European Mathematical Society - Robin Wilson
https://euro-math-soc.eu/author/robin-wilson
enEuler's pioneering equation
https://euro-math-soc.eu/review/eulers-pioneering-equation
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>Since The Mathematical Intelligencer conducted a poll in 1988 about which was the most beautiful among twenty-four theorems. Euler's equation $e^{i\pi}+1=0$ or $e^{iπ}=−1$ turned out to be the winner, and that is still today largely accepted among mathematicians. Even among physicists this is true. In a similar poll from 2004, it came out second after Maxwell's equations. The subtitle of this book is therefore <em>The most beautiful theorem in mathematics</em>.</p>
<p>This may immediately raise some controversy, not about the choice of the formula, but perhaps about what it should be called: a theorem, an identity, an equality, a formula, an equation,... A theorem or a formula applies but these are quite general terms. The others refer to formulas with an equal sign. The term identity assumes that there is a variable involved and that the formula holds whatever the value of that variable. That applies to Euler's identity, which is the related formula $e^{ix}=\cos(x)+i\sin(x)$. The previous formula appears as a special case of this identity. Wilson calls the former formula and "equation" but the reader with some affinity to the French language would probably prefer to call it an equality because the French équation means it has to be solved for an unknown variable. But all the previous names have been used interchangeably to indicate the formula. Calling it <em>Euler's identity</em> may not be the most correct but it is probably the most common terminology.</p>
<p>Whatever it is called, the description, if not <em>most beautiful</em>, then certainly the qualification <em>most important</em> or <em>most remarkable</em>, would be well deserved. It involves five fundamental mathematical constants: 1,0,π,e, and i in one simple relation. The 1 generates the counting numbers. The zero took a while to be accepted as a number but also negative numbers were initially considered to be exotic. Rational numbers were showing up naturally in computations, but so did numbers like √2 and π. These required an extension of the rationals with algebraic irrationals like √2 and the transcendentals like π which results in the reals that include all of them. The constant e (notation by Euler) relates to logarithms and its inverse the exponential function growing faster than any polynomial. Finally the imaginary constant i = √-1 (which is another notation introduced by Euler) was needed to solve any quadratic equation. This i allowed to introduce the complex numbers so that the fundamental theorem of algebra could be proved. The exponential and complex exponential are essential in applied mathematics. Euler's identity is most remarkable because it relates exponential growth or decay of the real exponential, and the oscillating behaviour of sines and cosines in the complex case.</p>
<p>All these links allow Wilson to tell many stories about mathematics that are usually discussed in books popularizing mathematics for the lay reader. There are indeed five chapters whose titles are the five previous constants and a sixth one is about Euler's equation. He does this in a concise way. The amount of information compressed in only 150 pages is amazing. This doesn't mean that it is so dense that it becomes unreadable. Quite the opposite. Because there are no long drawn-out detours, the story becomes straightforward and understandable. For example the first chapter (only 17 pages including illustrations) introduces children's counting rhymes, compares the names for numbers in seven different languages, and compares number systems: Roman, Egyptian, Mesopotamian, Greek, Chinese, Mayan, and the Hindu-Arabic. The latter was popularized in the West by Fibonacci and Pacioli. There are many illustrations not only of the notation of these different numerals in this chapter, but there are in fact many other illustrations throughout the book. This does not increase the number of pages needlessly because a picture sometimes says more than a thousand words. There are no colour illustrations but colour is not relevant for what they represent.</p>
<p>This is not the first book on Euler's equation. For example Paul Nahin. <a target="_blank" href="/review/dr-eulers-fabulous-formula"><em>Dr. Euler's Fabulous Formula</em></a>, Princeton University Press (2006), which is a bit more mathematically advanced, and a more recent one by David Stipp. <em>A Most Elegant Equation</em>, Basic Books (2017), which has more info about the person Euler. In the current book Euler's name appears frequently but as a person he is largely absent. For most of the five constants, separate popularizing books have been written or they are discussed in a chapter of more general popular books about mathematics, too many to list them here. Wilson refers to some of them in an appendix with a short list of additional literature, conveniently listed by subject.</p>
<p>There is of course mathematics in this book. It would be weird if there wasn't. But there is nothing that should shy away a reader with a slight affinity for mathematics. Some of it can be skipped, but the exponential and trigonometric functions, series, and an occasional integral do appear. The more advanced definitions or computations, are put in one of the eleven grey-shaded boxes distributed throughout the book, so that skipping is easy. Most of the topics are placed in their historical context. For example, the history of the computation of π is well represented, and also the history of the logarithms as they were derived by Napier and Briggs and how they relate is nicely explained. There are some notes to explain how complex numbers can be generalised to quaternions and even octonions, and several examples from applied mathematics illustrate the meaning and relevance of the exponential function.</p>
