A Quote by G. H. Hardy
A chess problem is simply an exercise in pure mathematics.
Related Quotes
A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful-"important" if you like, but the word is very ambiguous, and "serious" expresses what I mean much better.
As an exercise of the reasoning faculties, pure mathematics is an admirable exercise, because it consists of reasoning alone and does not encumber the student with any exercise of judgment.
The broader the chess player you are, the easier it is to be competitive, and the same seems to be true of mathematics - if you can find links between different branches of mathematics, it can help you resolve problems. In both mathematics and chess, you study existing theory and use that to go forward.
I didn't feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.
Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.
Pure mathematics is on the whole distinctly more useful than applied... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.
Characters tend to be either for or against the quest. If they assist it, they are idealized as simply gallant or pure; if they obstruct it, they are characterized as simply villainous or cowardly. Hence every typical character...tends to have his moral opposite confronting him, like black and white pieces in a chess game.
The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who wishes to serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.
My sister Susan, who was the first one, was pretty good in mathematics and then chess, and my father chose chess because it was easier to measure the results.
Poker isn't the roulette wheel of pure chance, nor is it the chess of mathematical elegance and perfect information. Apart from the underlying mathematics, poker depends on the nuanced reading of human intention, interactions, and deceptions.
Chess is not Mathematics, where ten is always more than one; in chess the King with a pawn can beat opponent's King with all pieces if they are placed badly.
In mathematics, if I find a new approach to a problem, another mathematician might claim that he has a better, more elegant solution. In chess, if anybody claims he is better than I, I can checkmate him.
It was as though applied mathematics was my spouse, and pure mathematics was my secret lover.
In mathematics I can report no deficiency, except it be that men do not sufficiently understand the excellent use of Pure Mathematics.
The Advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation.
It has been a fortunate fact in the modern history of physical science that the scientist constructing a new theoretical system has nearly always found that the mathematics. . . required. . . had already been worked out by pure mathematicians for their own amusement. . . . The moral for statesmen would seem to be that, for proper scientific "planning", pure mathematics should be endowed fifty years ahead of scientists.
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