P versus NP

In April 2025, J. Connell ran a small experiment. He asked ChatGPT-4 to review a dozen published papers that claimed to have finally cracked P versus NP. The AI didn’t flag any major flaws. Instead, it complemented parts of the method and even said some of the ideas made sense. That reaction puzzled Connell, because…

Think about your day as a founder. Before lunch, you’ve already answered questions that look harmless but are almost impossible to solve perfectly. Should these three engineers handle those five projects? How do your drivers visit thirty customers without wasting hours? Where should your limited marketing money actually go? These aren’t just messy business choices….

The P vs NP problem comes with a million-dollar prize, but the real concern goes far beyond the money. Almost all modern encryption, the stuff that keeps the internet safe, relies on assumptions we’ve never actually proved. If P ever turned out to equal NP, most public-key systems would fall apart overnight. RSA and elliptic-curve cryptography could be cracked easily, and the entire crypto and blockchain ecosystem could be in serious trouble. A lot of our security depends on “trapdoor” problems that are simple to verify but extremely hard to solve. And even though most computer scientists think P isn’t equal to NP, mainly because no one has found faster algorithms after decades of trying, the uncertainty still hangs over everything. That’s why startups don’t rely on a single cryptographic idea. They adopt post-quantum algorithms, build systems that can switch to new methods when needed, and understand that security is always evolving, no matter what the underlying theory says.