P = NP

"There are about half a dozen problems that almost all mathematicians agree are supremely important. One that I particularly like is the "P = NP" problem.

This concerns a situation that occurs not just in mathematics but also in everyday life: often it is easy to recognise a solution to a problem, but not at all easy to find one. For example, if you are asked to factorise 10541, you will have to spend a long time searching for factors amongst the primes. But if you are told that 10541 is 83 × 127, it is routine to check that it is true. A non-mathematical example is finding anagrams of words.

So far, so uncontroversial. However, one of the great gaps in our knowledge is that nobody knows how to show that searching for solutions really is harder than checking that the solutions are correct. This is the P = NP problem.

This problem gets to the heart of mathematics, because mathematical research itself has the property I have described: it seems to be easier to check that a proof is correct than to discover it in the first place. Therefore, if we found a solution to the P = NP problem it would profoundly affect our understanding of mathematics, and would rank alongside the famous undecidability results of Kurt Gödel and Alan Turing."

It is easy to determine the truthfulness of a mathematical equation by finding whether or not it contains any [-1] to it. Since there are no negative numbers [see below] any negative number is an unreal and should invalidate the equation in non-euclidian number theory. the subtlety [a] of a -1 can be slight, but even a minor -1 should do it. Furthermore, any equation in which there is no -1 accumulating should be 'true', as it exists. Again, watch for subtle [-1]. -4 = 4[-1]. -1 = 1 X -. A decrease from 1 producing a <100%. This could be lost e-, indicating unsustainability and a desire for not being, which is fulfilled. "Not a pereptual motion device."