How to Solve It: A New Aspect of Mathematical Method

Very interesting read and will be rereading in future to remind myself of its great ideas.

This book teaches you to dissociate yourself from the problem posed and ask yourself logical questions to decompose the problem before forming a plan.

This is a very good book that takes a lot of time to digest. So, get it well before your exam or you start your job as a trainee mathematical modeller! What I mean by that is, I read it, cover to cover, then returned to my university studies with renewed excitement and found I still got stuck. Par for the course in mathematics, but disappointing nonetheless. However, once I had solved the problem (or given up and checked the solution), then reflected on why I got stuck, a heuristic from this book often jumped out at me. Ah... if only I'd thought to try this it would've made the way forward so obvious! And that is essentially what the book is. You will not get a list of algorithms to take the creativity and hard work out of mathematical problem solving (frankly, that'd no more be a good thing than taking the creativity and hard work out of sport). What you will get is a discussion of thought processes that professional mathematicians use, probably unconsciously at that stage of education, that may help you make headway on your problem. Essentially, 'What are fruitful questions to ask when I don't know how to proceed or even begin?' (Hint: don't just sit there and stare at it waiting for the muse to strike you.) In fact, you probably use some of these already but don't even realise you're using the same strategy over and over again. In this way, Polya has done what mathematicians do: he has abstracted, generalised and systematised a hitherto hodgepodge of problem-solving recipes used implicitly in particular situations. A simple example for when you get stuck: 'Can you rewrite the equation?' I cannot count how many times I have fallen into this trap, realising after I've given up on a problem that the way to proceed would've jumped out at me had I only thought to rewrite it in a different form. On one level, it might simply be that you, personally, are really quite uncomfortable with a particular form of notation. Rewriting things might well put you at psychological ease with more familiar forms, or forms you're much better practised at manipulating. Hate Leibniz notation for your calculus? Why not rewrite it as Newtonian to solve your problem, then translate back into Leibniz? This strategy, in fact, is what we do all the time - when you learn trig identities or to move between forms of vectors, say, you are implicitly learning the strategy: 'Rewrite the equation to make it easier to deal with.' The other reason might simply be that by rewriting it, the solution jumps out at you. This is what happens whenever you multiply out, factor, substitute into equations etc. Just because your question doesn't specify you need to do something, doesn't mean you aren't allowed to try it! But it has to occur to you first to rewrite your problem into an equivalent form, in order for the light at the end of the tunnel to reach you. And really this is something you do already: whenever you look up a word in a dictionary, you're essentially seeing the term which you don't understand rewritten as something you do understand. Then you can proceed with your paragraph, just like you can then proceed with your mathematical problem.

I thought I would buy this book after seeing it reviewed on a Japanese mathmatics program on TV . I found the contents difficult to read not being a higher maths candidate myself. How ever after trying to digest the words of wisdom in the theory of solving problems I had to admit it is only suitable for those amongst us who have a higher maths certificae than myself.very much higher ! The authur G.Polya was an aclaimed world wide mathematician, so if you are in his league then the book is worth reading ..TR

Haven’t read it all yet. Good so far and fast delivery was much appreciated.

I have heard good things about this book, the content is good, now the book I got has it's cover all damaged and not clean

An excellent approach to problem solving, one that has value far beyond just mathematics.

Enlightening ones mathematical mind and thinking out side of all boxes.

数学の問題を解く方法が、学生を指導する、という視点で体系的に述べられています。 解答を導き出すための学生への質問集も用意されています。 考え方にびっくりするほどの斬新さは感じられませんが、数学教師や数学を志す人には役立つと思います。 では数学以外の一般的問題解決やプロジェクトなどの問題分析に役立つかというと、プロセスマネジメントが発達した現代ではそこまでの応用力を求めるのは無理かな、と感じました。 文章は簡潔で英語は読みやすいです。 今まで馴染みのなかった数学英語に接することも出来ました。また、錆付いた数学知識を（ある程度）思い出すきっかけになったと思います。 ガリレオ時代のフランスの学者 Descartes,Reneが引用されていたりもします。

I bought this because I was looking for algorithmic examples for teaching and learning. This sounded like it would be a good book, so I borrowed it from the University Library. After extending my borrowing period twice, I decided I absolutely need to buy this book. There are so many brilliant things to be learned from this book. Here is one: The algorithm of solving any problem in mathematics is the same as solving any problem in general. It will take a year I think for my step-son to learn those steps, but let's be clear on this. In the problem of reassembling his computer/study desk involved the same steps. He is beginning to see that Mathematics is just problem solving - there is a common set of steps to go through for any problem. I wish I read this book when I first started teaching physics. It would have added to my pedagogical tactics, and helped a lot of people. Being retired for almost ten years though, I am a little disappointed by not having read it. Don't make my mistake - get the book!! Use the book!! Tell others about the book!!

Als Student im Ingenieurwesen habe ich mir dieses Buch „How to Solve It“ gekauft, weil ich oft an komplexen Aufgaben sitze, bei denen ich nicht sofort weiß, wie ich anfangen soll. Was mich sofort überzeugt hat: Polya bringt einem keine langweiligen Formeln bei, sondern eine Denkweise. Er zeigt systematisch, wie man ein Problem zerlegt, neu formuliert und Schritt für Schritt einen Lösungsweg findet.Gerade im Studium, wo es nicht nur ums Ausrechnen, sondern ums Verstehen geht, ist diese Herangehensweise extrem hilfreich. Ich habe gemerkt, dass ich dadurch strukturierter an Übungsaufgaben, aber auch an Projekten und technischen Fragestellungen herangehe. Das Buch zwingt einen praktisch, über das eigene Denken nachzudenken – und das ist in den Ingenieurwissenschaften Gold wert.Der Schreibstil ist zwar teilweise ein bisschen altmodisch (das Buch ist ja auch schon älter), aber erstaunlich klar. Man merkt sofort, dass Polya Lehrer durch und durch war. Es ist kein „Schnell-mal-durchlesen“-Buch, sondern eher etwas, das man immer wieder zur Hand nimmt, wenn man feststeckt.Für mich als Student eine Investition, die sich wirklich gelohnt hat. Es ist weniger ein Mathebuch als eine Art Werkzeug für kluges Problemlösen – im Studium und darüber hinaus.

This is an interesting read

Un clásico!!