can NP-complete problems be solved efficiently in the physical universe? All hunches would say no, but then we only discovered polynomial time factorization using quantum algorithms 10 years ago.

2011-08-12: Markets being efficient and P != NP can’t both be true, it turns out. So either you can compute fast or make money on the stock market. It remains unclear whether you can MAKE MONEY FAST or not.
2017-01-04: The history of P != NP

In 1955, John Nash sent a remarkable letter to the National Security Agency, in which—seeking to build theoretical foundations for cryptography—he all but formulated what today we call the P=?NP problem, considered one of the great open problems of science. Here I survey the status of this problem in 2017, for a broad audience of mathematicians, scientists, and engineers. I offer a personal perspective on what it’s about, why it’s important, why it’s reasonable to conjecture that P≠NP is both true and provable, why proving it is so hard, the landscape of related problems, and crucially, what progress has been made in the last half-century toward solving those problems. The discussion of progress includes diagonalization and circuit lower bounds; the relativization, algebrization, and natural proofs barriers; and the recent works of Ryan Williams and Ketan Mulmuley, which (in different ways) hint at a duality between impossibility proofs and algorithms.

2022-12-03: Why are there complete problems, really?

This, then, is how universality of computation explains the existence of complete problems. For virtually any class we might define there will be a way of handicapping the universal computer such that it is still able to solve all of the problems in the class while at the same time not breaking the class specific resource constraint.

We can now see that the existence of complete problems is a direct result of one of the core features of computers that also makes them relevant to the real world.

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