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By MIGUEL Á. GOBERNA 10/10/2008, from El País
Mediocre alumno durante su niñez, du Satoy se apasionó por las matemáticas a los 13 años, a raíz de su inmersión en los acertijos de Martin Gardner y de su asistencia a unas charlas divulgativas (las Royal Institution Lectures) de las que salió prometiéndose dominar un día aquel intrincado lenguaje. Después de graduarse en matemáticas por la Universidad de Oxford y de trabajar algunos meses en un kibbutz israelí, aceptó una irresistible oferta de empleo de la Royal Society, por 10 años, que le permitiría compatibilizar la investigación en su Universidad con la divulgación científica.
Hoy, a sus 43 años, du Sautoy es un reputado investigador, más selecto que prolífico (sus 36 publicaciones reseñadas en MathScinet han dado lugar a 302 citas por 184 autores) y figura indiscutible de la divulgación matemática: es comentarista de temas científicos y educativos en diferentes medios de comunicación escrita (como el diario londinense The Guardian), presentador de programas divulgativos en cadenas de radio y de televisión, programador de las Royal Institution Lectures y autor de libros tan excelentes como A Mathematician’s Journey Through Symmetry y el que nos ocupa. Algunas de las claves del éxito de este último son (en mi opinión) que du Satoy es un consumado especialista en el problema elegido como hilo conductor del libro (¿cuántos números primos son inferiores a un natural dado?), que nos puede contar anécdotas de muchos protagonistas de la historia porque los conoce personalmente o a través de amigos comunes y que atesora el don de hacer accesibles a lectores no matemáticos los conceptos más abstractos a través de poderosas metáforas: los números primos serían los átomos del universo numérico (puesto que todos los números se obtienen a partir de los naturales y éstos son productos de números primos) mientras que los ceros de la función que determina la distribución de los números primos (la función zeta de Riemann) pueden imaginarse como los puntos a la orilla del mar en cierto paisaje (el determinado por su gráfica).
Para du Sautoy, la tarea fundamental del matemático es probar teoremas acerca de una realidad que está fuera de él (un platonismo anacrónico para los filósofos). Los números primos, sin ir más lejos, están en la naturaleza: las especies de cigarras que han superado la selección evolutiva son aquellas cuyos ciclos de vida son números primos (se han encontrado especies con ciclos de vida de 13 y 17 años, por lo que sólo compiten cada 13×17=221 años). Las demostraciones deben ser irrefutables y no pueden ser sustituidas por experimentos, por numerosos que éstos sean (una escrupulosidad ridícula para los físicos). Así, aunque la hipótesis de Riemann (la parte real de todos los ceros no triviales de la función zeta es 1/2) es cierta para los 6.000 millones de ceros que se han calculado hasta ahora, sigue sin ser un teorema.
Aunque no todos los problemas matemáticos sean tan difíciles como el de Riemann -forma de suicidio intelectual de muchos matemáticos (como Nash, cuya biografía inspiró Una mente maravillosa)-, el informe semanal típico del investigador podría ser: el lunes concebí una conjetura para el problema que estoy estudiando, de martes a jueves no conseguí ningún avance y el viernes probé que la conjetura era falsa. Claro está que la resolución del problema proporciona (cuando se consigue) una satisfacción (que du Sautoy compara con un orgasmo) proporcional a la dificultad del reto. Muchos lectores dudarán de la utilidad de los números primos y creerán, además, que ya sabemos todo sobre ellos tras más de 2.000 años de investigación. Nada de eso. No sólo subsisten viejas conjeturas como la de Goldberg (todo número par mayor que 2 es la suma de dos números primos), sino que algunos problemas son la base del comercio electrónico: las tarjetas de crédito se codifican multiplicando dos números primos grandes (secretos), mientras que su descodificación por los hackers requiere la descomposición de su producto (público) en sus factores primos, estableciéndose así una feroz competencia entre buscadores de primos enormes y de algoritmos de factorización. Ojalá estas líneas hayan suscitado el interés del lector por tan formidable libro.
Miguel Á. Goberna es catedrático de Estadística e Investigación Operativa en la Universidad de Alicante
1) Can you remember or do you have some anecdote or a moment in your life, (as Du Sautoy did) that influenced you in your relationship with maths?
2) What is the objective of a mathematician for Marcus du Sautoy?
3) What is the daily work of a mathematician?
Nice article
1) Since always, I liked more maths than languages or whatever, and I have always been fascinated by Physics. But one day, I read a book that “opened” my eyes, that was called “L’enigma de Fermat” that made me “like” even more maths.
