Did Pólya say, “can” or “cannot”?

Most mathematicians are familiar with the mathematical problem-solving book How to Solve it, by George Pólya. And for those who are not, especially young mathematicians, I would recommend dropping everything and reading it immediately.

In the foreward of many editions of this book, John Conway attributes to Pólya the advice,

“If you can’t solve a problem, then there is an easier problem you can’t solve: find it.”

Meanwhile, one can also find many people quoting Pólya as having said,

“If you can’t solve a problem, then there is an easier problem you can solve: find it.”

I have added emphasis for the difference.

The former quotation appears in Conway’s foreward to How to Solve it. The latter quotation, meanwhile, appears on the How to Solve it Wikipedia page, and also in many other places. Online, it seems that the quotations are split about 50/50 between these two versions.

My question is, what did Pólya actually say? Are the latter quotes simply mis-quoting Conway’s version? Or did Conway make an innovation?

I haven’t found Conway’s version in Pólya’s writing explicitly, although he does have remarks with similar substance in How to Solve it. But there there were evidently many editions of this book, and perhaps I have simply missed the right place.

Personally, I find the Conway version of Pólya’s quote more erudite and valuable. One can, of course, always find an easier problem of a problem that one can solve, simply by trivializing it, but that doesn’t seem important. What is important, however, is to find an easier-but-still-difficult version of your problem, coming into the boundary between the solved and the unsolved from above.


I will quote exactly what as I see on my version of the book (Second Edition, 1957) on page 114.

If you cannot solve the proposed problem do not let this failure afflict you too much but try to find consolation with some easier success, try to solve first some related problem; then you may find courage to attack your original problem again. Do not forget that human superiority consists in going around an obstacle that cannot be overcome directly, in devising some suitable auxiliary problem when the original one appears insoluble.

From all the sources I’ve read, it doesn’t seem like he explicitly wrote the commonly known quote on his book.

Source : Link , Question Author : JDH , Answer Author : projectilemotion

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