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L'equazione da un milione di dollari: E altri enigmi matematici che rifiutano di lasciarsi risolvere
Che cos'hanno in comune i fulmini, i broccoli, e il mercato azionario? Perché Beckham ha scelto la maglia numero 23? Perché il più grande numero primo che sia mai stato scoperto fino a oggi - un numero di quasi tredici milioni di cifre - prende il nome da un monaco del XVII secolo? Nella Quinta di Beethoven c'è un messaggio in codice? Ma soprattutto: come mai il nostro pianeta non è una ciambella? Per rispondere a tutte questa domande, e a molte altre, non occorre essere un indovino o un tuttologo, ma un matematico. "Lo strumento più potente mai creato dagli esseri umani per orientarsi nel mondo selvaggio e complesso in cui viviamo è la matematica" scrive infatti Marcus du Sautoy. E, guidandoci con competenza e humour alla scoperta della regolarità che scandisce l'ordine della natura, ci dimostra che la vita è un'equazione: dai quadrati magici all'algebra da casinò, dai segreti dell'ISBN alla lettura crittografica del pensiero, dal corner di Wayne Rooney al metodo per falsificare un quadro di Pollock, dall'aritmetica dei chicchi di riso agli istinti assassini degli icosaedri.
Questo libro raccoglie con un contagioso gusto dell'esplorazione curiosità, aneddoti e molti giochi ideati da Marcus du Sautoy per permettere al lettore di cimentarsi con le maggiori menti matematiche del passato. Perché anche dietro un piccolo rompicapo può celarsi un grande enigma come l'ipotesi di Riemann, il problema irrisolto che vale un milione di dollari. E perché "la matematica è il cuore di tutto ciò che vediamo e facciamo".
Questo libro raccoglie con un contagioso gusto dell'esplorazione curiosità, aneddoti e molti giochi ideati da Marcus du Sautoy per permettere al lettore di cimentarsi con le maggiori menti matematiche del passato. Perché anche dietro un piccolo rompicapo può celarsi un grande enigma come l'ipotesi di Riemann, il problema irrisolto che vale un milione di dollari. E perché "la matematica è il cuore di tutto ciò che vediamo e facciamo".
365 pages, Hardcover
First published February 2, 2011
123 people are currently reading
1004 people want to read
About the author
Marcus du Sautoy
35 books503 followersMarcus Peter Francis du Sautoy, OBE is the Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.
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Displaying 1 - 30 of 60 reviews
February 15, 2017
Cute book about the magic of numbers.
The author is a well-regarded mathematician and a Professor of Mathematics at the University of Oxford, so his credentials are impeccable. He is also a great popularizer of the mathematical sciences, and this book is well written with passion and enthusiasm, with clear and lucid explanations and brilliant examples.
My relatively low rating does not reflect so much the intrinsic value of this book, but the value I personally got out of it: unfortunately the book is a bit simplistic (the maths depth is at high school level, so more mathematically complex but also fascinating subjects such as complex analysis, Fourier analysis or group theory are not represented in this book), but other users, who might be better identifying themselves with the target audience of this book, would most likely give it a higher rating.
Some of the subjects treated by the book are: number theory and prime numbers, basics of topology, fractals, basic probability calculus, basics of cryptography, and an introduction to chaotic systems. All these subjects are treated at introductory level, so there was nothing new that I found here, but they are treated by the author with concise clarity and precision, delivering a very readable and cute book - it is a fun, lightweight book perfect for a breezy, quick and relaxing reading experience that keeps the reader constantly engaged.
The author is a well-regarded mathematician and a Professor of Mathematics at the University of Oxford, so his credentials are impeccable. He is also a great popularizer of the mathematical sciences, and this book is well written with passion and enthusiasm, with clear and lucid explanations and brilliant examples.
My relatively low rating does not reflect so much the intrinsic value of this book, but the value I personally got out of it: unfortunately the book is a bit simplistic (the maths depth is at high school level, so more mathematically complex but also fascinating subjects such as complex analysis, Fourier analysis or group theory are not represented in this book), but other users, who might be better identifying themselves with the target audience of this book, would most likely give it a higher rating.
Some of the subjects treated by the book are: number theory and prime numbers, basics of topology, fractals, basic probability calculus, basics of cryptography, and an introduction to chaotic systems. All these subjects are treated at introductory level, so there was nothing new that I found here, but they are treated by the author with concise clarity and precision, delivering a very readable and cute book - it is a fun, lightweight book perfect for a breezy, quick and relaxing reading experience that keeps the reader constantly engaged.
December 31, 2023
Finding out I'm not much of a non-fictional reader. Or at least I have to be slow and steady with them. Took me a while to get through this one, taking only a few pages at a time. It is not too heavy on the maths, but I still can't read much at once as I want to take it all in. Some of the concepts were particularly interesting, especially the final ones on chaos theory, which left a very positive final impression. Overall it's a 3.5/5.
September 19, 2025
Cinc capítols, cinc misteris. Cinc problemes matemàtics. Formen part de la llista dels set Problemes del Mil·lenni establerta l’any 2000 per l’Institut Clay. Per a cada un dels set, l’Institut Clay ofereix un milió de dòlars a la persona que el resolgui. A data d’avui, només un ha estat resolt i, sorprenentment, la persona que el va resoldre va refusar els diners. Ho llegirem al capítol dos.
Els propis nombres són els protagonistes del primer misteri que Marcus du Sautoy ens presenta. Concretament, quina posició van ocupant els nombres primers al llarg de la filera de tots els nombres.
