Apple’s recent AI research paper, “The Illusion of Thinking”, has been making waves, but not everyone agrees with its conclusion.

A rare and bewildering intermediate between crystal and glass can be the most stable arrangement for some combinations of ...

Quantum gravity research aims to merge general relativity and quantum mechanics, potentially reshaping our understanding of ...

In this week‘s Friday Philosophy, Dr. David Gordon looks at the methodology of Timothy Williamson. While Williamson might not ...

The Persian mathematician Kamal al-Din al-Farisi formulated the fundamental theorem of arithmetic, which states that any positive integer larger than one can be expressed uniquely as a product of ...

Dot Physics The Fundamental Theorem of Calculus; Integrals as Anti-Derivatives Posted: May 19, 2025 | Last updated: May 19, 2025 Physics and Python stuff. Most of the videos here are either ...

Charles Hermite called it a “deplorable evil.” To understand why Weierstrass’ result was so unnerving, it helps to first understand two of the most fundamental concepts in calculus: continuity and ...

He believed that Pythagoras’ theorem is so fundamental to trigonometry ... with an infinite sequence of smaller triangles and use calculus to find the lengths of the larger triangle’s sides.

Many mathematicians over the years have proved the theorem using algebra and geometry. Yet proving it using trigonometry was long thought impossible, as the fundamental formulae of trigonometry ...

Many mathematicians over the years have proved the theorem using algebra and geometry. Yet proving it using trigonometry was long thought impossible, as the fundamental formulae of trigonometry ...

The techniques he developed in the field of complex numbers have found use in tackling a wide range of fundamental equations ... extending the mathematics of calculus, died on Sept.