Singularity theory

Transhumanism is a philosophical movement that advocates the enhancement of the human condition by developing and making widely available new and future technologies to enhance longevity, cognition, and well-being. Influenced by seminal works of science fiction, the transhumanist vision of a transformed future humanity has many supporters and detractors from a wide range of perspectives, including philosophy and religion. Some critics argue that transhumanism amounts to little more than a "rebranding" of eugenics.

matrix of second derivatives

in calculus, the points of an equation where the derivative is zero

area of mathematics

point on a curve where a moving point on the curve must start to move backward

where the curve is not given by a smooth embedding of a parameter

mathematics term

thumb|right|An acnode at the origin (curve described in text)

theorem that the set of the critical values of a smooth function has measure zero

three dimensions self-intersecting surface

point of an algebraic variety without a defined tangent space

operation that takes a differentiable function f and produces a polynomial, the truncated Taylor polynomial of f, at each point of its domain

branch of mathematics which studies the limit cases of manifold structures

painting by Salvador Dalí

intersection of a small sphere around the origin with the singular hypersurface defined by x₁^k₁ + … + xₙ^kₙ = 0

Function in image processing

thumb|right|214px|A tacnode at the origin of the curve defined by (x^2+y^2-3x)^2 - 4x^2(2-x) = 0.