Du Sautoy sempre fa una introducció per arribar a concretar el problema a la part final. Aquí comença amb un viatge fascinant per la història de l’escriptura dels nombres, èpoques, llocs i llengües. També inclou curiositats relacionades amb l’assumpte, com per exemple l’estrany i matemàtic comportament d’uns animals i com això va lligat a les propietats dels nombres primers... i tot plegat amb una preciosa cançó de Bob Dylan de fons.
Al final, la famosíssima Hipòtesi de Riemann. Inoblidable el primer cop que vaig llegir sobre ella, precisament en un llibre anterior de Marcus du Sautoy, ”La música de los números primos”. Un llibre realment excepcional.
Si el primer misteri versava sobre nombres, el segon té com a protagonistes les formes.
Comencem amb els cinc sòlids platònics. Tots cinc descoberts fa milers d’anys... i no n’hi ha més. Aquest fet (que només n’hi hagi cinc, i que siguin cinc), ja em sembla misteriós.
Du Sautoy avança en el capítol explicant-nos la relació superfície/volum i aprenc que, donat un volum, l’esfera és la menor superfície que el pot contenir i el tetraedre la major.
També aprenc que, dels cinc sòlids platònics, el cub és l’únic que permet empaquetar-ne varis sense que resti cap espai buit.
Seguidament passem al fascinant món de les formes fractals.
Trobem el floc de neu de Koch i sembla màgia el fet que, al augmentar-ne l’escala tres vegades, la longitud augmenta tres vegades, però també quatre, segons com ho considerem.
Són conceptes que em fan explotar el cap. Com les dimensions fractals. Du Sautoy ens explica que les formes fractals van obrir una nova definició de dimensió. Tots tenim interioritzat el concepte de dimensió. Una dimensió (línies), dues dimensions (superfícies), tres dimensions (volums)...
Sembla força clar i lògic que incrementin d’aquesta forma: 1, 2, 3...
Em sembla revolucionari que les formes fractals tinguin dimensions “intermèdies” entre aquestes, amb decimals, per exemple 1,26, etc...
Per les formes planes Du Sautoy ens ensenya el mètode de mesura usant paper quadriculat i veiem com s’obté un nombre que no és enter.
També ens explica que a la natura abunden les que tenen dimensió entre 1,3 i 1,5, de manera que el cervell ha evolucionat en aquest entorn i ens sentim atrets per aquestes formes.
La fascinació continua quan ho vincula als quadres de Pollock.
Finalment, Marcus du Sautoy fa un símil amb la música, dient que ens agrada la que té una complexitat que es situa entre allò massa regular i allò massa aleatori. Conceptes nous per a mi, que em semblen innovadors, revolucionaris,
Du Sautoy ens els explica d’una forma científica, matemàtica i, a la vegada, molt entenedora.
Continuant encara dins el capítol de les formes, passem a la branca de les matemàtiques anomenada topologia. Primer, Du Sautoy ens introdueix en el mètode d’estudiar les formes mitjançant el que ell anomena el “diccionari” de Descartes, és a dir, “traduint” formes físiques a conjunts de coordenades.
I sembla màgia quan les formes físiques amb més de tres dimensions ―que ja no podem veure (com per exemple, un cub de quatre dimensions)―, les podem continuar estudiant sense problema usant l’altra part del diccionari (les coordenades), que segueix funcionant perfectament.
Desprès de tots aquests antecedents, tota aquesta preparació, arribem a la part final, el misteri concret del capítol dos. L’anomenada Conjectura de Poincaré.
Aquest és l’únic problema del cinc, que ja està resolt. Ho va aconseguir el matemàtic rus Grigori Perelman. I va refusar el premi del milió de dòlars!
Coneixia aquesta història gràcies a l’excepcional llibre “La conjetura de Poincaré” de Donal O’Shea.
Són conceptes complicats per a mi. Si ho entenc correctament, bàsicament diu que una forma tridimensional, de certes característiques, sempre és una esfera. Una esfera de tres dimensions. (La esfera a la que estem acostumats, una superfície, té dues dimensions).
Podria ser… la forma de l’univers!
Hi pot haver tema més fascinant?
Un altre llibre que em ve al cap i recomano, aquest de ficció, és “La decisió de Mamperel”, de Jordi de Manuel, que s’inspira en la figura real de Perelman per vestir una meravellosament ben narrada aventura.
M’encanten els exemples i anècdotes que Du Sautoy inclou per fer-nos entenedors aquests conceptes matemàtics. Ja al capítol tres, els llangardaixos de tres colors, o com Christie’s va guanyar a Sotheby’s un dret de subhasta.
Aquest capítol tracta de les probabilitats, dels jocs, per finalment arribar al problema concret del milió de dòlars, els anomenats problemes NP-complets.
Hi ha tota una sèrie de jocs, com el Sudoku, que tenen relació amb aquesta branca de les matemàtiques però, com bé ens adverteix Du Sautoy, aquest no és només un assumpte per a jugar. Avançar en el seu coneixement té transcendentals implicacions en la comprensió del comportament de fenòmens que ens afecten i aplicacions a la vida pràctica i els negocis, per exemple. Problemes i situacions que adopten formes diverses. Relació entre elements, interaccions creuades, repartiments, connexions, xarxes de camins, la millor ruta, elecció, distribució o empaquetament d’elements...
El quart capítol tracta de codis i hi trobo algunes històries que ja havia llegit amb anterioritat, com ara la màquina Enigma i el que van significar les idees del gran matemàtic Alan Turing en el naixement del concepte mateix d’ordinador.
Hi ha un moment en que la lectura m’evoca el film “Zodiac” o els ballarins de Sherlock Holmes.
Llegeixo també una gran explicació de la característica del codi ISBN, que identifica els llibres, i conté un element de protecció dins el propi codi.