1) Hmmm… yep. Unfortunately, I do have a (not good) memory related with math. It wasn’t really nice for me to see my FIRST FAILED EXAM (and it was math). Yeah, I’m not a robot, ya know? (I sometimes wish to be one, but always in math lessons) I also fail math exams…
Well, I remember that in the exam, i got… a 3. Well, I was expecting that, cuz I wasn’t understanding anything and we did that unit (I don’t remember what was it about) a bit too fast for me. I think I was in… 3rd of primary, maybe? I don’t know if I was in 3rd or in 4th, but I failed anyway, heheh. I was warning my family that the exam didn’t go “really smoothly” and when I brought it to home… I was surprised because they weren’t angry (I suppose they had enough with seeing my face hehe). So you wanted to know more about me, right? Then I hope this was useful for you, even if it’s embarrasing or shameful, heheh.
2) I think, as the text says, that Sautoy’s objective is “prooving theorems about a reality which is outside him”. I don’t really understand it, but I think it means he is trying to know more about the world in which we live.
3) Hehehee, I don’t know. Depending in who the mathematician is! (There are some of them which are very lazy!) Mathematicians (AKA pattern searchers) are always looking for patterns, and they want to go beyond and beyond and… did I mention beyond? Well, the point is that no matter what they do or discover, they will always be helpin’ us (specially me and the people who like more languages) to understand (as I said before) the world AND US.
1) Well I think that I don’t have some experience like this. But I thing that I can remember one. I remember that I have one experience like Cristina’s experience. When I was in primary, I didn’t studied a lot for exams, but I approved all the exams. Bu when I arrived in 6th of primary I didn’t studied a lot for the first exam and well I didn’t failed it but I think that I had a six or some note like this. And after the exam I studied a lot for all the exams of maths, because if I don’t study… :S
2)I think that the text says that Sautoy says that a mathematician’s objective is prooving theorems about a reality which is outside. I don’t understand is so much.
3) I don’t know very well what is the daily work of a mathematicians but I think that this is depending of wich mathematician. For example if we talk about a really mathematician, I think that his daily work is look for patterns and look for do some things of mathemathics more easy, or he looks for formulas… , But I think that a mathematician is not always doing maths. But for example if we talk about a maths teacher (that I think that is mathematician too), his daily work is teach maths to other people.
I
Hey!!
1) Well, yes, I also have a moment where my relation with maths made a very big change. When I was from five to ten I didn’t like maths. I thought them where stupid, that you couldn’t apply them to the real life, borings, strange, without reason. But when I arrived to sixth of primary a new teacher for my changed all that. She showed my what maths are and how they can be funny and easier to learn. Then I Start to love maths, but´ all that only was during one year, after I didn’t turn to feel like that for maths.
In my opinion teachers can make things more easier and interesting, because I love some subjects because some teachers taught me how its real are, I mean a positive way for see them. For last t I would like to say that maths are not only practice, you also have to study.
2) For Marcus Du Sautoy the objective of a mathematicians is : prove that the theorems about a reality which are outside of it”. That means that mathematician try to relate theorems with the real life, apply maths, I mean use some cases that are in the nature for use them as proofs that the theorem is correct. In the new, the incredible example is about how prime numbers are a way for predict how the nature will change for do the next step of evolutionary selection. It’s really incredible because It means that you can know trough numbers what is going to happen some years after, It’s great!!
3)Well, there is not a specific “daily work ” for a mathematician. First of all, because it depends of the type of mathematician. I mean, it depend if the mathematician do apply or pure maths, or if for example teach maths, scientific investigations, etc.
For Marcus Du Sautoy there is a way, but I think that This way is his way of be a mathematic.
Just for finish I would like do a touchdown. In the last paragraph, in my opinion there is a reference of applying mathematician, the hackers. They are mathematicians, because if you see which is they work, you arrive to the conclusion that they are mathematics. They try to decode codes and also look for patterns and solve the mystery that is behind the process to do passwords.
That’s all!
1) I think that this anectod it isn’t soo important but i will explain it.
In Primary, I didn’t study maths, but I have really good notes. All of then I think that were from 9 to 10 because the exams are problems easy that use practise like problems of sum, subtract , multiply and divide. But in 6th of primary, the classes started to have geometry , theory and soo on. What I say, I don’t study Maths and I fale the exam. Because that I start to study any exam if is difficult or easy understandeble or inunderstandeble.
2) I think that Marcus du Sautoy objective is to proof and obtain theorems in the real world that it has got Maths every where for example: Primes numbers are in the Nature. Definitely that du Sautoy will like obtain theorems that where at the world.
