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Letters to a Young Mathematician
The first scientific entry in the acclaimed Art of Mentoring series from Basic Books, Letters to a Young Mathematician tells readers what Ian Stewart wishes he had known when he was a student and young faculty member. Subjects ranging from the philosophical to the practical--what mathematics is and why it's worth doing, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others--are dealt with in Stewart's much-admired style, which combines subtle, easygoing humor with a talent for cutting to the heart of the matter. In the tradition of G.H. Hardy's classic A Mathematician's Apology , this book is sure to be a perennial favorite with students at all levels, as well as with other readers who are curious about the frequently incomprehensible world of mathematics.
224 pages, Hardcover
First published January 1, 2006
112 people are currently reading
3103 people want to read
About the author
Ian Stewart
266 books756 followersIan Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.
--from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.
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Displaying 1 - 30 of 168 reviews
March 19, 2017
This book attempts to answer the following questions. 1) Is mathematics a worthwhile career? 2) What being a mathematician is like. 3) What type of jobs/careers are available? The main strength of Ian Stewart’s book is the way he addresses these questions in an entertaining manner. He manages to keep his explicit advice witty and brief.
Stewart reviews mathematics from high school to daily life to post docs. He also discusses the importance of mathematic teachers and the valuable role they play. Stewart encourages women to enter the field of math. Stewarts goal is opening the door into the world of mathematics and enticing the reader inside; he accomplishes this goal.
I read this as an audiobook downloaded from Audible. It is about five and half hours long. Jason Huggins does a good job narrating the book. Huggins is from Wales. He is an actor and audiobook narrator.
Stewart reviews mathematics from high school to daily life to post docs. He also discusses the importance of mathematic teachers and the valuable role they play. Stewart encourages women to enter the field of math. Stewarts goal is opening the door into the world of mathematics and enticing the reader inside; he accomplishes this goal.
I read this as an audiobook downloaded from Audible. It is about five and half hours long. Jason Huggins does a good job narrating the book. Huggins is from Wales. He is an actor and audiobook narrator.
March 12, 2013
Being no mathematician myself (and certainly lacking in talent), I don't think I have ever been this engrossed in reading a book about math. I basically devoured it. In fact, I believe anyone can devour it: there are no exotic symbols or scary formulas to put one off; the focus is on the humanistic side rather than the technical side; the book reads almost like a story as the imagined "Meg" (to which the book is supposed to be addressed) grows from a curious youngster to an established mathematician. On top of all that, Professor Ian Stewart (author) provides quite a bit of interesting inside information about the field, and doesn't forget to use humour to engage the reader. This little book really is a page turner.
February 13, 2020
বইটা যদিও গণিতের উপর, তবে এর মূল বক্তব্য আসলে যেকোন বিষয়ের জন্যই প্রযোজ্য। গণিত কিংবা অন্য যেকোন বিষয়ে উচ্চশিক্ষা নিয়ে কিশোর মনে যেসব প্রশ্ন থাকে, সেগুলোর সহজ-সুন্দর উত্তর আছে এ বইয়ে। উচ্চশিক্ষা কিংবা গবেষণা কী, এটা খুব কঠিন নাকি সহজ, স্কুল-কলেজের সিলেবাস থেকে কতটা আলাদা, কীভাবে গবেষণা করতে হয়, এরপর কি করা যাবে, এরকম সব বিষয়ে পরামর্শ আছে এ বইতে। বিএসসি পড়াকালীন সময়ের জন্য খুবই কার্যকর হবে, এমনকি স্কুল-কলেজের ছাত্র-ছাত্রীদেরও উপকারে আসবে।
February 11, 2023
This book presented in the form of a compilation of letters seeks to address the subject of mathematics, its difference from the school subject of arithmetic, role in everyday life, the career map, and how a student must approach this seemingly daunting subject. The to-be-freshman Meg writes to the author, a kin, asking him an array of questions that span the history of the subject, its application in the real-world, competition in the field, the correct attitude to wear while stuck in a pit of equations, numbers and Greek symbols. The author laments the way the subject is presented in schools, limiting the imagination and interest of students. Teaching arithmetic under the banner of ‘mathematics’ only dampens the awe with which it should be greeted. The repetitive, boring nature of the problems in school books that result in ‘correct’ or ‘incorrect’ answers leads them to believe there is nothing more to mathematics than long pages of calculation with side calculations, more side calculations and a very messy last page. This makes the likelihood of anyone learning the subject abhor the thought of more Mathematics outside the syllabus, which is an issue not faced by other subjects like physics and economics.
