{"id":918,"date":"2017-12-24T22:22:55","date_gmt":"2017-12-24T22:22:55","guid":{"rendered":"http:\/\/www.dongpingzhang.com\/?p=918"},"modified":"2017-12-23T03:31:52","modified_gmt":"2017-12-23T03:31:52","slug":"how-to-solve-it","status":"publish","type":"post","link":"http:\/\/www.dongpingzhang.com\/?p=918","title":{"rendered":"How To Solve It: A New Aspect of Mathematical Method"},"content":{"rendered":"

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My book of this week is <\/span>How to Solve It: A New Aspect of Mathematical Method<\/span><\/i> by eminent mathematician <\/span>George Polya<\/span><\/a>. Polya was one of the most influential mathematicians of the 20th century. O’Connor<\/span> and <\/span>E F Robertson wrote a short <\/span>biography<\/span><\/a> of Polya, giving us a glimpse of this extraordinary scientist and teacher. <\/span><\/p>\n

In the book <\/span>Mathematical People: Profiles and Interviews<\/span><\/i><\/a>, <\/span><\/i>there is <\/span>a quote from Polya: \u201cI came very late to mathematics. … as I came to mathematics and learned something of it, I thought: Well it is so, I see, the proof seems to be conclusive, but how can people find such results? My difficulty in understanding mathematics: How was it discovered?\u201d <\/span><\/i>This might be one motivation behind Polya\u2019s writing of a book like <\/span>How to Solve It<\/span><\/i>. I like this short review of the book: <\/span><\/p>\n

How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be \u201creasoned\u201d out – from building a bridge to winning a game of anagrams. Generations of readers have relished Polya\u2019s deft – indeed, brilliant – instructions on stripping away irrelevancies and going straight to the heart of the problem.<\/span><\/i><\/p>\n

How to Solve It <\/span><\/i>was first published in 1945. While reading this book, I could not help questioning myself: how did I not come across and read it in my early teens? Damn me for the hefty loss of not having done so! It would have enlightened and saved me from many struggles of searching for ways to solve problems not only in maths, but also other subjects. As I had not read it back then, I cannot tell what a young student would think of this book. I am indeed curious to know your thoughts, if you had. As a trained computer scientist with a lot of passion for mathematics, many articles in this book brought me moments of epiphany. Polya\u2019s words brought me the realisation of what we have learned to do through our scientific education and research, with the shortcoming that we have done so with less reflection and less articulation of what that set of thought processes are. \u00a0<\/span><\/p>\n

How did I come across <\/span>How to Solve It<\/span><\/i> eventually? I owe this discovery to two gentlemen: Nuwan Jayasena and Charles Simonyi. Many thanks to Nuwan that I attended a Stanford Engineering Hero Lecture, given by Charles Simonyi in 2015. In <\/span>this lecture<\/span><\/a>, Charles noted how much he valued the book <\/span>How to Solve It<\/span><\/i> and recommended everyone to read it. How fascinating that it took one Stanford PhD (Nuwan) to invite me to a talk given by another Stanford PhD (Charles), in which I was connected with a book by a Stanford Professor (George Polya)! I am very grateful. \u00a0<\/span><\/p>\n

You might start to wonder: woman, are you ever going to tell me what this book is about? <\/span><\/p>\n

There are four parts: In the Classroom; How to Solve It: A Dialogue; Short Dictionary of Heuristics; Problems, Hints and Solutions. Here I focus on the \u201cHow to Solve It\u201d list and some of the heuristics discussed in the book. <\/span><\/p>\n

In the \u201cHow to Solve It\u201d list, Polya distilled the problem solving processes to the following four steps. These suggestions and questions are quoted directly from the book. <\/span><\/p>\n

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  1. Understanding the problem<\/strong>\n