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Realm of Numbers
This is the first of Asimov’s three “Realm” books published with Houghton-Mifflin (OK, four, if you count An Easy Introduction to the Slide Rule). This is a book that Asimov was very fond of, partly because it whipped if off in just a few weeks, and partly because he managed to go from counting on fingers to transfinite quantities in the space of fewer than 150 pages.
The book is rather breezy, and I’m not sure how well it would work as an introduction to the more basic subjects if someone doesn’t know about them (such as multiplication and division). On the other hand, the book does a marvelous job in explaining the why of our numeral system, the four basic arithmetic operations, powers, logarithms, complex numbers, and so on, and, in the later sections, the fact that most of us do not actually need to use complex numbers and so on in our daily life means that it doesn’t really matter if you don’t leave the book able to multiply (7 + 3i) and (5 - 8i) in your head. (The answer is 59 - 41i, by the way.)
There are a couple of points that provoke a wry smile, perhaps, talking about a slide rule, for one, or Asimov’s lament that inventing a new “The Sign” symbol instead of using “i.” Mathematics, however, unlike other sciences, does not get obsolete very easily, and there is little, if anything, in the book which is actually out-dated. The result is a nicely fresh little volume providing an enjoyable introduction to numbers and basic mathematics.
The book is rather breezy, and I’m not sure how well it would work as an introduction to the more basic subjects if someone doesn’t know about them (such as multiplication and division). On the other hand, the book does a marvelous job in explaining the why of our numeral system, the four basic arithmetic operations, powers, logarithms, complex numbers, and so on, and, in the later sections, the fact that most of us do not actually need to use complex numbers and so on in our daily life means that it doesn’t really matter if you don’t leave the book able to multiply (7 + 3i) and (5 - 8i) in your head. (The answer is 59 - 41i, by the way.)
There are a couple of points that provoke a wry smile, perhaps, talking about a slide rule, for one, or Asimov’s lament that inventing a new “The Sign” symbol instead of using “i.” Mathematics, however, unlike other sciences, does not get obsolete very easily, and there is little, if anything, in the book which is actually out-dated. The result is a nicely fresh little volume providing an enjoyable introduction to numbers and basic mathematics.
Mass Market Paperback
First published June 1, 1959
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About the author
Isaac Asimov
4,666 books27.2k followersWorks of prolific Russian-American writer Isaac Asimov include popular explanations of scientific principles,
The Foundation Trilogy
(1951-1953), and other volumes of fiction.
Isaac Asimov, a professor of biochemistry, wrote as a highly successful author, best known for his books.
Asimov, professor, generally considered of all time, edited more than five hundred books and ninety thousand letters and postcards. He published in nine of the ten major categories of the Dewey decimal classification but lacked only an entry in the category of philosophy (100).
People widely considered Asimov, a master of the genre alongside Robert Anson Heinlein and Arthur Charles Clarke as the "big three" during his lifetime. He later tied Galactic Empire and the Robot into the same universe as his most famous series to create a unified "future history" for his stories much like those that Heinlein pioneered and Cordwainer Smith and Poul Anderson previously produced. He penned "Nightfall," voted in 1964 as the best short story of all time; many persons still honor this title. He also produced well mysteries, fantasy, and a great quantity of nonfiction. Asimov used Paul French, the pen name, for the Lucky Starr, series of juvenile novels.
Most books of Asimov in a historical way go as far back to a time with possible question or concept at its simplest stage. He often provides and mentions well nationalities, birth, and death dates for persons and etymologies and pronunciation guides for technical terms. Guide to Science, the tripartite set Understanding Physics, and Chronology of Science and Discovery exemplify these books.
Asimov, a long-time member, reluctantly served as vice president of Mensa international and described some members of that organization as "brain-proud and aggressive about their IQs." He took more pleasure as president of the humanist association. The asteroid 5020 Asimov, the magazine Asimov's Science Fiction, an elementary school in Brooklyn in New York, and two different awards honor his name.
http://en.wikipedia.org/wiki/Isaac_As...
Isaac Asimov, a professor of biochemistry, wrote as a highly successful author, best known for his books.
Asimov, professor, generally considered of all time, edited more than five hundred books and ninety thousand letters and postcards. He published in nine of the ten major categories of the Dewey decimal classification but lacked only an entry in the category of philosophy (100).
People widely considered Asimov, a master of the genre alongside Robert Anson Heinlein and Arthur Charles Clarke as the "big three" during his lifetime. He later tied Galactic Empire and the Robot into the same universe as his most famous series to create a unified "future history" for his stories much like those that Heinlein pioneered and Cordwainer Smith and Poul Anderson previously produced. He penned "Nightfall," voted in 1964 as the best short story of all time; many persons still honor this title. He also produced well mysteries, fantasy, and a great quantity of nonfiction. Asimov used Paul French, the pen name, for the Lucky Starr, series of juvenile novels.
