Thoughts of a Problem Solver
Mathematics, to me, is not just a tool, nor is it only a language for reading our universe. To me, mathematics is an art: the art of logic; and like any other form of art, it is beautiful. This is because the mathematical universe is perfect: here every piece of argument, every theorem is a constellation of reasoning all built upon the strict axioms of the mathematical universe. The proper way of exploring this beauty is problem solving. By problem solving, I do not mean simply trying to fit a problem in a cookie cutter technique or a formula. Sure, formulae and techniques have their places, but exploring mathematics through problem solving is much more than that. It is about finding the divine connection between …show more content…
Nothing gives me more pleasure than spending hours on a problem trying to find a clue to how to attack it. Often I fail to find anything useful even after a lot of effort. But patience is very important in this sport. From my experiences I know the more effort I put in solving a problem, the greater the joy and learning. This is why Paul Erdos, possibly the most prolific mathematician of our time, said “Problems worthy of attack prove their worth by fighting back.” If I am persistent enough, I finally find something to work with: maybe some intuition, some out of the box ideas or something similar that I worked on before. At times, I write down whatever observation I have made related to the problem, set them aside for the time being, and come back later invigorated to attack it with the might of a freshened mind. Again, just like finding hidden treasures on an adventure, while contemplating on a problem, sometimes I come across new insights that may not be useful for that specific problem, but are important in their own regards. In fact, this is how I found a certain result in number theory which recently has been accepted as a paper in the Bachman Math Journal. Eventually, I am able to connect all the different pieces and fill up the gaps to finally reach the solution. In mathematical problem solving, while the solution is the original goal, the journey to reach it is equally important and
Mathematics, to me, is not just a tool, nor is it only a language for reading our universe. To me, mathematics is an art: the art of logic; and like any other form of art, it is beautiful. This is because the mathematical universe is perfect: here every piece of argument, every theorem is a constellation of reasoning all built upon the strict axioms of the mathematical universe. The proper way of exploring this beauty is problem solving. By problem solving, I do not mean simply trying to fit a problem in a cookie cutter technique or a formula. Sure, formulae and techniques have their places, but exploring mathematics through problem solving is much more than that. It is about finding the divine connection between …show more content…
Nothing gives me more pleasure than spending hours on a problem trying to find a clue to how to attack it. Often I fail to find anything useful even after a lot of effort. But patience is very important in this sport. From my experiences I know the more effort I put in solving a problem, the greater the joy and learning. This is why Paul Erdos, possibly the most prolific mathematician of our time, said “Problems worthy of attack prove their worth by fighting back.” If I am persistent enough, I finally find something to work with: maybe some intuition, some out of the box ideas or something similar that I worked on before. At times, I write down whatever observation I have made related to the problem, set them aside for the time being, and come back later invigorated to attack it with the might of a freshened mind. Again, just like finding hidden treasures on an adventure, while contemplating on a problem, sometimes I come across new insights that may not be useful for that specific problem, but are important in their own regards. In fact, this is how I found a certain result in number theory which recently has been accepted as a paper in the Bachman Math Journal. Eventually, I am able to connect all the different pieces and fill up the gaps to finally reach the solution. In mathematical problem solving, while the solution is the original goal, the journey to reach it is equally important and