# How to Solve It  ## Metadata - Author: G. Polya and John H. Conway - Full Title: How to Solve It - Category: #problem-solving ## Highlights - First. You have to understand the problem. ([Location 149](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=149)) - Second. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution. ([Location 155](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=155)) - Third. Carry out your plan. ([Location 170](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=170)) - Fourth. Examine the solution obtained. ([Location 175](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=175)) - “Mathematics, you see, is not a spectator sport. To understand mathematics means to be able to do mathematics. And what does it mean [to be] doing mathematics? In the first place, it means to be able to solve mathematical problems.” ([Location 195](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=195)) - “If you can’t solve a problem, then there is an easier problem you can’t solve: find it.” ([Location 209](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=209)) - Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice. Trying to swim, you imitate what other people do with their hands and feet to keep their heads above water, and, finally, you learn to swim by practicing swimming. Trying to solve problems, you have to observe and to imitate what other people do when solving problems and, finally, you learn to do problems by doing them. ([Location 340](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=340)) - Trying to find the solution, we may repeatedly change our point of view, our way of looking at the problem. We have to shift our position again and again. Our conception of the problem is likely to be rather incomplete when we start the work; our outlook is different when we have made some progress; it is again different when we have almost obtained the solution. ([Location 350](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=350)) - First, we have to understand the problem; we have to see clearly what is required. Second, we have to see how the various items are connected, how the unknown is linked to the data, in order to obtain the idea of the solution, to make a plan. Third, we carry out our plan. Fourth, we look back at the completed solution, we review and discuss it. ([Location 353](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=353)) - It is foolish to answer a question that you do not understand. It is sad to work for an end that you do not desire. ([Location 362](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=362)) - We have a plan when we know, or know at least in outline, which calculations, computations, or constructions we have to perform in order to obtain the unknown. The way from understanding the problem to conceiving a plan may be long and tortuous. In fact, the main achievement in the solution of a problem is to conceive the idea of a plan. ([Location 395](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=395)) - In order to be able to see the student’s position, the teacher should think of his own experience, of his difficulties and successes in solving problems. ([Location 400](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=400)) - Good ideas are based on past experience and formerly acquired knowledge. Mere remembering is not enough for a good idea, ([Location 402](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=402)) - Look at the unknown! And try to think of a familiar problem having the same or a similar unknown. ([Location 409](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=409)) - If you cannot solve the proposed problem try to solve first some related problem. ([Location 416](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=416)) - By looking back at the completed solution, by reconsidering and reexamining the result and the path that led to it, they could consolidate their knowledge and develop their ability to solve problems. ([Location 482](https://readwise.io/to_kindle?action=open&asin=B0073X0IOA&location=482))