En aquest capítol, el problema del mil·lenni tracta d’un sistema que té aplicació en l’encriptació de codis i que es basa en certes propietat de les corbes el·líptiques.
El cinquè i últim misteri que Marcus du Sautoy ens explica és el caos.
Amb la fórmula de Galileu de la caiguda lliure, Du Sautoy comença indicant-nos la capacitat predictiva de les equacions, i m’aboca l’últim llibre llegit, “La història del senyor Sommer”, de Patrick Süskind.
Un QR ens porta al fascinant vídeo de l’astronauta a la lluna deixant caure un martell i una ploma.
Du Sautoy continua explicant-nos altres exemples d’equacions que prediuen el moviment dels cossos. Seguidament ens relata el cas del problema dels tres cossos, el concurs del rei Òscar II i Henri Poincaré, ―el gran matemàtic francès, que ja havíem trobat al capítol 2, pren altre cop tot el protagonisme, i de nou recordo l’excepcional llibre de Donal O’Shea, i com mai ha deixat de fascinar-me aquest fenomen del caos des que el vaig conèixer―.
Marcus du Sautoy ho resumeix meravellosament:
El problema del milió de dòlars en aquest cas són les equacions de Navier-Stokes, que s’usen per predir el comportament de fluids, com ara la turbulència.
Els propis nombres són els protagonistes del primer misteri que Marcus du Sautoy ens presenta. Concretament, quina posició van ocupant els nombres primers al llarg de la filera de tots els nombres.
Du Sautoy sempre fa una introducció per arribar a concretar el problema a la part final. Aquí comença amb un viatge fascinant per la història de l’escriptura dels nombres, èpoques, llocs i llengües. També inclou curiositats relacionades amb l’assumpte, com per exemple l’estrany i matemàtic comportament d’uns animals i com això va lligat a les propietats dels nombres primers... i tot plegat amb una preciosa cançó de Bob Dylan de fons.
Al final, la famosíssima Hipòtesi de Riemann. Inoblidable el primer cop que vaig llegir sobre ella, precisament en un llibre anterior de Marcus du Sautoy, ”La música de los números primos”. Un llibre realment excepcional.
Si el primer misteri versava sobre nombres, el segon té com a protagonistes les formes.
Comencem amb els cinc sòlids platònics. Tots cinc descoberts fa milers d’anys... i no n’hi ha més. Aquest fet (que només n’hi hagi cinc, i que siguin cinc), ja em sembla misteriós.
Du Sautoy avança en el capítol explicant-nos la relació superfície/volum i aprenc que, donat un volum, l’esfera és la menor superfície que el pot contenir i el tetraedre la major.
També aprenc que, dels cinc sòlids platònics, el cub és l’únic que permet empaquetar-ne varis sense que resti cap espai buit.
Seguidament passem al fascinant món de les formes fractals.
Trobem el floc de neu de Koch i sembla màgia el fet que, al augmentar-ne l’escala tres vegades, la longitud augmenta tres vegades, però també quatre, segons com ho considerem.
Són conceptes que em fan explotar el cap. Com les dimensions fractals. Du Sautoy ens explica que les formes fractals van obrir una nova definició de dimensió. Tots tenim interioritzat el concepte de dimensió. Una dimensió (línies), dues dimensions (superfícies), tres dimensions (volums)...
Sembla força clar i lògic que incrementin d’aquesta forma: 1, 2, 3...
Em sembla revolucionari que les formes fractals tinguin dimensions “intermèdies” entre aquestes, amb decimals, per exemple 1,26, etc...
Per les formes planes Du Sautoy ens ensenya el mètode de mesura usant paper quadriculat i veiem com s’obté un nombre que no és enter.
També ens explica que a la natura abunden les que tenen dimensió entre 1,3 i 1,5, de manera que el cervell ha evolucionat en aquest entorn i ens sentim atrets per aquestes formes.
La fascinació continua quan ho vincula als quadres de Pollock.
Finalment, Marcus du Sautoy fa un símil amb la música, dient que ens agrada la que té una complexitat que es situa entre allò massa regular i allò massa aleatori. Conceptes nous per a mi, que em semblen innovadors, revolucionaris,
Du Sautoy ens els explica d’una forma científica, matemàtica i, a la vegada, molt entenedora.
Continuant encara dins el capítol de les formes, passem a la branca de les matemàtiques anomenada topologia. Primer, Du Sautoy ens introdueix en el mètode d’estudiar les formes mitjançant el que ell anomena el “diccionari” de Descartes, és a dir, “traduint” formes físiques a conjunts de coordenades.
I sembla màgia quan les formes físiques amb més de tres dimensions ―que ja no podem veure (com per exemple, un cub de quatre dimensions)―, les podem continuar estudiant sense problema usant l’altra part del diccionari (les coordenades), que segueix funcionant perfectament.
Desprès de tots aquests antecedents, tota aquesta preparació, arribem a la part final, el misteri concret del capítol dos. L’anomenada Conjectura de Poincaré.
Aquest és l’únic problema del cinc, que ja està resolt. Ho va aconseguir el matemàtic rus Grigori Perelman. I va refusar el premi del milió de dòlars!
Coneixia aquesta història gràcies a l’excepcional llibre “La conjetura de Poincaré” de Donal O’Shea.
Són conceptes complicats per a mi. Si ho entenc correctament, bàsicament diu que una forma tridimensional, de certes característiques, sempre és una esfera. Una esfera de tres dimensions. (La esfera a la que estem acostumats, una superfície, té dues dimensions).
Podria ser… la forma de l’univers!
Hi pot haver tema més fascinant?
Un altre llibre que em ve al cap i recomano, aquest de ficció, és “La decisió de Mamperel”, de Jordi de Manuel, que s’inspira en la figura real de Perelman per vestir una meravellosament ben narrada aventura.