He addresses many common questions one may not know who to ask, from the saturation of mathematics in research and fear of proofs to teaching and participating in the mathematical community. The tone is friendly, patient, and the reader cannot be blamed if they believed for a moment that ‘Uncle’ Ian is helping them out in their career conundrum or doling out a lecture on quirky mathematical curiosities. The book addresses every facet of a mathematician's life from high-school to university and can be read by anyone, irrespective of age and experience, interested in mathematics or wanting to understand the trajectory of a mathematician’s life. While a parent could read it out to a 13-year old kid while internalising what it might take to guide them, every PhD candidate across STEM fields must read this before starting with their research and projects to provide an idea of a realistic approach to their discipline.
An essential read for students, parents, researchers and hobbyists to put into perspective what it means to become a mathematician, and is absolutely necessary (but not sufficient) for those who may not have people to mentor or guide them. This book serves as an inspiration at every level of enthusiasm for a wide range of experience.
‘Calling them [arithmetic] mathematics debases the currency of mathematical thought. It is a bit like using the term composing to describe routine exercises and playing musical scales’
- Chapter 5 (Audible)
He addresses many common questions one may not know who to ask, from the saturation of mathematics in research and fear of proofs to teaching and participating in the mathematical community. The tone is friendly, patient, and the reader cannot be blamed if they believed for a moment that ‘Uncle’ Ian is helping them out in their career conundrum or doling out a lecture on quirky mathematical curiosities. The book addresses every facet of a mathematician's life from high-school to university and can be read by anyone, irrespective of age and experience, interested in mathematics or wanting to understand the trajectory of a mathematician’s life. While a parent could read it out to a 13-year old kid while internalising what it might take to guide them, every PhD candidate across STEM fields must read this before starting with their research and projects to provide an idea of a realistic approach to their discipline.
An essential read for students, parents, researchers and hobbyists to put into perspective what it means to become a mathematician, and is absolutely necessary (but not sufficient) for those who may not have people to mentor or guide them. This book serves as an inspiration at every level of enthusiasm for a wide range of experience.
October 21, 2014
This book is amazing! Stewart did a great job in casually describing (to "Meg") what to expect in the life of a mathematician (in academia), as well as the splendor of mathematics. What I really REALLY liked was how the book described the beauty of mathematics in its own right, as well as the beauty of its applications in the real world. As a mathematics PhD candidate, I evidently am aware of the elegance of the subject, so a lot of the description was not new to me. Nevertheless, I ultimately favored how the book answered the common (naive) layperson question, "What is all this math good for?". Lots of people may not realize that math is EVERYWHERE (from the arrangements of an atom, to the biology of animals, to the automobiles we use, to the everyday electronics we cannot live without, etc.). Stewart truly depicted how remarkable the subject is, which was great reading in one paperback. I favored how this book is not written TO mathematicians, but to to ANYONE who is interested in mathematics altogether, and/or the life of a mathematician. Definitely recommended!
May 24, 2022
Más que un libro de divulgación sobre matemáticas en una autobiografía y ensayo acerca de lo que un matemático que ha pasado por todas las etapas académicas piensa sobre su propia disciplina. No son cartas a una joven matemática, son cartas a sí mismo acerca de lo que (creo) le hubiese gustado que le dijesen en el momento adecuado.
El libro es ameno y fácil de leer, quizá sea útil para aprenderse los nombres de los distintos campos de las matemáticas, pero poco se puede aprender acerca de ellas, por suerte tiene un buen apartado de referencias útiles al final del libro para quien quiera indagar más.
El libro es ameno y fácil de leer, quizá sea útil para aprenderse los nombres de los distintos campos de las matemáticas, pero poco se puede aprender acerca de ellas, por suerte tiene un buen apartado de referencias útiles al final del libro para quien quiera indagar más.
May 26, 2025
Simpático, es una serie de consejos epistolares a una estudiante de matemática universitaria. Le explica lo que va a encontrar en su vida estudiantil, profesional y docente. Con algunas reflexiones sobre ciertos problemas relevantes de la disciplina. Me hubiera aprovechado mucho leerlo en mis años universitarios...
