Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish t
Illuminated letter P at the beginning of Adelard of Bath's translation of Euclid's Elements, which starts "Punctum est illud cui pars non est" (A point is that which has no part). Geometry is shown personified as a woman, following Martianus Capella's De nuptiis Philologiae et Mercurii.
This is the Ulam spiral, which illustrates the distribution of prime numbers. The dark diagonal lines in the spiral hint at the hypothesized approximate independence between being prime and being a value of a quadratic polynomial, a conjecture now known as Hardy and Littlewood's Conjecture F.
On the surface of a sphere, Euclidean geometry only applies as a local approximation. For larger scales the sum of the angles of a triangle is not equal to 180°.
Image of Problem 14 from the Egyptian Moscow Mathematical Papyrus. The problem includes a diagram indicating the dimensions of the truncated pyramid.
In the context of the philosophy of mathematics, pure mathematics is an informal term to describe the study of mathematical concepts independently of any application outside mathematics. These concept
Pure mathematics is an informal term to describe the study of the properties and structure of abstract objects, such as the Mandelbrot set. This may be done without focusing on concrete applications of concepts in the physical world.