The infamous enigmas.

This world is an enigma, yet to be solved. And so are the many unsolved problems in many different fields. Among them is the infamous mathematics (and computer science) problem P vs. NP.

P vs. NP is a millennium prize problem. The first being providing even the nearest correct solution would be awarded US$ 1,000,000.

What is P vs. NP?

Well P vs. NP is the name of a problem that many mathematicians, scientists and computer programmers want to answer. P and NP are the two groups of the mathematics problems. P problems are generally considered “easy” for a computer to solve, whereas NP problems are easy for a computer to check.

Now, you have a NP problem and say the solution to your problem is ‘I N F O’, a computer can figure out in a beat if the solution is correct or not, but it may take like forever for a computer to come up with ‘I N F O’ on its own.

The ‘P versus NP’ asks whether these two classes of problems are actually identical; i.e. whether every NP problem is also a P problem. If P=NP, every NP problem would contain a hidden shortcut which a computer can find in a reasonable amount of time. But if not, then a computer’s ability to solve problems remains fundamentally and potentially limited.

If P=NP…….

If the above stated would be true (which isn’t), it would bring something like second industrial revolution. It would completely revolutionize the world we live in.

There would be a short program which, given detailed constraints on any engineering task, would quickly generate a design which meets the given criteria, if one exists.

And there would be a short program which, given data on some phenomena and modeling restrictions, would quickly generate a theory to explain that data within the modeling constraints, if one exists. Many things that scientists hope to explain, like about how the brain works, the nature of dark matter and dark energy, the structure and function of proteins, etc. could potentially be done in a wink!

But we live in the real world, not in the utopia described above. And in here P is not equal to NP.

Not the End!

So we can see P vs. NP as, for students it is easier to understand a lecture than to come up with the matter for one from scratch on their own.

Now as for me, I’m just another curious homo sapien on his quest for knowledge, which for humans can never end. And we’ve only just begun! Let us advance ahead and unwind the enigma behind this code.