July 14, 2021
I have many things to say about this book. But it was a good read for any young mathematician out there. To me, the book really encompassed many of the aspects of being a mathematician that I hold near and dear to my heart, while also having great advice for anyone who feels lost entering the daunting world of mathematics.
When I first started to become interested in math in middle school, my father, an algebraic topologist, had many of these same conversations with me. What is a proof and why should we care about it? What does it mean to do math, and how do we look for solutions to our problems.
One particular chapter that was meaningful to me was when the author talked about how the addressee to the letters, Meg, had never really done mathematics before. As a child, when my father told this to me, I remember being irrationally angry, as if my father was erasing everything I had ever learned. But he was right! Ian Stewart does a fantastic job of explaining the realities of mathematics to someone who is newly engaged in mathematics.
I cannot recommend this book to any new mathematician in college or early grad school. A very helpful and insightful book.
When I first started to become interested in math in middle school, my father, an algebraic topologist, had many of these same conversations with me. What is a proof and why should we care about it? What does it mean to do math, and how do we look for solutions to our problems.
One particular chapter that was meaningful to me was when the author talked about how the addressee to the letters, Meg, had never really done mathematics before. As a child, when my father told this to me, I remember being irrationally angry, as if my father was erasing everything I had ever learned. But he was right! Ian Stewart does a fantastic job of explaining the realities of mathematics to someone who is newly engaged in mathematics.
I cannot recommend this book to any new mathematician in college or early grad school. A very helpful and insightful book.
October 8, 2022
“Com'è bella la matematica: Lettere a una giovane amica” è un libro a metà tra un memoir e un manuale, scritto in forma epistolare e rivolto a Meg, un'ipotetica ragazza, prima bambina, poi adolescente, studentessa universitaria e infine adulta, dottoranda e poi ricercatrice.
È una raccolta di lettere in un certo senso, e purtroppo, “a metà”: abbiamo l'occasione di leggere solo gli scritti dell'autore, il celebre matematico scrittore e divulgatore Ian Stewart, e non le risposte di Meg. Il resto dobbiamo immaginarlo a partire dalle frasi di Stewart, che ci fa intuire la crescita dal punto di vista anagrafico della ragazza, così come le nuove sfide scolastiche e formative, ma sempre matematiche, che le si pongono davanti. Stewart presenta la professione della persona ricercatrice in matematica approfondendo varie dimensioni, dalla scelta dell'argomento al valore dei teoremi e delle dimostrazioni, dalla matematica pura a quella applicata e alla inutilità di ritenere queste distinte. Pensando a Meg, inoltre, si può considerare anche il problema della disparità di genere e del soffitto di cristallo in ambito accademico.
C'è un aspetto che ritengo essere il più importante, o almeno, è quello che ha toccato me maggiormente: è il capitolo 14, intitolato “I gradini della carriera”, dove Stewart parla di quello che è l'ingrediente chiave per la crescita accademica, ovvero il fattore umano. E non penso che mi abbia colpito solo per il periodo instabile degli ultimi mesi, tipico di chi ha finito il dottorato da poco e si è messo a cercare una futura posizione in università, ma perché è fondamentale, non solo nella ricerca.
“Qui sta il paradosso del nostro mestiere: pur essendo un'attività solitaria, a volte persino erimitica, l'aspetto più importante della ricerca non è il campo che scegli, o i problemi che decidi di affrontare, ma i rapporti che intrattieni con chi ti circonda.” – Pag. 102
Stewart aggiunge che è importante identificare il proprio ruolo all'interno della tribù. Penso che questo processo possa svolgersi con l'avvio del dottorato, quando si potrebbe avere la non sempre garantita facoltà di scegliere il proprio supervisore. Oppure ciò potrebbe avvenire anche in seguito, ma ci si augura sia comunque il prima possibile. Tuttavia, penso anche che sia – che dovrebbe essere – un'attività che continui a ripetersi a ogni nuovo inizio.
Avrei preferito che si fosse tradotto il titolo inglese del libro, “Letters to a young mathematician”, in maniera letterale. La parola “amica” ha sostituito una professione. L'ho trovato forse un po', come dire, sminuente?
