All problems in the world can be reduced to connection problems. A connection problem is a situation where two parties are missing a potential positive connection .
Consider the issue of world hunger, there is a positive connection missing between those who are hungry and sources of food. Violence boils down to a lack of a positive connection between the parties involved (one party has a negative connection which causes them to create negative connections and become violent).
Problems in mathematics follow the same pattern, the hardest problem in mathematics is the boolean satisfiability problem. The problem goes somewhat like this, ‘I have a lock. Does a key exist which can open this lock?’, the lock can be of any shape, size or form and so can the key.
So in effect the hardest problem in mathematics boils down to being able to connect a key to a lock. This is the connection problem. The reason why connection problems can be difficult to solve is because there is some luck involved!
Problems can be solved though, people solve problems every day, this is not due to an incredible amount of luck people happen to possess. Instead, it turns out that a problem becomes easier to solve when it is related to a different problem which has already been solved.
This is why education and learning is important, observing problems which have already been solved and learning the method which solved them will give people the insight they need to solve different yet related problems.
This is a copy of my blog post,