Not that way!

Jan Waszkiewicz. "Not that way!." Mathematica Applicanda 40.2 (2012): null. <http://eudml.org/doc/293368>.

@article{JanWaszkiewicz2012,
abstract = {1. Seeing all the recent books popularizing mathematics, I ask myself the question “who are all these publications appearing on the market aimed at?” The natural target seems to be school pupils who are interested in mathematics. On the one hand, such a reader would be a young, mathematically talented person, whose future is likely to be involved with mathematics in some way (not necessarily as a mathematician, but in a profession requiring mathematical ability). I look nostalgically back at my own childhood, when I read such evergreen books as “Lilavati” and "Śladami Pitagorasa" (In the Footsteps of Pythagoras) by Jeleński(1926,1928) or “Matematyka na wesoło” (Mathematics is Fun) by Perelman(1948) (However, my childhood also included such strange and now forgotten books, such as “Dwurogi czarodziej” (The Double Horned Magician) by Siergiej Bobrow(1948) and “Matematyka dla milionów” (Mathematics for the Millions) by Lancelot Hogben(1937)). Later, when I decided to become a mathematics student, I was enthralled by “Geometria nieeuklidesowa” (Non-Euclidean Geometry) by Kulczycki, “O liczbach i figurach” (On Numbers and Figures) by Toeplitz and Rademacher and “Symetria” (Symmetry) by Weyl(1952). Such popular science books are also read by other types of pupil - those who have problems with the subject and are tempted by titles advertising mathematics as an easy and enjoyable subject without any secrets (very often such pupils are very disappointed by the content of these books and their attitude to mathematics becomes even more negative). Another important group of readers are teachers, a class I know from personal experience and observation. Anyone who teaches mathematics (at any level) will happily make use of other peoples’ ideas. They like to see how those better than them (in a given, maybe very specific, field) explain difficult concepts, what examples they use and how they convey the intuition of mathematical constructions and ideas. Also, it is important to keep your “finger on the pulse” - to obtain a better impression of what is happening in a field unrelated to your own than a pupil or student generally can have. One could be asked about some fashionable idea or discussable concept and it is best in such cases not to come across as being ignorant of such such matters. Professional colleagues of the authors are also important readers as they are influential in their field. Such people often read popular science books in order to learn something about fields unrelated to their own sphere of research, sometimes to relax and from time to time to get a wider point of view on their own field (this is particularly easy when reading authors such as Stewart or Davis). Another group of readers of popular science books are those who authors particularly aim their books at: those who are passionate about the subject. Such readers can be of any age and met in a wide range of environments. I am writing these thoughts for a journal particularly aimed at people interested in the applications of mathematics. Here a new group appears: those for who the applications of these ideas may well have an important meaning in the future. That is to say people, who thanks to their own training, possibly experiments and errors, intuition and possibly from despair (after trying all other routes), arrive at the conclusion that, in order to solve a practical problem they face, it is worthwile obtaining the help of a mathematician. In such a case, it is useful for a person who needs such help to know what they can expect: What can mathematics offer? What type of results can be expected? What does such cooperation require from the non-mathematician? In simple terms, it would be good if the potential clients of mathematicians knew something about mathematics outside the realm of what is taught in schools and universities. I must admit that I am actively looking for popular science books that fulfill such a role. Also, I very rarely find anything that is worth recommending. 2. This time, my initial reaction was very positive. The book has an attractive title and on the cover the following themes are announced: “From the plans for building the pyramids to investigating the infinite”, “The magical world of numbers, concepts and shapes”, “Chaos theory and twisted logic” “From Pythagoras to computers” - These themes cover the whole spectrum of mathematics and its historical development. The table of contents confirms such an ambitious plan, all in the space of barely 300 pages of B-5. The pleasant (possibly because of its simplicity) cover attracts ones attention and the impressive number of well chosen illustrations invites one to delve deeply into the book (as can be inferred from the comments on one of the illustrations, in the original English version the illustrations are in colour). First looks indicate that the book is not overladen with mathematical symbols. Hence, maybe this is what I was looking for? Something that will attract a general reader, convey the beauty of mathematics and its methods, give a good overview of mathematical concepts and show the importance and nature of mathematical theories. Unfortunately, the