È una raccolta di lettere in un certo senso, e purtroppo, “a metà”: abbiamo l'occasione di leggere solo gli scritti dell'autore, il celebre matematico scrittore e divulgatore Ian Stewart, e non le risposte di Meg. Il resto dobbiamo immaginarlo a partire dalle frasi di Stewart, che ci fa intuire la crescita dal punto di vista anagrafico della ragazza, così come le nuove sfide scolastiche e formative, ma sempre matematiche, che le si pongono davanti. Stewart presenta la professione della persona ricercatrice in matematica approfondendo varie dimensioni, dalla scelta dell'argomento al valore dei teoremi e delle dimostrazioni, dalla matematica pura a quella applicata e alla inutilità di ritenere queste distinte. Pensando a Meg, inoltre, si può considerare anche il problema della disparità di genere e del soffitto di cristallo in ambito accademico.
C'è un aspetto che ritengo essere il più importante, o almeno, è quello che ha toccato me maggiormente: è il capitolo 14, intitolato “I gradini della carriera”, dove Stewart parla di quello che è l'ingrediente chiave per la crescita accademica, ovvero il fattore umano. E non penso che mi abbia colpito solo per il periodo instabile degli ultimi mesi, tipico di chi ha finito il dottorato da poco e si è messo a cercare una futura posizione in università, ma perché è fondamentale, non solo nella ricerca.
“Qui sta il paradosso del nostro mestiere: pur essendo un'attività solitaria, a volte persino erimitica, l'aspetto più importante della ricerca non è il campo che scegli, o i problemi che decidi di affrontare, ma i rapporti che intrattieni con chi ti circonda.” – Pag. 102
Stewart aggiunge che è importante identificare il proprio ruolo all'interno della tribù. Penso che questo processo possa svolgersi con l'avvio del dottorato, quando si potrebbe avere la non sempre garantita facoltà di scegliere il proprio supervisore. Oppure ciò potrebbe avvenire anche in seguito, ma ci si augura sia comunque il prima possibile. Tuttavia, penso anche che sia – che dovrebbe essere – un'attività che continui a ripetersi a ogni nuovo inizio.
Avrei preferito che si fosse tradotto il titolo inglese del libro, “Letters to a young mathematician”, in maniera letterale. La parola “amica” ha sostituito una professione. L'ho trovato forse un po', come dire, sminuente?
March 1, 2014
a bit childish, but good,
a bit vague but interesting,
could have been better,
what he says in relation to G.H. Hardy I don't agree with at all and he doesn't demonstrate his claim ..at least not with any clarity and definitely not with any conviction.
he de-mystifies certain things when he is actually trying to mystify them.
he tried to write for a broad audience and ended up really talking to no one, or rather, not really really reaching anyone.
it was good, but lacked strong opinion and deep insight.
i STRONGLY recommend reading "letters to a young poet" by Raiker , this is the book in which M.Stewarts title is stolen and partially based on. that book, i feel, is more appropriate for a young anyone ,even a young mathematician.
and i also RECOMMEND reading "a mathematicians apology" by G.H. Hardy. this brief essay combined with M;Raikers book will do for you a lot more then Ian's attempt.
peace ,love & humility.
√2
a bit vague but interesting,
could have been better,
what he says in relation to G.H. Hardy I don't agree with at all and he doesn't demonstrate his claim ..at least not with any clarity and definitely not with any conviction.
he de-mystifies certain things when he is actually trying to mystify them.
he tried to write for a broad audience and ended up really talking to no one, or rather, not really really reaching anyone.
it was good, but lacked strong opinion and deep insight.
i STRONGLY recommend reading "letters to a young poet" by Raiker , this is the book in which M.Stewarts title is stolen and partially based on. that book, i feel, is more appropriate for a young anyone ,even a young mathematician.
and i also RECOMMEND reading "a mathematicians apology" by G.H. Hardy. this brief essay combined with M;Raikers book will do for you a lot more then Ian's attempt.
peace ,love & humility.
√2
January 9, 2016
I assigned this book to my Trig class, and they responded mostly well to it. The funniest part is that they were surprised to find that Meg wasn't real. This worked well as a launching point into discovering math all around, and the students still mention how math is everywhere, much to their chagrin/surprise! Sometimes the author was a little long-winded or over their head, but the students sometimes considered actually looking into the strange things mentioned. I hope to adapt portions of this book for future classes, especially the sections on learning math and teaching math. The book is rife with stories and urban legends of mathematicians through history and really goes to show what a profession in mathematics can be like.