M’encanten els exemples i anècdotes que Du Sautoy inclou per fer-nos entenedors aquests conceptes matemàtics. Ja al capítol tres, els llangardaixos de tres colors, o com Christie’s va guanyar a Sotheby’s un dret de subhasta.
Aquest capítol tracta de les probabilitats, dels jocs, per finalment arribar al problema concret del milió de dòlars, els anomenats problemes NP-complets.
Hi ha tota una sèrie de jocs, com el Sudoku, que tenen relació amb aquesta branca de les matemàtiques però, com bé ens adverteix Du Sautoy, aquest no és només un assumpte per a jugar. Avançar en el seu coneixement té transcendentals implicacions en la comprensió del comportament de fenòmens que ens afecten i aplicacions a la vida pràctica i els negocis, per exemple. Problemes i situacions que adopten formes diverses. Relació entre elements, interaccions creuades, repartiments, connexions, xarxes de camins, la millor ruta, elecció, distribució o empaquetament d’elements...
El quart capítol tracta de codis i hi trobo algunes històries que ja havia llegit amb anterioritat, com ara la màquina Enigma i el que van significar les idees del gran matemàtic Alan Turing en el naixement del concepte mateix d’ordinador.
Hi ha un moment en que la lectura m’evoca el film “Zodiac” o els ballarins de Sherlock Holmes.
Llegeixo també una gran explicació de la característica del codi ISBN, que identifica els llibres, i conté un element de protecció dins el propi codi.
En aquest capítol, el problema del mil·lenni tracta d’un sistema que té aplicació en l’encriptació de codis i que es basa en certes propietat de les corbes el·líptiques.
El cinquè i últim misteri que Marcus du Sautoy ens explica és el caos.
Amb la fórmula de Galileu de la caiguda lliure, Du Sautoy comença indicant-nos la capacitat predictiva de les equacions, i m’aboca l’últim llibre llegit, “La història del senyor Sommer”, de Patrick Süskind.
Un QR ens porta al fascinant vídeo de l’astronauta a la lluna deixant caure un martell i una ploma.
Du Sautoy continua explicant-nos altres exemples d’equacions que prediuen el moviment dels cossos. Seguidament ens relata el cas del problema dels tres cossos, el concurs del rei Òscar II i Henri Poincaré, ―el gran matemàtic francès, que ja havíem trobat al capítol 2, pren altre cop tot el protagonisme, i de nou recordo l’excepcional llibre de Donal O’Shea, i com mai ha deixat de fascinar-me aquest fenomen del caos des que el vaig conèixer―.
Marcus du Sautoy ho resumeix meravellosament:
”El universo puede comportarse como un reloj, pero nunca conoceremos la posición de los engranajes con la precisión suficiente para poder aprovechar su naturaleza determinista.”
El problema del milió de dòlars en aquest cas són les equacions de Navier-Stokes, que s’usen per predir el comportament de fluids, com ara la turbulència.
August 27, 2023
Dal titolo mi aspettavo di trovare approfondita un'unica equazione, ma non è così. Il libro è diviso in 5 capitoli, ognuno di un tema differente e al termine del quale viene mostrato un problema aperto per cui c'è in palio un montepremi.
L'ho trovata davvero impeccabile questa lettura. Moltissime curiosità: da aneddoti più storici, a parallelismi con la realtà moderna. Molto studiato e graduale anche il percorso costruito dentro ogni capitolo per entrare nell'argomento. La ciliegina sulla torta sono stati tutti i problemini e giochi che venivano proposti di volta in volta: utili sia per entrare nell'argomento sia da usare anche in contesti più amicali.
L'ho trovata davvero impeccabile questa lettura. Moltissime curiosità: da aneddoti più storici, a parallelismi con la realtà moderna. Molto studiato e graduale anche il percorso costruito dentro ogni capitolo per entrare nell'argomento. La ciliegina sulla torta sono stati tutti i problemini e giochi che venivano proposti di volta in volta: utili sia per entrare nell'argomento sia da usare anche in contesti più amicali.
February 7, 2013
I picked this up cheap having listened to and enjoyed his Brief History of Mathematics podcast through BBC Radio 4 (http://www.bbc.co.uk/podcasts/series/...). He's so enthusiastic and likeable that he really puts across the love of his subject.
So, despite disliking maths with a passion and having major 'number block' at the best of times I still gave it a read. It's a fun, lightweight and fairly superficial introduction to some mathematical fields, generally clear to follow with some nice historical anecdotes. To be honest, those are probably the best. Despite my maths grounding, I was fairly familiar with many of the concepts and areas discussed (especially the primes, geometry and chance/randomness) and suspect this book isn't that useful for anyone with an interest in maths; more a primer for the layperson.
The links were a good addition (though I mostly skipped them). The illustrations were pretty poor though, looking like a quick computer knock-up job - could have been better.
Overall, fun and easy to read (some equations, not so much) but probably too basic for most. A good intro for those who are curious.
So, despite disliking maths with a passion and having major 'number block' at the best of times I still gave it a read. It's a fun, lightweight and fairly superficial introduction to some mathematical fields, generally clear to follow with some nice historical anecdotes. To be honest, those are probably the best. Despite my maths grounding, I was fairly familiar with many of the concepts and areas discussed (especially the primes, geometry and chance/randomness) and suspect this book isn't that useful for anyone with an interest in maths; more a primer for the layperson.
The links were a good addition (though I mostly skipped them). The illustrations were pretty poor though, looking like a quick computer knock-up job - could have been better.
Overall, fun and easy to read (some equations, not so much) but probably too basic for most. A good intro for those who are curious.