<p>A minor glitch: Albert Girard (1595-1632) who was the first to have formulated the fundamental theorem of algebra, is called on page 116 a Flemish mathematician, which is strange because the man was born in France, but, as a religious refugee, moved to Leiden in what was then the Dutch Republic of the Netherlands. So I do not think that the characterization Flemish does apply here.</p>
<p>The book does not go deep into the subjects discussed, but I liked it because it is quite broad, touching upon so many mathematical subjects, mainly in their historical context, while readability remains most enjoyable notwithstanding its conciseness.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This is a book in which Wilson gives a popularizing account about the historical development of mathematics. His guidance is Euler's equality that connects five fundamental constants of mathematics: 1, 0, π, e, and i = √-1. Each of these is an incentive to discuss respectively different number systems, how counting extends to negative numbers and eventually the real numbers, the approximation and calculation of π, different logarithms, and complex numbers.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/robin-wilson" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Robin Wilson</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/oxford-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">oxford university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2018</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">9780198794929 (hbk); 9780198794936 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£ 14.99 (hbk); £ 9.99 (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">176</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://global.oup.com/academic/product/eulers-pioneering-equation-9780198794936" title="Link to web page">https://global.oup.com/academic/product/eulers-pioneering-equation-9780198794936</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a09" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a09</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/97a80" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97A80</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/01a50" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01A50</a></li></ul></span>Sun, 14 Apr 2019 07:22:45 +0000Adhemar Bultheel49288 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/eulers-pioneering-equation#commentsThe Mathematical World of Charles L. Dodgson (Lewis Carroll)
https://euro-math-soc.eu/review/mathematical-world-charles-l-dodgson-lewis-carroll
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Charles Lutwidge Dodgson (1832-1898) is the real name of Lewis Carroll, the author of <em>Alice's Adventures in Wonderland, Through the Looking Glass</em> and of other such books. He wrote these for Alice Liddell, the daughter of Henry Liddell, the dean of Christ Church in Oxford and he became forever famous as `the man who wrote <em>Alice</em>' and for a long time this was the only way he was remembered. Yet he was also a mathematician with very original ideas and a creditable photographer. These aspects were only properly recognized since the 1980s. His diaries and his collected publications were becoming available since the 1990s and with that material, more studies of his non-fiction work was possible. This book gives a survey of what is known so far.</p>
<p>
The book starts with a (short and in some respect only partial) biography, concentrating on the mathematician in him. Introduced by his father (a country parson) to mathematics as a young child, he excelled in this subject at school. Later, just like his father, he studied at Christ Church in Oxford and got a master degree in mathematics. While studying he gave private lessons to students. He was ordained a deacon when he was 29, but never became a priest. When Liddell became the dean of Christ Church, Dodgson was appointed as 'Master of the House' which gave him a reasonable income but also a large teaching load. He starts publishing his pamphlets as aids for teaching, and some work on the evaluation of determinants. He took on photographing as a hobby. He became rather good at it, using it as an art form, rather than as just a way to catch reality. Urged by Alice Liddell to write up the stories he told during their boat trips, he started working on <em>Alice's Adventures</em> which was published under his pen name Lewis Carroll. Teaching was his main occupation besides his writing and the photography. He became (reluctantly) Curator of the Christ Church Common Room for ten years when he was 50. This was a time-consuming burden requiring management and many decisions to take. In that context he could use his already existing interest in voting systems. He died a week before his 66th birthday.</p>
<p>
The next chapters are written by specialists and discuss in more detail Dodgson's contributions to different mathematical subjects. The first one deals with geometry. Dodgson was teaching geometry following Euclid's books as it was usual in those days. However there were some new ideas, among others by Sylvester, criticizing Euclid's approach. Euclid's arguments were not always waterproof in a mathematical sense, and there was the emerging hyperbolic geometry of Lobachevsky. Dodgson was defending however Euclid in his booklet <em>Euclid and his Modern Rivals</em>. The discussion about the parallel postulate involved either infinitely long lines or infinitely small quantities. So he tried to replace it by a finite alternative using an "obvious" property about areas outside and inside an hexagon inscribed in a circle. He thought of non-Euclidean geometry as nonsensical.</p>
