The original version of this story appeared in Quanta Magazine. The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the ...

A newly published proof demonstrates that perfect alignment between advanced AI systems and human goals is unattainable due to fundamental computational constraints. Drawing on Gödel’s incompleteness ...

Since the start of the 20th century, the heart of mathematics has been the proof — a rigorous, logical argument for whether a given statement is true or false. Mathematicians’ careers are measured by ...

A mathematician will turn a groundbreaking 100-page proof into computer code. The proof tool, Lean, lets users turn proofs written in prose into rules and logic for testing. Kevin Buzzard already uses ...

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The one source of truth is mathematics. Every statement is a pure logical deduction from foundational axioms, resulting in absolute certainty. Since Andrew Wiles proved Fermat’s Last Theorem, you’d be ...

In a digital era plagued by growing privacy concerns and eroding institutional trust, the power to prove something without disclosing sensitive data is not merely an academic exercise—it's a ...

Forbes contributors publish independent expert analyses and insights. Dr. Lance B. Eliot is a world-renowned AI scientist and consultant. In today’s column, I examine an insightful AI research study ...

For four decades, a quiet boundary in pure mathematics kept a powerful theorem locked inside the safe world of finite quantities. Now a new result known as Sebestyen’s theorem has pushed that boundary ...