October 18, 2013
Similar to another recent book (Nine Algorithms That Changed the Future: The Ingenious Ideas That Drive Today's Computers), this book focuses on the four of the six unsolved mathematical Millennium Prize Problems, with one chapter per. Variations and discussions of the math and importance of these problems is very accessible to the average reader. The illustrations help illustrate the concepts and shapes discussed. A fifth chapter describes the Poincaré conjecture, only mentioning Grigori Perelman's proof at the end without seriously delving into it.
May 31, 2012
An interesting look at how mathematics can help explain everyday situations. Unfortunately the digital (Kindle) edition doesn't make it easy to follow the examples. It also appears at times that the author becomes to enamored of the mathematical explanations making hard to follow the writing.
April 14, 2018
In this book there are references to external websites which can be accessed typing the address into a web browser or scanning QR codes printed in the book. Thus the book provides us with additional material. Currently (2018) some of the links are not available, though.
In each chapter there is a journey through a big mathematical theme, and at the end of the chapter a mathematical "mystery" is revealed. A problem no one has yet been able to solve. A million-dollar problem, prize by the Clay Institute. There are seven of these, though in this book we only read about five, as many as chapters.
Chapter 1 explores what we do understand about prime numbers. And not only primes, but numbering systems (the numbers of Egyptians, Greeks, Mayan, etc.). The million-dollar problem is here the Riemann hypothesis, which tells us about the deviation from the average distribution of the primes.
Chapter 2 presents the nature's weird and wonderful shapes: from the six-pointed snowflake to the spiral of DNA, from the perfectly spherical bubbles to the shape of our universe. The million-dollar problem addressed in this chapter is the Poincaré conjecture... solved in 2002 by Grigori Perelman, it is therefore a theorem. Poincaré had asked if the three dimensional sphere is characterized as the unique simply connected three manifold.
Chapter 3 is about games that allow us to develop ways of predicting how, given certain rules, events will unfold and to plan accordingly. They teach us about chance and unpredictability. Rock-paper-scissors, Monopoly, magic squares or the history of dice and what shapes make good dice. The million-dollar problem is now P vs NP, whose essence is knowing if it is easy to solve a given problem. Sometimes it is simple, if you give a solution, to check whether that is correct or wrong, but it is not so easy to find a solution starting from nothing.
Chapter 4 tells us how math has been used to create and break codes, how it lets us transmit information safely, efficiently and secretely. And there are also a few examples, like the structure of an ISBN. The million-dollar problem is here the Birch and Swinnerton-Dyer conjecture, which asks whether there is a way to tell which elliptic cureves will have an infinite number of points where both coordianates are whole numbers or fractions.
If you are interested in codes, I'd recommend you the wonderful book The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography, by Simon Singh.
Finally, chapter 5 is about the quest to predict the future. The reason a boomerang comes back, why an aeroplane flies, the motion of a pendulum, chaos theory. Even the reason why Roberto Carlos scored a goal with his amazing kick in a 1997 soccer game (France vs Brazil). At last, the final million-dollar problem is so called Navier-Stokes equations, which governs the flow of fluids such as water and air.
To expand knowledge, there are two more million-dollar problems. The Yang-Mills and Mass Gap (which suggest the existence of a "mass gap" in the solution to the quantum versions of the Yang-Mills equations) and the Hodge conjecture (which determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations). Hitherto, only the Poincaré conjecture has been proved.
In each chapter there is a journey through a big mathematical theme, and at the end of the chapter a mathematical "mystery" is revealed. A problem no one has yet been able to solve. A million-dollar problem, prize by the Clay Institute. There are seven of these, though in this book we only read about five, as many as chapters.
Chapter 1 explores what we do understand about prime numbers. And not only primes, but numbering systems (the numbers of Egyptians, Greeks, Mayan, etc.). The million-dollar problem is here the Riemann hypothesis, which tells us about the deviation from the average distribution of the primes.
Chapter 2 presents the nature's weird and wonderful shapes: from the six-pointed snowflake to the spiral of DNA, from the perfectly spherical bubbles to the shape of our universe. The million-dollar problem addressed in this chapter is the Poincaré conjecture... solved in 2002 by Grigori Perelman, it is therefore a theorem. Poincaré had asked if the three dimensional sphere is characterized as the unique simply connected three manifold.
Chapter 3 is about games that allow us to develop ways of predicting how, given certain rules, events will unfold and to plan accordingly. They teach us about chance and unpredictability. Rock-paper-scissors, Monopoly, magic squares or the history of dice and what shapes make good dice. The million-dollar problem is now P vs NP, whose essence is knowing if it is easy to solve a given problem. Sometimes it is simple, if you give a solution, to check whether that is correct or wrong, but it is not so easy to find a solution starting from nothing.
Chapter 4 tells us how math has been used to create and break codes, how it lets us transmit information safely, efficiently and secretely. And there are also a few examples, like the structure of an ISBN. The million-dollar problem is here the Birch and Swinnerton-Dyer conjecture, which asks whether there is a way to tell which elliptic cureves will have an infinite number of points where both coordianates are whole numbers or fractions.
If you are interested in codes, I'd recommend you the wonderful book The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography, by Simon Singh.
Finally, chapter 5 is about the quest to predict the future. The reason a boomerang comes back, why an aeroplane flies, the motion of a pendulum, chaos theory. Even the reason why Roberto Carlos scored a goal with his amazing kick in a 1997 soccer game (France vs Brazil). At last, the final million-dollar problem is so called Navier-Stokes equations, which governs the flow of fluids such as water and air.
