99% of the population might imagine Not only that but readers interested in mathematics likely to be the vast majority of the book's audience will find almost no details of the most noteworthy contributions of each person describedIoan James a few years earlier authored another book Remarkable Mathematicians From Euler to Von Neumann that profiles 60 outstanding mathematicians from roughly the same time period That's 7 pages per person so it's almost eually sketchy In both books the descriptions despite their brevity are mostly interesting lively colorful and well written But they're probably not too helpful for deriving useful general conclusions especially since little reliable biographical information is available for most of the subjects who worked in the first half of the time period Of the 20 mathematicians profiled in the book reviewed here all but 4 are also in the second book The exceptions are Ada Byron Lovelace R A Fisher Paul Dirac and Kurt Gödel What's common to these 4 is having contributed somewhat less to pure mathematics despite outstanding contributions in somewhat peripheral fields The slightly longer profiles in the second book have mathematical detailsSo in spite of the brevity of the book under review are there interesting general conclusions that can be drawn? Yes of course Firstly almost all the individuals profiled are extremely unusual and atypical of the general population But this is to be expected because of the selection bias inherent in dealing with people who've made contributions of historic proportions to the difficult abstruse field of mathematics Most contemporary professional mathematicians have certain peculiarities too but hardly to the same extentUnsurprisingly almost all the profiled mathematicians seem to possess exceptionally high general intelligence This again is to be expected from the selection bias even though the high intelligence is not simply in the mathematical sphere Many of the individuals also had exceptional memories and ability to concentrate Many were geniuses or prodigies in that they were recognized as unusually intelligent at a young age Many entered college or euivalent when unusually young and entered a professional mathematical career also uite young Other indications of high general intelligence were things like mastery of a number of foreign languages and noteworthy talent in non mathematical areas such as teaching music or other scientific fields Some also completely lacked such talents especially teaching However few individuals also had success in certain other fields such as law politics business or philosophy This is understandable since notable success generally reuires devotion of a considerable portion of one's time which would then be unavailable for mathematics In earlier eras people like Descartes Fermat Pascal Newton and Leibniz had great accomplishment in fields outside of mathematics But increasing specialization is certainly the historical trendIn a few cases some of the profiled mathematicians had only mediocre achievements or even disastrous failures in other aspects of their lives Galois couldn't stay out of trouble as a political radical and managed to get himself killed in a duel possibly of a suicide? before his 21st birthday Ramanujan had difficulty finding employment in India and could hardly cope with life in England Both Cantor and Gödel had distinct episodes of mental illness that left them unable to do mathematics for long periods of timeIndeed most of the individuals profiled had significant difficulties or abnormalities in dealing with other people Skillfulness in handling normal human interactions is generally not something that outstanding mathematicians are known for though there are exceptions to this too Cauchy was known for arrogance and religious zealotry Gauss for aloofness Hardy for evidence of insecurities Riemann for shyness and difficulties relating to people Wiener for strange behavior and Dirac for general strangeness The Strangest Man The Hidden Life of Paul Dirac Mystic of the Atom On the other hand a few were uite socially adept such as Jacues Hadamard and Emmy NoetherThere seem to be two types of psychological dysfunction that are often present to some degree or other in the examples presented Fitzgerald as a psychiatrist evidently took special notice of these One is cyclothymia mild bipolar disorder which involves mood swings between depression and mania It's impossible to figure out from the examples presented whether this is prevalent or less among outstanding mathematicians compared with the general public Determining that reuires an extensive study of living examples and the sample size of top mathematicians is likely to be rather small Additionally it isn't clear whether or not phases of either depression or mania could actually be helpful or harmful to mathematical productivityThe other dysfunction that may be relevant is the now famous Asperger syndrome There are a number of different diagnostic indicators of AS and in most individual cases not all will be present Most of the individuals considered in the book have at least some of the symptoms But it's uite hard to say whether specific individuals really have AS especially without a clinical evaluation The lack of much first hand evidence for most of the earlier mathematicians makes the determination essentially impossible AS disorder in a person generally manifests as difficulty in social interaction with others That seemingly should be detrimental to outstanding mathematical achievement and yet it seems to be rather common in the individuals profiled Interestingly 20th century examples Hardy Ramanujan Dirac seem to be especially rich in symptoms The book's co author Fitzgerald has argued in another work to include Gödel too Indeed he argues elsewhere for a significant connection between AS and creativity The other author James seems to agree in another book of his ownFinal conclusion? It may be impossible to find enough evidence regarding earlier mathematicians But the recent examples based on what's in this book do suggest that some degree of psychological dysfunction goes along with high achievement

  2. says:

    This book concerns mathematicians' behaviors and personalities The authors reference the ideas and insights of numerous psychologists and historians The beginning of the book examines musical and literary mathematicians savant skills hereditary influence and gender difference in mathematical ability and the impact of developmental personality and mood disorders in aforementioned ability The second part of the book relies greatly on biographical literature I may have read this book in the hopes of developing mathematical cognition paralleling that of the twenty mathematical personalities examined by Fitzgerald and James ie Gauss Dirichlet Ramanujan Gödel; although this did not come to fruition I was far from displeased upon finishing the book Surprisingly the authors do not offer much in the way of original thought Both Fitzgerald and James are experts in their fields psychiatry and math respectively Still I thoroughly delighted in reading this well researched book

  3. says:

    There are two parts to this book The first is about psychology particularly relating to mathematicians and the second is a collection of short biographies on mathematiciansThe book doesn't flow very well and seems mostly to be a summary of existing literature All the same the biographies are interesting The first part wasn't as enjoyable but was ok

  4. says:

    Loved the concise psychological and historical views on the tendencies of many mathematicians Favourite part was the concise bios on twenty of the most famous mathematicians from the last few centuries Really interesting

  5. says:

    This book was not what I expected

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