<p>
In the next chapter on algebra, it is explained what his condensation method for the evaluation of determinants is. This may be his most useful original contribution to mathematics. He was also opposed to the name 'matrix' with the meaning we give it today. He called it a 'block' because a matrix refers to the mould, rather than the object, which is the mould filled with numbers. To denote the elements in a matrix, which we denote by a letter with two indices, he had his own strange notation. His work on determinants was published but (like many of his mathematical publications) remained largely unnoticed for a long time.</p>
<p>
Logic has been one of Dodgson's favourite subjects and he wrote several texts about it. In those days, as we still have today, there existed several proposals for an approach to, and the notation of, formal logic. The one from Boole was, and still is, a very useful one. Dodgson adhered the formal approach which was not easily accepted by classical logicians, and required a lot of dispute. He developed several tools to deal with logic problems: a method with diagrams, he had his own formal notation, a method of trees, and an algorithm to solve syllogisms. Bertrand Russell once said about Dodgson' work that it was brilliant but largely useless.</p>
<p>
Dodgson also wrote several texts on voting systems. The problem of cycles (where each candidate can win from the next candidate in a cyclic way) was known several centuries before, but Dodgson was probably not aware of that. He detected it on his own and made proposals for a correct voting system, for assigning seats to parties in a political election, or for a correct outcome of a tournament. He wrote about these problems in terms of game theory, an approach that John Nash would bring to a culmination only much later.</p>
<p>
It is clear that the author of the <em>Alice</em> books would also be interested in recreational mathematics, puzzles, riddles, and games. Many examples are discussed as well the way in which Dodgson solved them. He also had techniques to remember dates and numerical data, and techniques to check divisibility which could be smuggled into a number game.</p>
<p>
It is strange that Dodgson was so little recognized for his mathematical work. Most of his, sometimes original, approaches were only discovered at the end of the 20th century. He was not the best salesman for his results. Perhaps he didn't take it seriously enough, and maybe he was too quarrelsome (sarcasm indeed happened sometimes), or perhaps he was rather obscure when sticking to his own notation and ideas. He had for example his own symbolic notation for the trigonometric functions. He also was stammering a bit, but that did not seem to be a serious hinder to him. Moreover his contributions are very diverse. He did not have a single field in which he became the renowned expert and finally perhaps he was also in the shadow of Lewis Carroll. The legend goes that Queen Victoria, charmed by reading <em>Alice's Adventures in Wonderland</em>, asked for his next book and promptly received his <em>An Elementary Treatise on Determinants</em>. This story is however a hoax. He may not have received during his life the recognition by mathematicians he deserved, but nevertheless this book has an extensive chapter discussing his mathematical legacy in geometry, trigonometry, algebra, logic, voting, probability, and cryptology as it became clear only recently.</p>
<p>
The book ends with a complete bibliography listing all his publications and a list of references for additional reading. With that this book completes a survey of the life and work of a (perhaps somewhat dull) mathematician that is in many ways the opposite (but in as many ways also the complement) of the light-hearted Lewis Carroll that authored the books witnessing of such a rich fantasy dedicated to a little girl called Alice. A man well known as Lewis Carroll, yet perhaps too long underestimated as Charles Dodgson. This nicely edited book with many illustrations and written by experts on the subject will certainly help to turn the tide by adjusting the image and allow you to form a proper opinion about Charles Dodgson.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This book starts with a biography of Charles Dodgson, the mathematician, best known for his books like <em>Alice's Adventures in Wonderland</em> under his pen name Lewis Carroll. Its main purpose however is to discuss his work and influence as a mathematician.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/robin-wilson" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Robin Wilson</a></li><li class="vocabulary-links field-item odd"><a href="/author/amirouche-moktefi" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Amirouche Moktefi</a></li><li class="vocabulary-links field-item even"><a href="/author/eds-1" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">(eds.)</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/oxford-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">oxford university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2019</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">9780198817000 (hbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£29.99</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">288</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/history-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">History of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://global.oup.com/academic/product/the-mathematical-world-of-charles-l-dodgson-lewis-carroll-9780198817000" title="Link to web page">https://global.oup.com/academic/product/the-mathematical-world-of-charles-l-dodgson-lewis-carroll-9780198817000</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/01-history-and-biography" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01 History and biography</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/01a70" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01a70</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/01a55" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01A55</a></li></ul></span>Wed, 20 Mar 2019 09:56:06 +0000Adhemar Bultheel49213 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/mathematical-world-charles-l-dodgson-lewis-carroll#commentsThe Turing Guide
