Mathematical logic and set theory provide the foundational language for modern mathematics, articulating precise notions of proof, computability and the hierarchy of infinities. Central themes include ...

Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core principles didn’t come easily. How do mathematicians decide that something ...

Descriptive set theory examines the structure and classification of definable sets within topological spaces, with a particular focus on Polish spaces—those that are separable and completely ...

A graduate student recently harnessed the complexity of mathematical proofs to create a powerful new tool in cryptography.

Then it’s kind of a mystery to try to figure out why and how they’re related.” The Riemann hypothesis has proved to be a font ...

OpenAI has revealed a breakthrough proof that overturns a nearly 80-year-old geometry conjecture posed by Paul Erdős.

Health and Human Services Secretary Robert F. Kennedy Jr. told a Senate Finance Committee hearing on 22 April 2026 that President Donald Trump uses a 'different way' of calculating drug price ...

Physicists are making new inroads into the world of post-quantum theories, uncovering what reality may look like on a level deeper and stranger than the already infamously odd quantum theory. In the ...

The "prisoner's dilemma" is one of the most famous ideas in game theory. For decades, this game has been used to explain why selfishness often beats cooperation. In the prisoner's dilemma, two players ...

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

AI is now embedded in critical digital infrastructure and that brings serious risk. Machine learning models perform well, but their opacity and ...

Liam Price just cracked a 60-year-old problem that world-class mathematicians have tried and failed to solve. He’s 23 years old and has no advanced mathematics training. What he does have is a ChatGPT ...