Would that I could encourage students like Mr. Stewart has encouraged me!
Would that I could encourage students like Mr. Stewart has encouraged me!
This entire review has been hidden because of spoilers.
March 7, 2015
"If you publish nothing for five years and then solve the Poincaré conjecture, you'll be set for life, assuming you are allowed to keep your job while you are doing it. If you publish nothing for five years and then fail to solve the Poincaré conjecture, you'll be out on your ear."
Please don't get me wrong, I simply liked it and recommend it to everyone (at least who has some interests in math). But in particular, in the first chapters, the book didn't seem that interesting to me, to get 4/5. It starts with typical mathematical concerns of a Bachelor student and then continues with PhD, post-doc and so on; and it is getting more interesting by the way!
Please don't get me wrong, I simply liked it and recommend it to everyone (at least who has some interests in math). But in particular, in the first chapters, the book didn't seem that interesting to me, to get 4/5. It starts with typical mathematical concerns of a Bachelor student and then continues with PhD, post-doc and so on; and it is getting more interesting by the way!
May 22, 2025
I thought this book had some good parts, but mostly I didn't find it engaging or relevant to me. I know that you shouldn't rate a book lower because it wasn't the book you wanted it to be, but I will make an exception here. I consider myself a young mathematician, but this book almost exclusively dealt with how to survive in academia, which is not the path I want to take. It was light on the math. Maybe the most applicable insight Stewart recommends for me is that if you get stuck in a textbook, instead of pounding your head against the wall, try and move on and see if the concept clicks as it is expounded upon.
March 3, 2014
Letters To A Young Mathematician is a great book if you're looking for a genereal idea of what it's like to do mathematics for a living. It answers many questions, including the old wondering: what is mathematics exactly?
The book is a series of letters addressed to an aspiring mathematician called Meg. This is a fresh and interesting way to deliver factual information to the reader, and even a better way to keep track of the author's thinking process.
The book is a series of letters addressed to an aspiring mathematician called Meg. This is a fresh and interesting way to deliver factual information to the reader, and even a better way to keep track of the author's thinking process.
March 26, 2022
El libro narra las conversaciones imaginarias entre Ian Stewart y una supuesta joven que decide encaminar su formación académica en el ámbito de las matemáticas. De esta manera, el autor le da a la joven Meg todos esos consejos que al propio Ian le hubiera gustado recibir cuando de joven se estaba abriendo camino en el mundo de las ciencias exactas. Según se va avanzando en los capítulos, se ve una evolución en la vida de Meg, cómo al principio decide elegir la rama de las matemáticas para estudiar en la universidad, más adelante como se abre hueco en la docencia una vez ha terminado sus estudios, más adelante cómo decide encaminarse a la investigación, y cómo termina firmando grandes trabajos junto a compañeros de prestigio.
Con el formato de cartas el autor nos permite entrar en su intimidad, en sus conversaciones más personales con una buena amiga, nos hace partícipes de los mejores consejos que un maestro le confía a su alumno preferido. La evolución de la protagonista nos permite ver lo que es la vida de un investigador empezando desde abajo hasta llegar a la publicación de grandes trabajos. Los capítulos son cortitos y se leen con rapidez, enganchan muchísimo. Un libro maravilloso.
Con el formato de cartas el autor nos permite entrar en su intimidad, en sus conversaciones más personales con una buena amiga, nos hace partícipes de los mejores consejos que un maestro le confía a su alumno preferido. La evolución de la protagonista nos permite ver lo que es la vida de un investigador empezando desde abajo hasta llegar a la publicación de grandes trabajos. Los capítulos son cortitos y se leen con rapidez, enganchan muchísimo. Un libro maravilloso.
June 15, 2024
Hace muchos años que quise leer este libro, pero no tuve la oportunidad. Sin embargo, el momento llegó y me ha encantado.
A pesar de que las cartas van dirigidas a Meg, una joven aspirante a estudiar Matemática (que luego vemos su viaje por este mundo científico) se ha sentido como si el autor hablara a tu propia alma para llevarte de la mano por cada etapa que pasa un profesional en matemática.
Considero que debería ser lectura obligatoria en las facultades de matemática, porque muestra la realidad de esta noble carrera, sus desafíos y lo mucho que puedes lograr a través de ella.