3) The daily work of the mathematicians it depens, what is the mathematician working: Apply or Pure mathematics and his objective and he’s caracter,because if for example, a mathematician will like to discobert a formula to obtain the perfect number, and this mathematicians is working hard, he’s daily working is to find the perfect number. Definetly the daily work of the mathematician is to obtain he’s objective.
1) I think that my mind changed a little bit about maths when Maria Merino explained me algebra. When she explained it to me all become clearer and since that i see the units in a different way, if at the begining i don’t understand all i know that finally i will understand it i only have to look for the way.
2) For him is prove theorems.
3)I think they look for formulas, patterns, theorems and new kind of things… I don’t know
1) Can you remember or do you have some anecdote or a moment in your life, (as Du Sautoy did) that influenced you in your relationship with maths?
I remember that in primary school and in first of ESO too, I never needed to study for any exam of maths, maybe because in those exams there wasn’t any theory asked. However, in second of ESO, which was my first year in the CLIL project, I went to the first exam of the unit one without studying and without knowing anything about how to do some things. Of course I failed this exam with the grade of 4.5, and that made me realize that I need to study for the math’s exams because in the future exams it will appear theory too.
2) What is the objective of a mathematician for Marcus du Sautoy?
The objective of a mathematician for Marcus Du Sautoy is to prove theorems about a reality which is outside him. It’s difficult to understand what Du Sautoy says about the objective of a mathematician.
3) What is the daily work of a mathematician?
The daily work of a mathematician depends on the type of mathematician he/she is. For example; there are the mathematicians that are always searching formulas and patterns, there are the ones (in my opinion) that teach other people (like Carlota), and in the text says that the hackers seems mathematicians because they search patterns to know the code of something.
So, in my opinion the daily work of a mathematician it depends on the type of mathematic it is.
1) Yes, I have an anecdote but it isn’t a good anecdote it’s a very bad anecdote.
When I start ESO I did maths in Catalan and it was difficult but I obtain good marks.
But, when in second of ESO I start to do maths in English, I started to fail all the exams. I think that in second of ESO I only obtain a “good” mark in two exams.
2) I think that the objective of a mathematician for Marcus du Sautoy is to prove theorems about a reality which is outside him. It’s difficult to understand it so, I don’t understand it.
3) I don’t know which is the daily work of a mathematician. But, as we did in class, I think that for some mathematicians the daily work is search patterns. To other mathematicians the daily work can be prove theorems and for others mathematicians it can be teach all that he know to the people. So, I think that every mathematician has his daily work.
1- I can’t remeber any anectod of something like that. That influenced my relatioship with maths but I will say that study Maths in English was a big change for me because in Primary school all that I did in maths was calculated and calculated things but now a days I know that maths is not only calculated numbers. Maths is a way to expresss things and not all is related with numbers there are also things of real life that have relation with maths.
2- For Marcus du Sautoy a mathematician have to proofs things that are in real life.
3- I think that the daily work of mathematician is as the other people say. Try to find everyday a thing that it can be proof that it was related with maths but not all hte mathematician things this because there are others that teach other people or maybe did other task that there are also related with maths. It could be a lot of things
1) Well, Now i can’t remember any anecdote that have change my concept of mathematics. But I can say something. I see that someone put in her opinion, that when she was a child, she thougt that maths were stupid because they couldn’t be applied in the real life, in my opinion I think this observation ( I respect it ) for me is not logical because in that age, you don’t think about apply maths in the real life. When you are a child you only think in learn how to add, multiplie… etc. I don’t know if you understand me. Well This was onlt an observation.
2) Marcus du Sautoy’s objective is to proof things that in the real life will be for the humans not logical, and they have to be discovered or they need a logic explanation.
3) It depends about the mathematician. There are mathematicians, that want to teach mathematics, or other that mabye want to stay home and wait for some idea. Well, I don’t know very well. I think that depends of the person. The quimics for example, can work in a laboratory or in other sides where they can apply what they know.
1)
Yes, I do. I remember that when I was about six or seven years old, I didn’t like maths, because I didn’t understand them. But one day, I was in my village with my father and he told me something, that everything was maths. I didn’t believe him (I though he just do it because he wanted me to love maths), but then he gave me a seed and he asked me what would happen to it. I answer that it would be a tree and he just told me yes, that everything has a finallity (like maths). I didn’t understand too much and he ask me what natural phenomenon do I liked most. I answer the rainbow and he made me compare with maths (semicircle).
Explained like that it seems like a film, but it wasn’t. In that moment I just though that my father was crazy, but maths started to like me too
2)
For Marcus du Sautoy, the fundamental task of a mathematician is to proof theorems about a reality out of it.