Most books of Asimov in a historical way go as far back to a time with possible question or concept at its simplest stage. He often provides and mentions well nationalities, birth, and death dates for persons and etymologies and pronunciation guides for technical terms. Guide to Science, the tripartite set Understanding Physics, and Chronology of Science and Discovery exemplify these books.
Asimov, a long-time member, reluctantly served as vice president of Mensa international and described some members of that organization as "brain-proud and aggressive about their IQs." He took more pleasure as president of the humanist association. The asteroid 5020 Asimov, the magazine Asimov's Science Fiction, an elementary school in Brooklyn in New York, and two different awards honor his name.
http://en.wikipedia.org/wiki/Isaac_As...
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Displaying 1 - 19 of 19 reviews
January 10, 2020
Ce introducere frumoasă în lumea matematicii ! Cu câtă claritate expune Asimov tărâmul numerelor și apariția acestora, de la numerele naturale pozitive, necesare pentru a număra obiectele din jurul nostru, la cele negative, apărute inevitabil ca o continuare a celor pozitive, dar și din necesități pragmatice, precum simbolizarea datoriilor, la fracțiile atât de necesare atunci când împărțirea se împotmolește în incapacitatea de a avea un rezultat exact între un deîmpărțit și împățitor precum 2 și 3 ș.a.
M-a surprins să aflu despre originea nenumăratelor cuvinte sau simboluri din matematică, care aruncă o nouă perspectivă asupra unor concepte pe care altfel le-am internalizat fără prea multă introspecție, precum plusul care apare care o prescurtare a formei scrise a simbolului ampersand ”&” sau cuvântul ”zero„ a cărui echivalent în arabă este ”sifr” și din a cărui rădăcină astăzi avem cuvintele ”cifru” sau ”descifra”, menite să simbolize misterul pe care zero l-a reprezentat.
Cu toate că mă așteptam să abordeze și concepte mai complexe precum integralele și derivatele, nu sunt dezamăgită, căci a prezentat destul de exhaustiv această introducere în ciuda dimensiunii mici a cărții, vorbind până și despre importanța lui zero și a diferitelor tipuri de infinit. Fascinația și entuziasmul meu față de scrierile de non-ficțiune ale lui Asimov continuă să crească astfel încât cred că voi continua în aventura pe care am început-o în a descoperi și alte astfel de scrieri ale autorului pe care încep să îl consider ca pe un mentor.
Și, desigur, finalul cărții mi s-a părut epic, demn de Asimov și de subiectul abordat:
”In a book dealing with the achievements of the human mind, then, one should not write THE END for there is no end. One should write only א∞ ”
M-a surprins să aflu despre originea nenumăratelor cuvinte sau simboluri din matematică, care aruncă o nouă perspectivă asupra unor concepte pe care altfel le-am internalizat fără prea multă introspecție, precum plusul care apare care o prescurtare a formei scrise a simbolului ampersand ”&” sau cuvântul ”zero„ a cărui echivalent în arabă este ”sifr” și din a cărui rădăcină astăzi avem cuvintele ”cifru” sau ”descifra”, menite să simbolize misterul pe care zero l-a reprezentat.
Cu toate că mă așteptam să abordeze și concepte mai complexe precum integralele și derivatele, nu sunt dezamăgită, căci a prezentat destul de exhaustiv această introducere în ciuda dimensiunii mici a cărții, vorbind până și despre importanța lui zero și a diferitelor tipuri de infinit. Fascinația și entuziasmul meu față de scrierile de non-ficțiune ale lui Asimov continuă să crească astfel încât cred că voi continua în aventura pe care am început-o în a descoperi și alte astfel de scrieri ale autorului pe care încep să îl consider ca pe un mentor.
Și, desigur, finalul cărții mi s-a părut epic, demn de Asimov și de subiectul abordat:
”In a book dealing with the achievements of the human mind, then, one should not write THE END for there is no end. One should write only א∞ ”
June 27, 2016
In just 150 pages, Asimov draws a complete and comprehensive guide to arithmetic. This book will inform you not only about mathematics, but also about the logic behind its greatest theories and theorems.
February 11, 2017
So it turns out that Isaac Asimov is possibly the only author to have a book in every major category of the Dewey Decimal System.
In this book, Asimov builds an understanding of basic mathematics from first principles, stacked one on top of the other in words that a child can understand (for example, me, at age 11).
In this book, Asimov builds an understanding of basic mathematics from first principles, stacked one on top of the other in words that a child can understand (for example, me, at age 11).
June 20, 2017
I wish someone would have handed me this book when I was a high school freshman. I would have found math much more interesting and less meaningless. I'm looking forward to reading more Asimov non-fiction.