Necesitaba una dosis de motivación para continuar redactando mi tesis de maestría en Matemática Aplicada y qué maravilla de libro para continuar con mi propio viaje en este mundo maravilloso de las matemáticas.
A pesar de que las cartas van dirigidas a Meg, una joven aspirante a estudiar Matemática (que luego vemos su viaje por este mundo científico) se ha sentido como si el autor hablara a tu propia alma para llevarte de la mano por cada etapa que pasa un profesional en matemática.
Considero que debería ser lectura obligatoria en las facultades de matemática, porque muestra la realidad de esta noble carrera, sus desafíos y lo mucho que puedes lograr a través de ella.
Necesitaba una dosis de motivación para continuar redactando mi tesis de maestría en Matemática Aplicada y qué maravilla de libro para continuar con mi propio viaje en este mundo maravilloso de las matemáticas.
May 5, 2020
La trama de la secuencia narrativa, sobre el interés de las matemáticas a personas que tienen ese interés en aprenderlas, estudiarlas, o trabajar sobre ellas no creo que pueda cautivar a todo el público sobre el maravilloso mundo de las matemáticas, por el contrario creo que solo abarca un segmento muy pequeño de la población cuando el propio contenido pudiese enamorar más profundamente.
Aún así el libro es abundante e increíble para leer más de una vez y recomendar a quien se quiera formar en esta rama
Aún así el libro es abundante e increíble para leer más de una vez y recomendar a quien se quiera formar en esta rama
April 6, 2022
Sorprendente aproximación al mundo universitario, doctoral y de investigación matemática, aunque aplicable a cualquier campo de estudio.
Stewart logra en un formato de cartas atraparte y mostrarte el interesante mundo matemático, sus posibilidades, sus preguntas por resolver y su capacidad de hacerte valorar más el mundo que te rodea.
Una grata sorpresa.
Stewart logra en un formato de cartas atraparte y mostrarte el interesante mundo matemático, sus posibilidades, sus preguntas por resolver y su capacidad de hacerte valorar más el mundo que te rodea.
Una grata sorpresa.
July 16, 2025
I think this is a great read for an early undergrad math major that is interested in pursuing a graduate career in math. A lot of it for me felt like I wasn’t the right audience, but the last few letters were good for me
July 2, 2025
The quality of each chapter fluctuates a little bit on the start. As the book progresses, this fluctuation stabilizes in a very intriguing and compelling reading.
As a msc mathematics student, like Meg in some point of her fictional career, I myself wondered about some of the questions answered by Ian Stewart. The Chapter 7 "How Mathematicians Think" was remarkably insightful.
Very good book, will be a recommendation to every freshman I tutor.
As a msc mathematics student, like Meg in some point of her fictional career, I myself wondered about some of the questions answered by Ian Stewart. The Chapter 7 "How Mathematicians Think" was remarkably insightful.
Very good book, will be a recommendation to every freshman I tutor.
May 5, 2022
4/5. Cumple con el objetivo de motivar a sus lectores a seguir por el camino de las matemáticas, aunque su enfoque es más directo para aquellos que gustan de los números. A pesar de que no hay demasiado uso de fórmulas y problemas, los que se utilizan son suficientes para enredar a los poco conocedores, sin embargo, la narrativa es sencilla para poder seguir el hilo de los temas y para irnos enganchando en esta ciencia. Sinceramente no es un libro para quienes no son muy fanáticos de las matemáticas.
May 27, 2024
Es el mejor libro de matemática divulgativa (en mi opinión de matemática) que he leído. Tiene un texto simple e informativo, con algunas curiosidades entre medio bien puestas y con su respectiva referencia. A lo largo de una serie de cartas da más o menos con la idea de qué va la ocupación de matemático con sus aristas y suavidades.
Agradecida de haberlo leído, es de esos libros que hubiera querido leer antes, aunque creo que empatizo mucho mejor con el autor con mi edad y formación actual.
Agradecida de haberlo leído, es de esos libros que hubiera querido leer antes, aunque creo que empatizo mucho mejor con el autor con mi edad y formación actual.
August 3, 2019
This book offers an insight into academics, explaining culture and customs of the mathematical community. Stewart says «Letters to a Young Mathematician is my attempt to bring some parts of G.H. Hardy's A Mathematician's Apology up to date, namely, those parts taht might influence the decisions of a young person contemplating a degree in mathematics and a possible career in the subject».
