Lance Fortnow on the current status and future outlook of solving the P-NP problem.

DEAR MISS MANNERS: I regret to tell you that, in the modern parlance, “You’re welcome” isn’t polite. It is currently more polite to say “No problem” or “No worries,” which imply that whatever was done ...

Real Madrid kicked off the new year with a 5–1 victory over Real Betis on Sunday afternoon, handing Manuel Pellegrini’s men their first away defeat of the season. After a brief holiday break, the ...

\begin{abstract} We present a locality--audit framework for proving circuit lower bounds for NP languages. We define an explicit NP--complete language equipped with structural invariances (``audits'') ...

Source: Darren Edwards What if one of the biggest unsolved problems in mathematics is not just about numbers or computers, but about observers like you and me? This isn’t a proposed solution to P vs ...

Forbes contributors publish independent expert analyses and insights. Analyzing tech stocks through the prism of cultural change. The most important number for active managers in 2025 is 80. That’s ...

It remains an open question when a commercial quantum computer will emerge that can outperform classical (non-quantum) machines in speed and energy efficiency while solving real-world combinatorial ...

Pope Leo XIV is on the side of the angels when it comes to matters of cinema. Last Saturday, after he gathered some of the film world’s luminaries at the Vatican, the pontiff delivered one of the most ...

Vanguard S&P 500 ETF offers a broader portfolio and lower expenses than Invesco QQQ Trust, Series 1 QQQ has delivered stronger recent returns, but with higher volatility and a deeper five-year ...