To expand knowledge, there are two more million-dollar problems. The Yang-Mills and Mass Gap (which suggest the existence of a "mass gap" in the solution to the quantum versions of the Yang-Mills equations) and the Hodge conjecture (which determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations). Hitherto, only the Poincaré conjecture has been proved.
January 12, 2018
Marcus du Sautoy, the Simonyi Professor for the Public Understanding of Science and Professor of Mathematics at the University of Oxford, is the author of this delightful book. The book is really two books in one; a traditional math popularization and the second is a nontraditional reference book.
The book is written in five chapters. Each chapter takes a topic, develops its background, shares multiple examples and culminates in the statement of one of the Clay Institute challenges. These challenges are unsolved mathematics problems that yield a $1,000,000 prize to whoever is able to successfully solve them. Now, there are more than 5 challenges (and one of the challenges he writes about has actually been solved) so the reader is at the mercy of the author's selection process.
The challenge in these kind of books is striking the balance between telling too much (losing the mathematical novice) and not telling enough (boring the mathematical journeyman.) He ends his book with the following: "And when you finally crack one of the big mathematical enigmas of all time, everyone will be thinking .... : How on Earth did you do that?"
Unfortunately, he left me with that thought in many areas of the book. He gives many examples of the topics he is covering. The examples are varying shades of interesting, ingenious and surprising. However, it is hard to trust the stated results in areas I don't know when I can see a handful of errors in areas that I do know.
If he spent more time justifying his results I would have enjoyed the book more.
The book within the book is a catalog of websites demonstrating many of the things he is writing about. It also includes a number of educational aids that would be of use in many points of the curriculum from 5 - 16. Yep, these demonstrations would be accessible to 5th graders and informational to college majors.
He is a Brit. He likes soccer. So, the reader should be prepared for lots of allusions to European football.
The book is written in five chapters. Each chapter takes a topic, develops its background, shares multiple examples and culminates in the statement of one of the Clay Institute challenges. These challenges are unsolved mathematics problems that yield a $1,000,000 prize to whoever is able to successfully solve them. Now, there are more than 5 challenges (and one of the challenges he writes about has actually been solved) so the reader is at the mercy of the author's selection process.
The challenge in these kind of books is striking the balance between telling too much (losing the mathematical novice) and not telling enough (boring the mathematical journeyman.) He ends his book with the following: "And when you finally crack one of the big mathematical enigmas of all time, everyone will be thinking .... : How on Earth did you do that?"
Unfortunately, he left me with that thought in many areas of the book. He gives many examples of the topics he is covering. The examples are varying shades of interesting, ingenious and surprising. However, it is hard to trust the stated results in areas I don't know when I can see a handful of errors in areas that I do know.
If he spent more time justifying his results I would have enjoyed the book more.
The book within the book is a catalog of websites demonstrating many of the things he is writing about. It also includes a number of educational aids that would be of use in many points of the curriculum from 5 - 16. Yep, these demonstrations would be accessible to 5th graders and informational to college majors.
He is a Brit. He likes soccer. So, the reader should be prepared for lots of allusions to European football.
February 7, 2021
I came to this book by Marcus du Sautoy not through the extremely popular math series he hosted on BBC but through his next book The Creativity Code . Having enjoyed reading that book and having liked the wide eyed, mischievous voice of the author in that - I picked this up. After all, du Sautoy is a mathematician and I wanted to see how much that inquisitive voice could inform me about the mysteries of mathematics about which I can only be called an informed novice.
But this is a book written by a previous du Sautoy. Here the familiar voice of someone trying hard to keep wide-eyed fascination for the subject while still including the expert opinion seems somehow less elegant. Let me explain. First, there is too much of that wide eyed fascination with mathematics here. Mr. du Sautoy is constantly including games, links to websites, real life situations to help make these otherwise complex mathematical issues palatable. I appreciated that at first. But by the time I got through half the book his how-to-win-a-million-dollars approach to each question felt too much like click-bait type advertising of the mathematical idea for my taste. So when he did include the expert opinion, the formulae and the workings caught me unprepared, requiring a separate part of my brain. Perhaps it is the juxtaposition of these two elements together or it might be my own lack of mathematical imagination but I found myself skipping both to spend more time in the fine explanations of mathematics - which are there.
So is a lot else to like here if you haven't come after reading a better book by the same author. I also was here after trying another book on great mathematic problems that got too technical on me. So this was a good primer. Only somehow I expected more from Marcus du Sautoy.
But this is a book written by a previous du Sautoy. Here the familiar voice of someone trying hard to keep wide-eyed fascination for the subject while still including the expert opinion seems somehow less elegant. Let me explain. First, there is too much of that wide eyed fascination with mathematics here. Mr. du Sautoy is constantly including games, links to websites, real life situations to help make these otherwise complex mathematical issues palatable. I appreciated that at first. But by the time I got through half the book his how-to-win-a-million-dollars approach to each question felt too much like click-bait type advertising of the mathematical idea for my taste. So when he did include the expert opinion, the formulae and the workings caught me unprepared, requiring a separate part of my brain. Perhaps it is the juxtaposition of these two elements together or it might be my own lack of mathematical imagination but I found myself skipping both to spend more time in the fine explanations of mathematics - which are there.
So is a lot else to like here if you haven't come after reading a better book by the same author. I also was here after trying another book on great mathematic problems that got too technical on me. So this was a good primer. Only somehow I expected more from Marcus du Sautoy.
April 1, 2023
https://fromtheheartofeurope.eu/the-number-mysteries-a-mathematical-odyssey-through-everyday-life-by-marcus-du-sautoy/
This is a straightforward romp through various bits of mathematical theory – prime numbers, topology, probability, cryptography and dynamics. I didn’t learn a lot from it, but it is breezily done and will probably appeal to smart older kids who are presumably the target audience.
