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The PNP Mayfly

The PNP mayfly proves that p=np1

You'd have to know someting about complexity theory to understand the significance of this.
Computer scientists have been trying to prove p=np for decades.
"The relationship between the complexity classes P and NP is an unsolved question in theoretical computer science. It is generally agreed to be the most important such unsolved problem, and one of the most important unsolved problems in mathematics. The Clay Mathematics Institute has offered a USD 1,000,000 prize for a correct proof." (wikipedia).

The significance of the pnp mayfly theorum is far reaching.
This means, for instance, we can now solve the travelling brown trout problem in polynomial time. p-equals-np-mayfly

1 PNP, in this context, is roughly equivalent to the assertion: perseverence = nearly perfect

2 The Travelling Brown Trout Problem:
Given a number of holding lies and the costs of traveling from any lie to any other lie, what is the cheapest round-trip route that visits each lie exactly once and then returns to the starting lie? An equivalent formulation in terms of graph theory is: Given a complete weighted graph (where the vertices would represent the holding lies, the edges would represent the runs, and the weights would be the cost or distance of that run), find a Hamiltonian cycle with the least weight.

It can be shown that the requirement of returning to the starting lie does not change the computational complexity of the problem. The problem is of considerable practical importance, apart from evident transportation and logistics areas. Another classic example appears in spring creek fishing: scheduling of a route from rising fish to rising fish. In most highly optimized fishing strategies, the "holding lies" are fishing holes (of different sizes), and the "cost of travel" includes time for wading from spot to spot. Now that we have proven p=np, we know a solution can be calculated in polynomial time.
 
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