But for sheer intellectual surprise, and alarming insight, it is hard to think of any result that would approach the famous incompleteness theorem of Kurt Gödel. In 1900, when David Hilbert ...

We then speak of error-detecting and error-correcting codes. Shannon's second theorem, or the noisy-channel coding theorem (1948), guarantees the existence of such codes. We do not give any proof of ...

PAKHOMOV, FEDOR and WALSH, JAMES 2021. REFLECTION RANKS AND ORDINAL ANALYSIS. The Journal of Symbolic Logic, Vol. 86, Issue. 4, p. 1350. CHENG, YONG 2021. CURRENT ...

"Non-trivial text generation during the lifespan of our universe is almost certainly impossible," the researchers said.

Two students who discovered a seemingly impossible proof to the Pythagorean theorem in 2022 have wowed the math community ...

Turns out that monkeys (or chimps) can't randomly type Shakespeare's works even if they were given billions of years to try.

Donald Trump’s election victory will return him to the White House, but both his allies and detractors have made clear his second time around will look nothing like the first. With the ...

Armed with that experience, he expects officials in his second administration will better understand how to navigate complex agencies and policy processes, making a faster — and more ambitious ...

Commissions do not affect our editors' opinions or evaluations. If you’re planning to purchase a second home or refinance an existing one, current second home mortgage rates can significantly ...

Immunocompromised people and those who are age 65 or older should get a second dose of the 2024-2025 COVID-19 vaccine, according to the latest recommendations from the Centers for Disease Control ...