This is a straightforward romp through various bits of mathematical theory – prime numbers, topology, probability, cryptography and dynamics. I didn’t learn a lot from it, but it is breezily done and will probably appeal to smart older kids who are presumably the target audience.
August 18, 2021
The most basic foundation for life on our planet are known to the human beings as oxygen, food, and water. However, there's another key component that rules the human world in practicality, for its absence would have rendered human beings powerless and their existence on earth meaningless. This component governs every individual's routine, rules the minds of productive creatures, and reigns over their ability to perceive, evaluate, and even draw conclusions on the several aspects influencing the lives of humans and their fight for survival since generations. What is the component we are referring to? Is this component mysterious in nature? Do we human beings owe our life to this component?Any attempt at getting the answers right for these questions would make the lives of academicians such as mathematicians, physicists, statisticians, and computer scientists difficult. Marcus du Sautoy is one such Professor of Mathematics who takes the challenge head on and the component we refer to is the - Number, besides we have many forms of it to deal with. In The Number Mysteries, Marcus du Sautoy presents to the readers, an elaborated account on several kinds of number series predominantly the primes and their unique association with several mathematical mysteries. In this penned mathematical opera, the author channels his focus on unfolding the mysteries thereafter subjecting the readers to the unfolding mysteries. The Number Mysteries, as the title suggests is a mathematical journey to the world of numbers that encourages and motivates the wannabe math geniuses to take a deep dive into several unknown, hidden paradigms associated with primes and their derivatives. The math professor with his brain teasers succeeds in tickling our grey cells to get us to put our thinking caps on. The author with a definite, well defined vision regarding prospects of primes offering scope for innovation, further takes a leap forward presenting to the readers several undiscovered and unsolved conundrums on primes.
A book enthusiast who picks The Number Mysteries for a read is bound to experience and encounter broader aspects of applying principles of numbers to resolve various real world problems on football field dimensions to as contrasting an issue as the life evolution of cicadas and their predators. There is abundant scope in this compilation for making our interest for numbers more interesting and complicated. The author's juggling with the digits in numbers takes several infinite forms. To list a few - Beckham's 23, Real Madrid keeper's 1, the apparently hypothetical instance of using sunflowers and rabbits to find primes, the Hebrew-Mesoamerican-Babylonian representation of primes and several other mind baffling infinites. He employs unique innovative techniques to arrive at variant solutions to math riddles. He has notched up the craftsmanship of an artistic nature in posing questions to the readers - a throwing the ball in your court kind of sagacity. The preceding analogy would make more sense, for this 290 odd page book evens out on intellectual matter with its readers. With every page flip, the math enthusiasts are introduced to a new challenge in the book. The challenges put forth by the author vary from calculation of distance, estimation of the nature of various mathematical figures, determination of large complex numbers - few of which are indeterminates and left at reader's discretion, locating encrypted points and appropriately decrypting them, and discussing probabilities of various types - all these and more dealing with exciting ubiquitous elements of musical notes, sports, wars, geographical maps, among many other distinct real world problems. The principles of Enigma Machine, the Chappe brothers' code, Euler's theorem, gravitational force, the technicality of quadratic equations used in determining the curve traced by Wayne Rooney's volley, use of math to predict the future of our solar system, the mystery behind the boomerang's return to the starting point are dealt with concisely by the author in the book. However, there're mild shades of grey matter in the offing for the conservative readers in the book. These take the form of the math concepts governing the dreaded world of lotteries and casinos. In my viewpoint, the book's offering (primarily, the mathematical challenges) are not to be mistaken for a guidebook to make our presence felt as gamblers in the casinos world.
Caution to the audience of The Number Mysteries: Be game for a game challenge of the written kind if you get your hands on this compilation.
Briefly explained, The Number Mysteries by Marcus du Sautoy gives an informative and fascinating account on advanced concepts of mathematics putting into effective use the chunks of various number theories to deliver power packed solutions to real and digital world hurdles. This mathematical gem wins not a bounty of $1,000,000, but four points from my points pool. The book lovers can expect vast exposure to mathematical complexity exclusively included in the collection. Further, the math enthusiasts nurturing a liking for number symmetries, number enormities, number mysteries in addition to ambitions of winning the bounty could instantly pick this read without a second thought. An excellent mind-bender presenting an opportunity for addiction to numbers and the theories associated with them. A good read. Cheers.
A book enthusiast who picks The Number Mysteries for a read is bound to experience and encounter broader aspects of applying principles of numbers to resolve various real world problems on football field dimensions to as contrasting an issue as the life evolution of cicadas and their predators. There is abundant scope in this compilation for making our interest for numbers more interesting and complicated. The author's juggling with the digits in numbers takes several infinite forms. To list a few - Beckham's 23, Real Madrid keeper's 1, the apparently hypothetical instance of using sunflowers and rabbits to find primes, the Hebrew-Mesoamerican-Babylonian representation of primes and several other mind baffling infinites. He employs unique innovative techniques to arrive at variant solutions to math riddles. He has notched up the craftsmanship of an artistic nature in posing questions to the readers - a throwing the ball in your court kind of sagacity. The preceding analogy would make more sense, for this 290 odd page book evens out on intellectual matter with its readers. With every page flip, the math enthusiasts are introduced to a new challenge in the book. The challenges put forth by the author vary from calculation of distance, estimation of the nature of various mathematical figures, determination of large complex numbers - few of which are indeterminates and left at reader's discretion, locating encrypted points and appropriately decrypting them, and discussing probabilities of various types - all these and more dealing with exciting ubiquitous elements of musical notes, sports, wars, geographical maps, among many other distinct real world problems. The principles of Enigma Machine, the Chappe brothers' code, Euler's theorem, gravitational force, the technicality of quadratic equations used in determining the curve traced by Wayne Rooney's volley, use of math to predict the future of our solar system, the mystery behind the boomerang's return to the starting point are dealt with concisely by the author in the book. However, there're mild shades of grey matter in the offing for the conservative readers in the book. These take the form of the math concepts governing the dreaded world of lotteries and casinos. In my viewpoint, the book's offering (primarily, the mathematical challenges) are not to be mistaken for a guidebook to make our presence felt as gamblers in the casinos world.
