Mathematics
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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.
Mathematical logic
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Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly address
Portrait of young Kurt Gödel as a student in Vienna, 1925