So, this is a must-read for those who are contemplating a career in maths or beginning it. It's not the case for me, being already a graduate for 15 years. I have enjoyed it even now, but I'm sure I would have enjoyed it much more 20 years ago. The book is written in the form of letters addressed to "Meg", an imaginary correspondent, through her career in chronological order, from high school to a tenured position in a university.
Stewart talks about philosophy, career decisions, the mathematical community, the job of a profesional mathematician (he asures a typical day is ten or twelve hours long, with teaching commitments, research grants to pursue, proper mathematical research and certain amount of bureaucracy), the subject itself, a bunch of problems, pure vs applied mathematics, teaching (at college level), proofs, use of computers in research, a bit of his own life or the more modern work style with collaborations, not alone as it used to be.
I liked the metaphor he uses when saying a proof is a story. He says «it is a story told by mathematicians to mathematicians, expressed in their common language. It has a beginning (the hypotheses) and an end (the conclusion), and it falls apart instantly if there are any logical gaps». This has captivated me.
The author also explores how do mathematicians think. He quotes Hadamard or Poincaré, and he agree more or less in the next scheme: 1. Conscious work on a problem. 2. Stop thinking about the problem and do something else: let the subconscious do its job, leading to the big "aha!" moment. 3. Another conscious stage of writing everything down formally.
So, this is a must-read for those who are contemplating a career in maths or beginning it. It's not the case for me, being already a graduate for 15 years. I have enjoyed it even now, but I'm sure I would have enjoyed it much more 20 years ago. The book is written in the form of letters addressed to "Meg", an imaginary correspondent, through her career in chronological order, from high school to a tenured position in a university.
Stewart talks about philosophy, career decisions, the mathematical community, the job of a profesional mathematician (he asures a typical day is ten or twelve hours long, with teaching commitments, research grants to pursue, proper mathematical research and certain amount of bureaucracy), the subject itself, a bunch of problems, pure vs applied mathematics, teaching (at college level), proofs, use of computers in research, a bit of his own life or the more modern work style with collaborations, not alone as it used to be.
I liked the metaphor he uses when saying a proof is a story. He says «it is a story told by mathematicians to mathematicians, expressed in their common language. It has a beginning (the hypotheses) and an end (the conclusion), and it falls apart instantly if there are any logical gaps». This has captivated me.
The author also explores how do mathematicians think. He quotes Hadamard or Poincaré, and he agree more or less in the next scheme: 1. Conscious work on a problem. 2. Stop thinking about the problem and do something else: let the subconscious do its job, leading to the big "aha!" moment. 3. Another conscious stage of writing everything down formally.
March 26, 2008
Probably nothing drastically new here for many young mathematicians, but still includes some good stories and useful tips, and it's always interesting to hear how an established professional got into their field in the first place.
Stewart makes an interesting point that, unlike many other fields, you don't just happen to fall into math - it has to be something you're really into (although it may take a lot of lucky coincidences to let you realize that you're good at math and into it as well).
There's also a good illustrative story useful especially for mathematicians, about how committees work. The committee had to choose between 2 options, and the mathematician in the group realized at once that one of the choices was much much better, so immediately he explained why. His reasons were clear and logical and nobody disagreed. But since the other committee members hadn't had a chance to have their say yet, the discussion continued. He stayed out of it, knowing he'd already made the most important point... but when it came to the vote, everybody had forgotten his point in the face of all the other rambling, and they voted for the other (worse) option instead. So... Logic is crucial but timing is important too!
I also liked some of the comments he made about teaching - I don't know if I'd agree with all of it but it'd be worth returning to if I have a teaching position in the future. I especially like where he talks about how important it is to internalize lower-level ideas in math, not just recall their definitions or simplest expressions. For example, multiplying 5x4 is like taking four sets of five items each: 5+5+5+5. But you have to have some practice with the concept and internalize it before you can multiply 555x444, because it's not really sensible to do 555+555+... that many times. And once you've internalized it and reached a higher-level understanding, there's much more you can do with it than when you were still thinking in concrete terms of adding small sets of items.
Stewart makes an interesting point that, unlike many other fields, you don't just happen to fall into math - it has to be something you're really into (although it may take a lot of lucky coincidences to let you realize that you're good at math and into it as well).