Caution to the audience of The Number Mysteries: Be game for a game challenge of the written kind if you get your hands on this compilation.
Briefly explained, The Number Mysteries by Marcus du Sautoy gives an informative and fascinating account on advanced concepts of mathematics putting into effective use the chunks of various number theories to deliver power packed solutions to real and digital world hurdles. This mathematical gem wins not a bounty of $1,000,000, but four points from my points pool. The book lovers can expect vast exposure to mathematical complexity exclusively included in the collection. Further, the math enthusiasts nurturing a liking for number symmetries, number enormities, number mysteries in addition to ambitions of winning the bounty could instantly pick this read without a second thought. An excellent mind-bender presenting an opportunity for addiction to numbers and the theories associated with them. A good read. Cheers.
December 31, 2020
It was like listening to a friend who capture your attention from the beginning to the end. Surprisingly, his stories are what I have been learning throughout over decade of my school years.
For math haters, this book is full of surprises. What you have learnt in school might look more fascinating. Point of view towards everyday activities or objects might become different. For people who already favor in math, you can enjoy this book leisurely as bedtime story.
For math haters, this book is full of surprises. What you have learnt in school might look more fascinating. Point of view towards everyday activities or objects might become different. For people who already favor in math, you can enjoy this book leisurely as bedtime story.
January 11, 2018
An interesting read, at times unputdownable, at other times impenetrable. du Sautoy clearly loves his subject, and his passion consistently comes through the pages. It's when he gets into the meat of the maths that he sometimes struggles to bring his level down quite far enough for the layman to really enjoy. Certainly don't regret reading it, but not sure I'd read another.
November 20, 2020
In this book the author shares 5 mathematical mysteries and the history behind those mysteries. You can tell this is the first book the author wrote the writing isn’t as polished or engaging as his other books, but its still a good book to read that illuminates some interesting problems in mathematics. It’s a good exposure to different areas of mathematical disciplines.
October 17, 2020
Entreteníu y enllenu d'exemplos práuticos y de la vida cotidiana, anque quiciabes per momentos ye necesaria dalguna esplicación más cenciella porque'l conocimientu matemáticu que fae falta pa seguir completamente'l llibru ta dalgo penriba la media.
May 2, 2022
Pretty good insight into a mind obsessed with numbers.
Easy to read and full of insight.
I did feel as though there is a gimmick of winning £1million by reading this book. It's a funny kind of premise but one that Marcus du Sautoy only half-wanted to put in to the book.
Good read though
Easy to read and full of insight.
I did feel as though there is a gimmick of winning £1million by reading this book. It's a funny kind of premise but one that Marcus du Sautoy only half-wanted to put in to the book.
Good read though
March 10, 2025
It was a pleasure to be taken on a journey through some of these arcane and unsolved maths problems. It is an easy read at one level, but has some serious maths content to plough through as well. It deals with these unsolved problems well and nicely illustrates the beauty of mathematics.
January 4, 2019
Good in small doses.
Read in conjunction with the associated Oxford University Continuing Education course.
Read in conjunction with the associated Oxford University Continuing Education course.
September 24, 2019
An interesting read about how we can apply Mathematics to everyday situations. Suitable for someone without a lot of Maths knowledge and easy to understand (with plenty of helpful diagrams!)
September 2, 2020
Τα 5 άλυτα προβλήματα των μαθηματικών δίνουν έπαθλο στον επίδοξο λύτη 1 εκατομμύριο δολλάρια. Σίγουρα κερδισμένος θα βγει και ο αναγνώστης.
October 8, 2022
Just an interesting book about all the ways that math can be used to solve problems and the mysteries of math.
January 6, 2023
(ספר חביב מאד על מתימטיקה (וקצת פיסיקה
מכיל גם חידות למתענין ובעיות מיליון דולר שטרם נפתרו
נועד לענין צעירים במתימטיקה אבל גם מבוגרים ימצאו בו חן
הנושאים והענפים של המתימטיקה שבו הוא רב ומגוון
מכיל גם חידות למתענין ובעיות מיליון דולר שטרם נפתרו
נועד לענין צעירים במתימטיקה אבל גם מבוגרים ימצאו בו חן
הנושאים והענפים של המתימטיקה שבו הוא רב ומגוון
December 17, 2023
First part is pretty nice.
July 20, 2024
Full of fun maths facts for Caroline!
January 21, 2025
Awesome book!!! I learned so much about science and math applications in real life— from prime numbers, fractals, games and codes! I had fun reading it ❤️
Taught me to 'cheat' at Monopoly too 😂
Taught me to 'cheat' at Monopoly too 😂
May 11, 2025
Numbers, right?
Very entertaining, didatic and super fun. I've known Marcus from Numberphile's videos for some years now and he is such a great communicator.
Very entertaining, didatic and super fun. I've known Marcus from Numberphile's videos for some years now and he is such a great communicator.
January 13, 2026
Muy interesante y ameno sobre la presencia de las matemáticas en la vida cotidiana.
August 9, 2024
ooooo numbers are sooooooo mysterioussssss (i love numbers)
Displaying 1 - 30 of 60 reviews