August 4, 2020
En un inicio se tornaba algo interesante el hecho de explicar el "origen" de algunos fundamentos matemáticos, como remontarse a la historia de la ciencia (que es algo que siempre he tenido ganas de aprender) y durante la explicación del funcionamiento de las operaciones igual fue, en un inicio, interesante demostrar sin el uso del conocimiento actual como lo hacían las personas o tratar de representarlas en la antigüedad. Pero conforme avanza el libro en temas se va desviando de esa línea argumentativa y empieza a poner más ejemplo explicados textualmente de como se realiza la multiplicación, la división, la potencia y las raíces.
No esta mal si eres una persona que en algún momento no entendió sus clases de matemáticas o tiene la incertidumbre de porque algunas operaciones pero para alguien con un poco más de conocimiento sobre el tema se queda muy corto el libro. Tiene sus datos curiosos pero no lo suficientes como para leerlo por completo.
Al final se acomplejó de una forma vertiginosa ya que empieza muy tranquilo en los primeros capítulos y así sigue hasta el penúltimo, pero en el último capítulo se empieza a explayar bastante del hilo que traía anteriormente y sinceramente me perdí en su explicación ya que es más difícil (al menos para mí) comprender algunas cosas matemáticas si no se explica con números como debe de ser ya que de forma textual es obligatorio estar muy familiarizado con el tema o dominarlo para entender el lenguaje y no perderse como en los anteriores capítulos que por el dominio son fáciles de entender.
Lo recomendaría más para chicos de secundaria a prepa o estudiantes de universidad que no estén en una carrera de área 1.
Aparte de que en algunas partes (no se si sea por la edición) esta mal redactado o mal escrito las representaciones matemáticas y algunas palabras.
No esta mal si eres una persona que en algún momento no entendió sus clases de matemáticas o tiene la incertidumbre de porque algunas operaciones pero para alguien con un poco más de conocimiento sobre el tema se queda muy corto el libro. Tiene sus datos curiosos pero no lo suficientes como para leerlo por completo.
Al final se acomplejó de una forma vertiginosa ya que empieza muy tranquilo en los primeros capítulos y así sigue hasta el penúltimo, pero en el último capítulo se empieza a explayar bastante del hilo que traía anteriormente y sinceramente me perdí en su explicación ya que es más difícil (al menos para mí) comprender algunas cosas matemáticas si no se explica con números como debe de ser ya que de forma textual es obligatorio estar muy familiarizado con el tema o dominarlo para entender el lenguaje y no perderse como en los anteriores capítulos que por el dominio son fáciles de entender.
Lo recomendaría más para chicos de secundaria a prepa o estudiantes de universidad que no estén en una carrera de área 1.
Aparte de que en algunas partes (no se si sea por la edición) esta mal redactado o mal escrito las representaciones matemáticas y algunas palabras.
January 23, 2022
In 200 pages Asimov takes us from basic finger counting to endless endlessnesses. Towards the end it was getting a bit beyond me I'm not ashamed to say. It's sometimes difficult to 'read' numbers so that was a bit awkward for me. This was written in 1959 and I really liked seeing the differences with math then and today. For instance, he mentions charts of logarithms and also shows how a repeating decimal that we would put a line over today like 1.33333... would have a line over the 3's but back then I guess because of limitations with a typewriter maybe they put a dot over. I learned how to use an abacus and a slide rule. That may not seem vital in 2022 but I think it's important to learn how things used to be done not that long ago and to appreciate where we've come. I was also very impressed that some of the concepts he was using are right out of Common Core today. I wouldn't say the book was enjoyable really but I'm glad I read it.
April 11, 2024
Having read both of Asimov books on Numbers that is this one and "Asimov on Numbers" I would vouch for...both, but still if you want one better is this one
Reason is this book is more focused and also more explanatory to it's stuff
Though there are something which this book doesn't cover but other one does but I will stay upto this, only in case you are beginner
But if you are not, the you should choose the other one namely "Asimov on Numbers".
After all it's Asimov, it's a loss of millions to leave his any work unread
Reason is this book is more focused and also more explanatory to it's stuff
Though there are something which this book doesn't cover but other one does but I will stay upto this, only in case you are beginner
But if you are not, the you should choose the other one namely "Asimov on Numbers".
After all it's Asimov, it's a loss of millions to leave his any work unread
August 27, 2020
Asimov obviously delights in the beauty of numbers. It is an excellent review of all the mathematical theory I have forgotten since high school and college. I stopped trying to follow it about halfway through, and just read for the pleasure. I will probably go back and read it again if I need to remember how to do certain types of math.
August 29, 2017
interesting subject but i had a bad audio copy and i struggled with it
October 17, 2019
Read in Russian and English. Hi was interesting to see what Isaac had to say about the numbers.
February 4, 2022
This is a book intended for 5th graders but can be highly useful for adults too. Is a fascinating read for amateur mathematicians & number lovers alike. I very much recommend!!!