answer to this question is negative. This is not a book that I would recommend to readers who want or need to understand what mathematics is about, regardless of which of the above groups a person belongs to. In fact, the book is an almost clinical example of how not to write a book popularizing mathematics. Leaving aside the illustrations, which are almost the only thing that can be used to defend “Fascynująca matematyka”(2011) (original title “The Story of Mathematics”(2009)), let us look at the contents. Truly, the range of material takes ones breath away. From primitive methods of counting to computers, from the beginnings of geometry to fractals, from the fundaments of mathematics to its applications. Obviously, not all of this can be presented in depth. However, if only the book conveyed ideas and intuition, showed what mathematics is about. The contents are presented in two forms - in short chapters and asides, written in boxes, which cover lighter material (interesting information, anecdotes, as well as entries from encyclopedias and the Internet). Naturally, the boxes catch ones eye and so one concentrates on them. Opening the book at random, I read (p. 280): “In 1988 the firm Hitachi produced a system based on fuzzy logic to drive trains ...”. It even sounded interesting. Since somebody patented a triangle and someone else the number 1, maybe firms had started to produce logic? Unfortunately, further reading showed that the way in which fuzzy logic is used is poorly described. Maybe, the language editing was poor? For sure. The situation is worse with the section “Everything about $e$” (p. 60): "$e$ is a very important number in mathematics. One way of defining it is as the sum of all the numbers in the series ..." It is clear that the translator does not know such mathematical terms as “infinite series”. This hypothesis is confirmed by the next line, in which we are told that $n!$ is the product of successive “digits”. Hence, the translator and editorship failed (The editors of the book are as follows: chief editor (B. Zborski), subject editior (M. Gryn), technical editor (E. Bryś) and language editor (T.Kępa)). They should not have taken on a book which went way beyond their mediocre mathematical qualifications. This is evidenced by the dictionary at the end of the book, from which we learn, among other things, that: “a limit is the “smallest or largest value obtained from the calculation of a function” , “a real number is “any positive or negative number, which does not contain the square root of the number -1”, “integral calculus is “the method of calculating the area under a curve by obtaining an approximation using a vast number of infinitely narrow slices of a plane” “differential calculus is “the method of calculating the slope of a curve at a given point” “differential and integral calculus are “fields of mathematical research considering infinitely small values in order to obtain the approximate value of the area under a curve or an indicator of the change in a curve”. Even if the original author had proposed such definitions herself, the translator put them barely into the form of Polish and the editorship left them without any comment! Moreover, it is difficult to trust in the competency of the author herself. She is not an expert in mathematics and her knowledge is second hand. She generally writes correctly about very elementary questions. However, she loses herself completely in more complex issues. Her definitions (?) of a logarithm (p. 58) and a complex number (p.80) are perplexing. Maybe it would be naive and pedantic to expect precision in such a book. However, should it contain: “obvious errors (on p. 137 it is claimed that the area of the regular hexagon inscribed in the circle takes the value ? = 3.125, when it is actually equal to 3); ” gross oversimplification (the story of the adoption of arabic numerals in Western Europe p. 83-85); “subjects taken out of context which are of little meaning to the reader, and, I am afraid, probably also to the author (e.g. the application of number theory to cryptography p. 86); “pure nonsense (“Proofs serve to find promising associations between mathematical theorems and objects” - p. 284); “or even gobbledygook (the comments of the author on deduction p. 287). I also feel that it is not good when the only proofs presented in a book on mathematics are two well known fallacies (p. 286, 288), especially when the first is not accompanied by any commentary. Finally, was it appropriate to translate the unpretentious title of the original “The story of mathematics” with the bravado of an advertising agent as “Fascinating mathematics”? The answers to the above questions are obvious to me. The identity of the author is less obvious. I found out from the Internet that Ann Rooney is a professional writer of, among other things, children’s books (also for adults) and popular books on mathematics, computers (apparently very good ones, especially for younger pupils), volcanoes, transmittable diseases, Einstein, zombies, knights of the Round Table (not those who negotiated the end of Polish communism, but those of England in the Dark Ages) and scores on other themes. Records show that she is the author of around a hundred books. Maybe so, praiseworthy, especially if she found a publisher and readers (her books are highly praised by readers’ reviews on Amazon.com). However, I was interested to find out from an Internet biography that she possesses a doctorate from Trinity College, Cambridge in ancient English and French literature. It could be expected then that the historical content of the book would be of professional standards. Unfortunately, this is not so and I am under the impression that in places the author gives expression not just to her own knowledge, but to her personal prejudices, for example in relation to the Catholic church (and maybe Christianity in general). The author describes the centuries long (XII-XVI C.) dispute of the Abacists and Algorists (i.e. supporters of traditional methods and arithmetic notation - calculating with the aid of an abacus and using the Latin system of numbers) with the supporters of the Arabic system of digits - using the decimal system to carry out numerical calculations. The author remarks on this theme (p. 83): “Since there existed the danger that the Hindu-Arabic system would democratize numeracy skills, individuals who had an interest in limiting the possession of these skills to a chosen elite tried to demonize the decimal system. If the general population could develop numeracy skills, asource of power would be lost. The Catholic church wished to maintain control over education and the number system, especially since the decimal system came from the Islamic world. The church protected mathematicians practising arcane systems of calculating using an abacus. It was said that the resistance to the Hindu-Arab system was so great, that several poor souls were burned at the stake due to accusations of heresy”. We breathe a sigh of relief at the end of this chapter, since we learn that the French revolution with the aid of a few laws (no mention of the guillotine) freed the country from the curse of using the abacus, in this way givng an example to the rest of the civilized world. It is a chapter so full of deception, slander, falsehood and ill will that it would not shame any Soviet museum of atheism. It would take a good few pages to set the rubbish presented by these few sentences straight. I could direct the interested reader to the classic “Historia matematyki w wiekach średnich” (A history of mathematics in the middle ages) [jusz69:historia], where this subject is treated with the required respect. 3. In rage, I threw my copy of “Fascynująca matematyka” into the recycling bin. However, I later took it out. It would have been a waste of some useful illustrations. },
author = {Jan Waszkiewicz},
journal = {Mathematica Applicanda},
keywords = {},
language = {eng},
number = {2},
pages = {null},
title = {Not that way!},
url = {http://eudml.org/doc/293368},
volume = {40},
year = {2012},
}

TY - JOUR
AU - Jan Waszkiewicz
TI - Not that way!
JO - Mathematica Applicanda
PY - 2012
VL - 40
IS - 2
SP - null
AB - 1. Seeing all the recent books popularizing mathematics, I ask myself the question “who are all these publications appearing on the market aimed at?” The natural target seems to be school pupils who are interested in mathematics. On the one hand, such a reader would be a young, mathematically talented person, whose future is likely to be involved with mathematics in some way (not necessarily as a mathematician, but in a profession requiring mathematical ability). I look nostalgically back at my own childhood, when I read such evergreen books as “Lilavati” and "Śladami Pitagorasa" (In the Footsteps of Pythagoras) by Jeleński(1926,1928) or “Matematyka na wesoło” (Mathematics is Fun) by Perelman(1948) (However, my childhood also included such strange and now forgotten books, such as “Dwurogi czarodziej” (The Double Horned Magician) by Siergiej Bobrow(1948) and “Matematyka dla milionów” (Mathematics for the Millions) by Lancelot Hogben(1937)). Later, when I decided to become a mathematics student, I was enthralled by “Geometria nieeuklidesowa” (Non-Euclidean Geometry) by Kulczycki, “O liczbach i figurach” (On Numbers and Figures) by Toeplitz and Rademacher and “Symetria” (Symmetry) by Weyl(1952). Such popular science books are also read by other types of pupil - those who have problems with the subject and are tempted by titles advertising mathematics as an easy and enjoyable subject without any secrets (very often such pupils are very disappointed by the content of these books and their attitude to mathematics becomes even more negative). Another important group of readers are teachers, a class I know from personal experience and observation. Anyone who teaches mathematics (at any level) will happily make use of other peoples’ ideas. They like to see how those better than them (in a given, maybe very specific, field) explain difficult concepts, what examples they use and how they convey the intuition of mathematical constructions and ideas. Also, it is important to keep your “finger on the pulse” - to obtain a better impression of what is happening in a field unrelated to your own than a pupil or student generally can have. One could be asked about some fashionable idea or discussable concept and it is best in such cases not to come across as being ignorant of such such matters. Professional colleagues of the authors are also important readers as they are influential in their field. Such people often read popular