A few years ago I started looking at the unsolved conjecture about twin primes and set out to find a solution. A Greek mathematician named Euclid proved over 2,300 years ago that there were infinitely many prime numbers–numbers that are only divisible by one and themselves (2, 3, 5, 7, 11, 13, 17, 19, …), but it has never been proved that there are infinitely many twin primes. Twin primes are primes that are only two digits apart like: (3, 5), (11, 13), (18409199, 18409201).
There have been thousands of individuals over several thousands of years that are far more intelligent than I who have never found a solution, so why try? I won’t delve too much further into the maths involved or the work I’ve done on this problem, but I did want to mention three benefits of trying to tackle a problem of this magnitude.
The first benefit of a hard problem is pushing your limits. When you first pick up a problem like this you quickly learn your limits and come to the realization that you know very little. Knowing your limits is a good thing, because it’s difficult to push past them if you do not understand where they are. As you begin to investigate your problem you’ll probe the knowledge of other and increase your own understanding. Maybe in the end you’ll become an expert in the subject, but you’ll definitely be more knowledgeable.
A second benefit of a tough problem is that it gives courage. When you stand before the impossible something changes in you. You develop an attitude that says, “I’m going to try anyway.” Many people give up too quickly. They say it’s too hard, or it can’t be done, when they should have said, I just don’t want to put fourth the effort. It reminds me of the biblical story of David and Goliath where the little shepherd boy faced an impossible task. The mightiest warriors in Israel failed, but this 16 year old won the day.
The third benefit is that it keeps you sharp. A few weeks ago I was cutting weeds with a machete and handed it to my father for just a second. As he put it down to his side the blade barely touched the finger of his other hand and drew a line of blood. It was sharp and it did it’s job easily and efficiently. I think it’s the tough problems that help keep us sharp. They keep us focused on the impossible solution always trying something new and honing current knowledge.
Maybe math is not your thing, but that’s OK. I challenge you to find a hard problem, maybe even one deemed impossible, and set out to find the answer. You might have a long struggle ahead of you, but you’ll grow. And maybe, you’ll find a solution that nobody’s thought of.