3)
I think that the daily work of a mathematician is to look for new patterns, new relationsheeps…
1) I think that the only experience I have with maths is similar of the expreriences of my classmates. The change of doing math in primary and doing math in the high school. I primary I didn’t study for the math exams because they were with operations and with easy problems and I had good marks. But when I start doing math in 1st of ESO I saw that math were more than that, they were more complicated and that I have to study more to get good marks in the exams.
2) For Marcus du Sautoy the objective of a mathematician is to prove theorems about the reality that is outside him.
3)I think that the daily work of a mathematician is to look for patterns and formulas, to proof something, to discover new things ….
1)
Well, I think that I don’t have any anecdote like that, but I started to see maths in another way when I joined this project. It’s true that I don’t like much maths (they’re difficult…), but when I joined this project I saw that maths don’t have to be always boring like I thought.
2)
Well, I have to say that I didn’t understand really the words of Marcus du Sautoy, but I think that mathematicians want to proof theorems and apply them to real life
3)
I think that the daily work of a mathematician is look for patterns, try to proof some theory… maybe search the next prime number… I don’t know.
I’m agree with Raquel in the first question if you don’t understand something you have to search for some ways to understand it and I remember, when I read raquel’s opinion that this summer with my cousin we went to a swimmingpool and the we wanted to return at home by one of the roate that when we were child we remember but we have to jump a wall and then we cannot follow the way and we went back and we discover a new way and better than the other to go home. And I think that we can apply this theory with everything because in my opinion there isn’t anything with only one solution.
See you!
1) No. Don’t remember any experience in relation with maths. Only that in prymary school I prefered maths that catalan or spanish, ‘cause I thought that they were more useful, because in school we learned the typical questions of: If I had 5 pencils and I lose . How many pencils do I have?? And I think that this questions were more useful than If I buy x apples, I multiplied by pi, using the result I do the cubic root and I obtain the square root of 11. What is x? So, I think that primary maths are more useful than secondary maths, And Mathematicians always says that a statement is true until ther is an other that contradicts it, isn’t it true? So I need a contradiction.
2) It’s proof theorems about the real life that is outside him. I understand this phrase like: The mathematicians try to proof statements about everything that the humans (The rest) don’t appreciate or that they cannot reach? Im not sure, I’m not a philosopher .
3)
Or, I’m sorry I forgot to answer the third!!!! I think that mathematics have what we say love to art, in this case maths. So they wake up at morning smiling and thinking: Today I’m going to find a pattern about the prime numbers, for example. They are always trying to find patters (Because patterns are everywhere in the nature, aren’t them?)
1) I have more than one anecdote with maths… and all of them are not good..
As Claudia Maravalle said, in the primary, the problems are very easy (like the pencils’ example that she has writen),so you don’t study because are logical problems, but then when you arrive to the ESO… is like: be careful! Then you get bad marks, and you have to study. Maths are difficult, and I think that most of my partners know that.
Well, my anecdote is like my other partners. I got bad marks, when I was thinking that I would take a 9.
2) Marcus du Sautoy’s objective is to prove theorems about the reality that is outside him. I really don’t understand it very much, but I think that he wants to apply all that he can to the real life.
3)I think that there are some types of mathematicians. There are mathematicians that are searching for formulas, patterns… But there are also mathematicians teachers that they want to teach to their students her/his knowledge.
1) Well, I doubt if you will believe my anecdote. You know, in general, I understand math and I don’t really have problems with this subject, but when I was young I thought that maths were so easy (just like adding and subtracting) and I didn’t pay a lot of attention in class. One day, during the summer, I realised that I forgot how to divide. This was very annoying for me, and I started learning how to divide again by my own. Then the school year started again, I didn’t pay attention at the math classes and… the next summer I realised that I has forgotten how to divide again! I felt so ashamed of my-self. Then I promised my-self that I would learn again to divide and that I would pay a lot of attention in the math classes.
(I think that now I know how to divide well XD)
2) I think that Marcus du Sautoy’s objective is to prove theorems in general. In some way, I think that every mathematician tries to prove as many things as he can. The more things he proves, the more useful he feels. First he observes something and then he thinks “Why did it happen?” I think that they apply this question to everything they know (because, as we said in class, almost everything is related to math, no?)
3) I agree with Julia, Miquel, etc. when they say that the daily work of a mathematician depends on what kind of mathematics he is working with. The conversation with Louise made me realise about how big is the world of mathematics. I think that you cannot study well all mathematics (you would became mad!) you must specialize in some special subject (just like Louise in statistics) and then try to extend and discover more things about the knowledge of this specific branch of mathematics.
you are such a hard worker.http://www.geriquest.com