science books in order to learn something about fields unrelated to their own sphere of research, sometimes to relax and from time to time to get a wider point of view on their own field (this is particularly easy when reading authors such as Stewart or Davis). Another group of readers of popular science books are those who authors particularly aim their books at: those who are passionate about the subject. Such readers can be of any age and met in a wide range of environments. I am writing these thoughts for a journal particularly aimed at people interested in the applications of mathematics. Here a new group appears: those for who the applications of these ideas may well have an important meaning in the future. That is to say people, who thanks to their own training, possibly experiments and errors, intuition and possibly from despair (after trying all other routes), arrive at the conclusion that, in order to solve a practical problem they face, it is worthwile obtaining the help of a mathematician. In such a case, it is useful for a person who needs such help to know what they can expect: What can mathematics offer? What type of results can be expected? What does such cooperation require from the non-mathematician? In simple terms, it would be good if the potential clients of mathematicians knew something about mathematics outside the realm of what is taught in schools and universities. I must admit that I am actively looking for popular science books that fulfill such a role. Also, I very rarely find anything that is worth recommending. 2. This time, my initial reaction was very positive. The book has an attractive title and on the cover the following themes are announced: “From the plans for building the pyramids to investigating the infinite”, “The magical world of numbers, concepts and shapes”, “Chaos theory and twisted logic” “From Pythagoras to computers” - These themes cover the whole spectrum of mathematics and its historical development. The table of contents confirms such an ambitious plan, all in the space of barely 300 pages of B-5. The pleasant (possibly because of its simplicity) cover attracts ones attention and the impressive number of well chosen illustrations invites one to delve deeply into the book (as can be inferred from the comments on one of the illustrations, in the original English version the illustrations are in colour). First looks indicate that the book is not overladen with mathematical symbols. Hence, maybe this is what I was looking for? Something that will attract a general reader, convey the beauty of mathematics and its methods, give a good overview of mathematical concepts and show the importance and nature of mathematical theories. Unfortunately, the answer to this question is negative. This is not a book that I would recommend to readers who want or need to understand what mathematics is about, regardless of which of the above groups a person belongs to. In fact, the book is an almost clinical example of how not to write a book popularizing mathematics. Leaving aside the illustrations, which are almost the only thing that can be used to defend “Fascynująca matematyka”(2011) (original title “The Story of Mathematics”(2009)), let us look at the contents. Truly, the range of material takes ones breath away. From primitive methods of counting to computers, from the beginnings of geometry to fractals, from the fundaments of mathematics to its applications. Obviously, not all of this can be presented in depth. However, if only the book conveyed ideas and intuition, showed what mathematics is about. The contents are presented in two forms - in short chapters and asides, written in boxes, which cover lighter material (interesting information, anecdotes, as well as entries from encyclopedias and the Internet). Naturally, the boxes catch ones eye and so one concentrates on them. Opening the book at random, I read (p. 280): “In 1988 the firm Hitachi produced a system based on fuzzy logic to drive trains ...”. It even sounded interesting. Since somebody patented a triangle and someone else the number 1, maybe firms had started to produce logic? Unfortunately, further reading showed that the way in which fuzzy logic is used is poorly described. Maybe, the language editing was poor? For sure. The situation is worse with the section “Everything about $e$” (p. 60): "$e$ is a very important number in mathematics. One way of defining it is as the sum of all the numbers in the series ..." It is clear that the translator does not know such mathematical terms as “infinite series”. This hypothesis is confirmed by the next line, in which we are told that $n!