https://euro-math-soc.eu/review/turing-guide
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Jack Copeland is a professor at the University of Canterbury, NZ, director of the <a href="http://www.alanturing.net/">Turing Archive for the History of Computing</a>, co-director of the <a href="http://www.turing.ethz.ch/" target="_blank">Turing Center of the ETH Zürich</a>, and he has written or edited several books about Turing and his work. So he seems to be also the driving force behind this new collection of papers devoted to the life and the legacy of Alan Turing. Only four authors are explicitly mentioned on the cover of this book, but the collection contains 42 papers authored by 33 persons with very diverse backgrounds. Fifteen of the 42 papers were (co)authored by Copeland. Four of the papers by older authors (three of them have known or collaborated with Turing) are published posthumously.</p>
<p>
Alan Turing (1912-1954) hardly needs any introduction. Most people will know him as a codebreaker of the German Enigma at Bletchley Park during the second World War. They probably also have heard of his tragic death covered by a veil of uncertainty: was it an accident or suicide. He was convicted in 1952 to chemical castration for having a gay relationship. Only in 2013 he was rehabilitated by a royal pardon. Some may also have an idea of what a Turing Test is. A mathematician or a computer scientist will almost certainly also know that he proved independently but almost simultaneously with Alonso Church that Hilbert's <em>Entscheidungsproblem</em> was unsolvable. Turing proved it by reducing it to a halting problem which is undecidable on a universal Turing Machine. Many books and even films tell the story of Turing and of all the activities at Bletchley Park. The Turing Centenary Year 2012 which triggered the publication of many more and the recent (loosely biographical) film <em>The Imitation Game</em> (2014) have spread the knowledge about Turing in a broader audience. Bletchley Park may now be a major tourist attraction park, but the confidentiality that was kept by the British authorities about what was developed there during the war concerning cryptanalysis and the early digital computers has delayed the historical disclosure of the role played by Turing and other scientists in that period. Somewhat less known, but very familiar to biologists is Turing's work on morphogenesis which he developed during a later stage in his life. The book has eight parts that cluster papers about eight different aspects of Turing's life and legacy.</p>
<p>
Thus Turing was much more than just a codebreaker. His universal machine was an essential theoretical model in proving results about the foundations of mathematics, logic, and computer science. Because of his work at Bletchley Park while the first digital computing machines were being assembled during and just after the war, he was intensively involved in writing original software, a user's manual, and he has even contributed to the design of circuits and hardware. The introduction of machines that could be instructed to perform less trivial tasks raised concern about the future of Artificial Intelligence and Turing contributed with several variants of his Turing test in an attempt to define what intelligence really meant. He called his ultimate version of 1950 the 'imitation game'.</p>
<p>
It should not be forgotten, that, even though his scientific interest and contributions are broad, Turing was fundamentally a mathematician. It is less known that his Kings College Fellow Dissertation (1935) involved a proof of the Central Limit Theorem. It was little known that this was proved already in 1920 by Jarl Lindeberg and so Turing's result was never published. He also worked on group theory, in particular the word problem, on number theory (the Riemann hypothesis and normal numbers) and of course the code breaking involved statistical analysis and hypothesis testing. Turing exploited these statistics in his algorithms Banburismus and later Turingery. After the war he was also doing numerical analysis (LU decomposition, error analysis,...). His work on morphogenesis was also mathematical and involved diffusion equations that model the random behaviour of the morphogenes.</p>
<p>
This collection of papers is produced for an interested but general audience. Formulas are kept to a minimum and technical discussion is maintained at an accessible level. It may not be the best choice to read as a first introduction to Turing and his work. Better introductions that are less chopped up in different papers are available. On the other hand, if you have read already several books about Turing and his work, I am sure you will find here some anecdotes and historical facts that you did not know yet in each of the eight parts of the book.</p>
<p>
A first part is biographical. The timeline by Copeland is useful to place everything in a proper historical sequence. There is a testimony of Sir John Dermot Turing, Alan's nephew, and another by the late Peter Hilton an Oxford professor who worked with Turing at Bletchley Park.<br />
Part two is more history in which Copeland explains about the Universal Turing Machine conceived by Turing to solve the Entscheidungsproblem. It has also a noteworthy contribution by Stephen Wolfram, the creator Mathematica and Wolfram-alpha, who praises Turing for initiating computer science.<br />
