Quotes & Sayings About Mathematics Problem Solving

Solving a problem for which you know there's an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. And it's not always at the top of the mountain. It might be in a crack on the smoothest cliff or somewhere deep in the valley. — Yoko Ogawa

I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future. — Andrew Wiles

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. — George Polya

Outside observers often assume that the more complicted a piece of mathematics is, the more mathematicians admire it. Nothing could be further from the truth. Mathematicians admire elegance and simplicity above all else, and the ultimate goal in solving a problem is to find the method that does the job in the most efficient manner. Though the major accolades are given to the individual who solves a particular problem first, credit (and gratitude) always goes to those who subsequently find a simpler solution. — Keith Devlin

Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem. — Harold Davenport

After two years of undergraduate study, it was clear that I was bored by the regime of problem-solving required by the Cambridge mathematical tripos. A very sensitive mathematics don recommended that I talk to the historian of astronomy, Michael Hoskin, and the conversation led me to enroll in the History and Philosophy of Science for my final undergraduate year. — Philip Kitcher

When an official report in the UK was commissioned to examine the mathematics needed in the workplace, the investigator found that estimation was the most useful mathematical activity. Yet when children who have experienced traditional math classes are asked to estimate, they are often completely flummoxed and try to work out exact answers, then round them off to look like an estimate. This is because they have not developed a good feel for numbers, which would allow them to estimate instead of calculate, and also because they have learned, wrongly, that mathematics is all about precision, not about making estimates or guesses. Yet both are at the heart of mathematical problem solving. — Jo Boaler