June 27, 2017
Unspeakably tedious. It's like sitting in on a maths class from your primary school days, with a perhaps overly enthusiastic teacher. For a while it is somewhat interesting to learn about why we subtract, add, multiply and divide in the way that we do, but then an hour passes, and then another, and it becomes more than I able to bear.
April 6, 2015
In this book, Asimov takes you through the development of numbers, from the initial set of positive integers through the transfinite alephs. The progression is logical, he first establishes the infinitude of the positive integers and then explains the reasons why negative numbers are needed. Along with the negative integers, he explains the basic rules of addition, subtraction, multiplication and division as applied to integers. Subtraction is used to justify the need for negative integers and then division to explain the need for fractions. Asimov uses the applications for commerce to describe how negative numbers and fractions came to be accepted.
At one point, he argues that the most powerful force driving the development of early mathematics was the need for the rulers of civilization to assess the values of land and collect the appropriate taxes. Interesting thought, and quite likely true. Negative numbers no doubt have their origin in the computation of back taxes and plane geometry and fractions arose from the need to measure and subdivide land. The more complicated computations of the areas of non-rectangular regions also led to the development of a great deal of geometry.
After fractions are covered, he then goes on to explain infinite decimals, starting with those that repeat and then to the ones that do not. Complex numbers are next, although here, he is somewhat limited in the explanation of the details in how arithmetic is done on complex numbers.
Written at the level of the middle school student, Asimov is once again at his best, explaining the various categories of numbers and showing why they are needed in the modern world. This book is very suitable reading for students at that level.
This review also appears on Amazon
At one point, he argues that the most powerful force driving the development of early mathematics was the need for the rulers of civilization to assess the values of land and collect the appropriate taxes. Interesting thought, and quite likely true. Negative numbers no doubt have their origin in the computation of back taxes and plane geometry and fractions arose from the need to measure and subdivide land. The more complicated computations of the areas of non-rectangular regions also led to the development of a great deal of geometry.
After fractions are covered, he then goes on to explain infinite decimals, starting with those that repeat and then to the ones that do not. Complex numbers are next, although here, he is somewhat limited in the explanation of the details in how arithmetic is done on complex numbers.
Written at the level of the middle school student, Asimov is once again at his best, explaining the various categories of numbers and showing why they are needed in the modern world. This book is very suitable reading for students at that level.
This review also appears on Amazon
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December 19, 2016Este libro fue uno de mis favoritos en mi adolescencia y fue el que me dió un impulso para tomar la matemática en serio. Es uno de los libros del Isaac Asimov científico que pocos conocen, no del autor de ciencia ficción que a todos encanta.
Es de saberse que este gran escritor, fue en su momento, prominente científico en la hoy extinta Unión Soviética y maestro prestigioso pero como muchos (v. gr. Sakharov) tuvo que dejar en algún momento su patria.
Este libro es prácticamente un tratado de aritmética desde los más recónditos inicios y con ejemplos prácticos que no dejan lugar a duda. Al parecer, fue la forma en que enseñaba aritmética en la URSS. Este libro es para las mátemáticas lo que El Juego de la Lógica, de Lewis Carroll (otro gran matemático y escritor) a la ciencia de la Lógica.
¡Muy recomendado!
Es de saberse que este gran escritor, fue en su momento, prominente científico en la hoy extinta Unión Soviética y maestro prestigioso pero como muchos (v. gr. Sakharov) tuvo que dejar en algún momento su patria.
Este libro es prácticamente un tratado de aritmética desde los más recónditos inicios y con ejemplos prácticos que no dejan lugar a duda. Al parecer, fue la forma en que enseñaba aritmética en la URSS. Este libro es para las mátemáticas lo que El Juego de la Lógica, de Lewis Carroll (otro gran matemático y escritor) a la ciencia de la Lógica.
¡Muy recomendado!
October 19, 2011
From zero to infinity and anything in between. Isaac Asimov, the famed science popularizer, beautifully and elegantly explained, in layman's terms, the origins of mankind's mathematical knowledge from the simplest known numbers to infinity. It contains bits of information that is not typically discussed inside a classroom. A great supplementary book for mathematics enthusiasts.
September 8, 2013
The Great Explainer discusses a widfe range of mathematical topics, my favorites concerning imaginary, complex and hypercomplex numbers. These are especially of interest to me from their use in fractal art, and Asimov makes clear here even the hairiest areas, including the notion of infinity and transfinite numbers in his usual lucid style.
October 22, 2011
Isaac Asimov covers the history of numbers. I love reading about how the understanding of numbers have evolved. Well written, and fascinating.
March 10, 2012
This is the book that got me interested in math as a young girl.
March 25, 2025
Good book.
Displaying 1 - 19 of 19 reviews