There's also a good illustrative story useful especially for mathematicians, about how committees work. The committee had to choose between 2 options, and the mathematician in the group realized at once that one of the choices was much much better, so immediately he explained why. His reasons were clear and logical and nobody disagreed. But since the other committee members hadn't had a chance to have their say yet, the discussion continued. He stayed out of it, knowing he'd already made the most important point... but when it came to the vote, everybody had forgotten his point in the face of all the other rambling, and they voted for the other (worse) option instead. So... Logic is crucial but timing is important too!
I also liked some of the comments he made about teaching - I don't know if I'd agree with all of it but it'd be worth returning to if I have a teaching position in the future. I especially like where he talks about how important it is to internalize lower-level ideas in math, not just recall their definitions or simplest expressions. For example, multiplying 5x4 is like taking four sets of five items each: 5+5+5+5. But you have to have some practice with the concept and internalize it before you can multiply 555x444, because it's not really sensible to do 555+555+... that many times. And once you've internalized it and reached a higher-level understanding, there's much more you can do with it than when you were still thinking in concrete terms of adding small sets of items.
February 2, 2011
230 de 230. Me hubiera gustado leer Cartas a una Joven Matemática cuando estudiaba la prepa, de seguro me hubiera dedicado a las matemáticas y es que Ian Stewart te presenta todo ese mundo que va desde las mismas matemáticas hasta los matemáticos de una forma tan extraordinaria y fácil de comprender, abriéndote los ojos y borrando estereotipos que se tiene sobre ellas.
Sin embargo hay veces que se muestra más de un lado que le del otro, no es imparcial en algunos aspectos que debería serlo haciendo suponer que su opiniones son las ideales y correctas (tal vez lo sean). Pero en general es un buen libro y le servirá de mucha ayuda a esas personas que quieran hacer una carrera formal en las matemáticas pero los típicos comentarios mal infundados los hacen dudar.
Sin embargo hay veces que se muestra más de un lado que le del otro, no es imparcial en algunos aspectos que debería serlo haciendo suponer que su opiniones son las ideales y correctas (tal vez lo sean). Pero en general es un buen libro y le servirá de mucha ayuda a esas personas que quieran hacer una carrera formal en las matemáticas pero los típicos comentarios mal infundados los hacen dudar.
January 11, 2013
OK,I was out of my element here.My math teacher lend me the book and though it's recommended to high school students but I think if you're a high school student should really like maths and you read books about them then you should read this.I as mostly romance reader couldn't exactly follow the idea of the book because it's plotless.Stewart just talks about maths all by himself.It might had helped if Meg's letters were also inside the book since sometime he answered things to her that I did not knew she had asked.If you like maths you will find this book interesting.If you want to read about maths but you're a newbie I would suggest to start with another book before you read this.
July 19, 2014
Letters to a young mathematician is a series of epistles to an up and coming yet fictitious mathematician. The scope of material is broad, consisting of mathematical topics both new and old. Certain topics are discussed in greater depth and detail than others allowing for Stewart's immense mathematical knowledge and ingenious modus operandi to shine through. The book will appeal more to existing mathematicians rather than to wannabes... where the thrill, exhilaration and beauty of mathematics and the mathematical ordeal is often lacking.
October 10, 2022
Some very valuable advice given through letters. I think some chapters will become much more relevant as I progress through a little bit more of life, and some chapters near the end might never be really relevant at all, but at least it has confirmed to me that mathematics is what I want to do.
Ah, and then the last chapter has truly confirmed that applying for MathPhil is the right choice. I can now sleep happily.
Ah, and then the last chapter has truly confirmed that applying for MathPhil is the right choice. I can now sleep happily.
December 23, 2022
-some good career advice
*(only work with people you actually want to work with, work with a Phd supervisor who will actually pay attention to you,
-some good general math tips
*(don't reread lines until you finish a chapter, learn backwards, read around your subject, look for invariants when solving problems, a proof is a story, state easier problems when a harder one is stumping you)
-Lots of rambling
*(only work with people you actually want to work with, work with a Phd supervisor who will actually pay attention to you,
-some good general math tips
*(don't reread lines until you finish a chapter, learn backwards, read around your subject, look for invariants when solving problems, a proof is a story, state easier problems when a harder one is stumping you)
-Lots of rambling
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