$ is the product of successive “digits”. Hence, the translator and editorship failed (The editors of the book are as follows: chief editor (B. Zborski), subject editior (M. Gryn), technical editor (E. Bryś) and language editor (T.Kępa)). They should not have taken on a book which went way beyond their mediocre mathematical qualifications. This is evidenced by the dictionary at the end of the book, from which we learn, among other things, that: “a limit is the “smallest or largest value obtained from the calculation of a function” , “a real number is “any positive or negative number, which does not contain the square root of the number -1”, “integral calculus is “the method of calculating the area under a curve by obtaining an approximation using a vast number of infinitely narrow slices of a plane” “differential calculus is “the method of calculating the slope of a curve at a given point” “differential and integral calculus are “fields of mathematical research considering infinitely small values in order to obtain the approximate value of the area under a curve or an indicator of the change in a curve”. Even if the original author had proposed such definitions herself, the translator put them barely into the form of Polish and the editorship left them without any comment! Moreover, it is difficult to trust in the competency of the author herself. She is not an expert in mathematics and her knowledge is second hand. She generally writes correctly about very elementary questions. However, she loses herself completely in more complex issues. Her definitions (?) of a logarithm (p. 58) and a complex number (p.80) are perplexing. Maybe it would be naive and pedantic to expect precision in such a book. However, should it contain: “obvious errors (on p. 137 it is claimed that the area of the regular hexagon inscribed in the circle takes the value ? = 3.125, when it is actually equal to 3); ” gross oversimplification (the story of the adoption of arabic numerals in Western Europe p. 83-85); “subjects taken out of context which are of little meaning to the reader, and, I am afraid, probably also to the author (e.g. the application of number theory to cryptography p. 86); “pure nonsense (“Proofs serve to find promising associations between mathematical theorems and objects” - p. 284); “or even gobbledygook (the comments of the author on deduction p. 287). I also feel that it is not good when the only proofs presented in a book on mathematics are two well known fallacies (p. 286, 288), especially when the first is not accompanied by any commentary. Finally, was it appropriate to translate the unpretentious title of the original “The story of mathematics” with the bravado of an advertising agent as “Fascinating mathematics”? The answers to the above questions are obvious to me. The identity of the author is less obvious. I found out from the Internet that Ann Rooney is a professional writer of, among other things, children’s books (also for adults) and popular books on mathematics, computers (apparently very good ones, especially for younger pupils), volcanoes, transmittable diseases, Einstein, zombies, knights of the Round Table (not those who negotiated the end of Polish communism, but those of England in the Dark Ages) and scores on other themes. Records show that she is the author of around a hundred books. Maybe so, praiseworthy, especially if she found a publisher and readers (her books are highly praised by readers’ reviews on Amazon.com). However, I was interested to find out from an Internet biography that she possesses a doctorate from Trinity College, Cambridge in ancient English and French literature. It could be expected then that the historical content of the book would be of professional standards. Unfortunately, this is not so and I am under the impression that in places the author gives expression not just to her own knowledge, but to her personal prejudices, for example in relation to the Catholic church (and maybe Christianity in general). The author describes the centuries long (XII-XVI C.) dispute of the Abacists and Algorists (i.e. supporters of traditional methods and arithmetic notation - calculating with the aid of an abacus and using the Latin system of numbers) with the supporters of the Arabic system of digits - using the decimal system to carry out numerical calculations. The author remarks on this theme (p. 83): “Since there existed the danger that the Hindu-Arabic system would democratize numeracy skills, individuals who had an interest in limiting the possession of these skills to a chosen elite tried to demonize the decimal system. If the general population could develop numeracy skills, asource of power would be lost. The Catholic church wished to maintain control over education and the number system, especially since the decimal system came from the Islamic world. The church protected mathematicians practising arcane systems of calculating using an abacus. It was said that the resistance to the Hindu-Arab system was so great, that several poor souls were burned at the stake due to accusations of heresy”. We breathe a sigh of relief at the end of this chapter, since we learn that the French revolution with the aid of a few laws (no mention of the guillotine) freed the country from the curse of using the abacus, in this way givng an example to the rest of the civilized world. It is a chapter so full of deception, slander, falsehood and ill will that it would not shame any Soviet museum of atheism. It would take a good few pages to set the rubbish presented by these few sentences straight. I could direct the interested reader to the classic “Historia matematyki w wiekach średnich” (A history of mathematics in the middle ages) [jusz69:historia], where this subject is treated with the required respect. 3. In rage, I threw my copy of “Fascynująca matematyka” into the recycling bin. However, I later took it out. It would have been a waste of some useful illustrations. 
LA - eng
KW -
UR - http://eudml.org/doc/293368
ER -