Slide rules are indeed a very old technology. In fact, the underlying principle goes all the way back to Noah.
After Noah got off the Ark, he sent the animals to go forth and multiply. And each month he went out to see how they were doing. As you might guess, after the first month or so there were baby rabbits, then baby cats and dogs soon after, and even a baby elephant after the first year. But month after month, Noah could find no baby snakes.
Finally it dawned on him that the snakes were cold blooded, and needed to sun themselves in order to get active. But the wet ground, and the lack of trees, had been perfect for bushes, weeds, and all kinds of plants, and the snakes were getting shaded out as it were. So Noah went back to the Ark, collected some timbers he'd used to strengthen the decks, and used them to build a table. And sure enough, the next month there were baby snakes! (scroll down...)
Which just shows to go, even an adder can multiply if you give him a log table.
An editor might put a period after your 'vs'.
If you read the press release from MIT, this discovery was about problems squarely inside P. Namely, they were (for a certain class of problems in P) able to reduce the complexity from N^^5 or N^^6 down to N^^2 or N^^3. So there would seem to be no implications for the P=NP problem.
Prove it and you'll be famous.
(Or you can write a note in the margin of a book on algorithmic complexity saying that the margin is too small to contain your proof.)
"Spock, did you see the looks on their faces?" "Yes, Captain, a sort of vacant contentment."