The third part is the most extensive one and puts the codebreaking and Bletchley Park in the spotlight. Some of the texts are by people who worked there and who give an account of how everyday life was during the war, other papers are explaining how the Enigma machine worked and how it could be broken.<br />
In part four the first computers as they developed after the war are in the focus. The Colossus machines were computers that were used since 1943 for codebreaking, These facts were only declassified in 2000 so that one got the impression that the original ideas and prototypes came from von Neumann at Princeton who developed the ENIAC and the EDVAC. However, the University of Manchester had a small scale computer <em>Baby</em> (1948) that was running a few months before the ENIAC and Turing at the National Physical Laboratory developed the Automatic Computing Engine (ACE) that was operational in 1950. Turing even wrote a manual on how to program the machine to play musical notes.<br />
The fifth part is about computers and the mind: chess computers, neural computing, and the working of the human brain. It also has a remarkable text by novelist David Leavitt about Turing and the paranormal.<br />
The next two parts are about Turing's biological (morphogenesis) and mathematical (cf. supra) contributions. The final part has two papers contemplating the Turing thesis (1936) which claims that a Turing machine can do any task a human computer can do. Similar claims were made by Zuse and Church, but whether the whole universe can be seen as a computer, obviously depends on what you call a computer.<br />
In the last chapter about Turing's legacy in different disciplines we find many references to books and other media that can be consulted for further information.</p>
<p>
The remaining pages offer a short biography of the contributors, references to some books about Turing, and a list of published papers by Turing. The many references and notes from the contributions are also gathered at the end. The book ends with a very detailed index, which is of course very welcome and obviously non-trivial with that many different authors.</p>
<p>
In summary, this is a welcome addition to the existing generally accessible literature that gives additional testimony of the brilliant mind of Alan Turing. There is historical as well as technical material that will be appreciated also by specialists whatever their discipline: history, mathematics, biology, computer science, or philosophy.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a collection of papers about Alan Turing, his life and legacy. It has biographical and historical details and explains the influence of Turing on codebreaking, artificial intelligence, computer science, mathematics, biology, and philosophy.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/jack-copeland" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Jack Copeland</a></li><li class="vocabulary-links field-item odd"><a href="/author/jonathan-bowen" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Jonathan Bowen</a></li><li class="vocabulary-links field-item even"><a href="/author/mark-sprevak" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mark Sprevak</a></li><li class="vocabulary-links field-item odd"><a href="/author/robin-wilson" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Robin Wilson</a></li><li class="vocabulary-links field-item even"><a href="/author/et-al" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">et. al</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/oxford-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">oxford university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2017</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-1987-4782-6 (hbk), 978-0-1987-4783-3 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">£ 75.00 (hbk), £ 19.99 (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">576</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/history-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">History of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="https://global.oup.com/academic/product/the-turing-guide-9780198747833" title="Link to web page">https://global.oup.com/academic/product/the-turing-guide-9780198747833</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/00-general" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00 General</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00-01</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a99" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a99</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/00a09" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a09</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/00a65" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a65</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/01a60" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">01a60</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/03d10" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">03D10</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/03b07" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">03B07</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/68-06" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">68-06</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/68q05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">68Q05</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/92c15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">92C15</a></li></ul></span>Tue, 13 Mar 2018 07:33:47 +0000Adhemar Bultheel48322 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/turing-guide#comments