13. EFFORT WORTHWHILE FOR DOING A MATH PROBLEM

All the students took exception to the idea that you either get a problem quickly or you don't. However, the examples they give are very general or else are not drawn from their own experience but rather problems that inspired professional mathematicians and took years or even centuries to solve, e.g. Fermat's last theorem. This question was probably not worded quite right to get the kind of insight into their attitudes as I would have liked and I will revise it for subsequent offerings of the course.

"This is an untrue statement. Determination, hard work, and perserverance can make all the difference."

"No, you have to approach a problem with a lot of patience. Sometimes you don't understand exactly what was asked, or what you want your solution to be. So you have to decipher it. Solving a math problem can take more than days."

"No, as you live hint to the answer pop up after you exhausted ideas and stopped. Live a little and try again."

"Of course this statement is wrong. There are plenty of examples in history, where years were spent on solution to a problem. I can think of the famous example of Fermat's last theorem, where the solution was figured out after seven years of isolation, practically."

"My experience is that either you know how to do something or you don't. But that may just be due to the type of mathematical problems I have encountered. On other problems, such as the 3 x 3 square problem #1, the answer will take longer to come up with and may not be readily apparent."

"Solutions do not just come in a given amount of time. One must work hard and attempt to find a solution. Sometimes it takes years to find it Ð but one must never give up."

"No, because we will not understand the solution without struggling."

"Definitely not. Fermat's theorem, case and point."

"I disagree. One can have an 'AHA' moment a week after working on a problem."

"False! I believe that solving a mathematical problem often involves having a certain perspective which may not be clear at first. Sometimes if a problem is causing me some difficulty I move on, and when I return to it later I often am in a different 'frame of mind' which may cause me to think about the problem in an entirely new way."