P=NP Proving Challenges

Understanding of the intricacies of the world and its application has been the focus of human intellectual evolution. Our knowledge allowed us to build concepts that leads us to where we are now, in the modern 21st century information era. Mathematics and computer science has been concerned about proving and verification of various mathematical concepts with the help of automated and fast computational power of computers. From checking the validity of the conjecture to a certain maximum value, mathematicians are able to see if a particular conjecture holds to a bigger sets of variables. Computer science also has it's own problem, more commonly known as proving P=NP.


The proof has a very profound implication on our systems as proving that all problems can be verified easily on polynomial time has a way to be solved in polynomial time. Big O notation is the metrics that was developed to evaluate the complexity and speed of an algorithm. Polynomial time suggest computationally possible solution using the traditional Von Neumann computer. As most computer scientist attempted proving the P=NP problem in the past years, the degree of difficulty is easily seen. Algorithms are developed to solved problems. Some problems can be solved by a better algorithm for that same purpose of solving a given problem. Suggesting that fast verifying of of the result of a calculation may have a way to get the result as easy as the way it was checked is a possibility. That is why a million dollars is to be given to a person able to solve and prove that P=NP or P!=NP.

For the proof to work, it must be sufficient to include all problems to be solvable in polynomial time regardless of its difficulty or the complexity of the algorithm required to solved the problem. The metric of time is visioned being a mathematical function expressed in Big O notation. We think that problems might not have better and faster way of being computed given the current technological state or the intellectual leap. It is logical to say that P!=NP can be proven if a certain problem can be proven that cannot be solved in P in any possible way. A thorough investigation of a specific problem will result to the proof, which is also the case in mathematical conjectures and their proofs.