The Kleene fixed-point theorem is a fundamental result in theoretical computer science and mathematical logic, particularly in the context of domain theory and functional programming. Named after Stephen Cole Kleene, it provides a framework for understanding the existence of fixed points in certain types of functions. In simple terms, a fixed point of a function \( f \) is a value \( x \) such that \( f(x) = x \).

Spijker's lemma is a result in functional analysis, specifically dealing with the properties of bounded linear operators on Banach spaces. The lemma provides conditions under which certain sequences of bounded linear operators exhibit specific convergence properties. While Spijker's lemma does not have one widely acknowledged statement applicable in all contexts, it typically relates to convergence properties in the context of compact operators or the spectral theory of linear operators.

Manjul Bhargava is an Indian-American mathematician known for his significant contributions to number theory, particularly in the areas of algebraic number theory and arithmetic geometry. He was born on August 8, 1974, in Hamilton, Ontario, Canada, and later moved to the United States. Bhargava gained widespread recognition for his work on the geometry of numbers and the distribution of algebraic numbers.

Andrew Wiles's proof of Fermat's Last Theorem, completed in 1994, is a profound development in number theory that connects various fields of mathematics, particularly modular forms and elliptic curves. Fermat's Last Theorem states that there are no three positive integers \(a\), \(b\), and \(c\) such that \(a^n + b^n = c^n\) for any integer \(n > 2\).

The Rubik's Cube is a 3D combination puzzle that was invented in 1974 by Hungarian architect and professor Ernő Rubik. It consists of a cube made up of smaller cubes, with six faces, each of a different solid color. The objective is to twist and turn the rows and columns of smaller cubes until each face of the larger cube is a single solid color.

"Measuring the World" is a historical novel written by the German author Daniel Kehlmann, first published in 2005. The book tells the story of two prominent figures from the Age of Enlightenment: the Prussian mathematician and geodesist Carl Friedrich Gauss and the naturalist Alexander von Humboldt. The narrative intertwines their lives and work in the late 18th and early 19th centuries, focusing on their respective quests to measure and understand the world around them.

Skewb is a type of twisty puzzle that is similar to a Rubik's Cube but has a distinctive mechanism and a unique way of being solved. Instead of rotating layers like the classic 3x3 cube, the Skewb rotates around its corners, with the rotational axes located at the corners of the cube. The Skewb puzzle is generally shaped like a cube, but it can be scrambled and solved by turning the corners, which creates a different kind of challenge.

Yoshimoto Cube is a type of puzzle that consists of a geometric shape made up of several smaller pieces, typically featuring a unique design that allows for multiple configurations. It was created by Japanese puzzle designer and artist Akira Yoshimoto. The puzzle can be manipulated to form various three-dimensional shapes, providing both a challenge and a visual appeal. The Yoshimoto Cube is known for its aesthetic qualities in addition to its functionality as a puzzle.

In mathematics, particularly in the fields of topology and differential geometry, the term "submersion" refers to a specific type of smooth map between differentiable manifolds. A smooth map \( f: M \to N \) is called a submersion at a point \( p \in M \) if its differential \( df_p: T_pM \to T_{f(p)}N \) is surjective.

Cybiko is a brand of handheld wireless communication devices that were popular in the early 2000s. It was designed for teenagers and featured various functions, including messaging, gaming, and basic internet capabilities. The devices had a small form factor, resembling a cross between a pager and a handheld gaming console. Cybiko devices operated on a proprietary wireless network, allowing users to connect with each other for messaging and multiplayer games within a limited range.

FireChat is a messaging application that allows users to communicate even without an internet connection or a mobile network. It uses mesh networking technology, which enables devices to connect directly to each other via Bluetooth and Wi-Fi. This means that users can send messages to others nearby, and the app relays messages through nearby devices, effectively creating a decentralized communication network. FireChat gained attention during events where traditional communication networks were overwhelmed or unavailable, such as protests or natural disasters.

Z-Wave is a wireless communication protocol designed for home automation and smart home devices. It operates on a low-energy, low-frequency radio signal, making it well-suited for control and monitoring applications in residential environments. Here are some key features and characteristics of Z-Wave: 1. **Mesh Networking**: Z-Wave devices form a mesh network, where each device can communicate with others within range. This allows for extended coverage and improved reliability, as signals can hop from one device to another.

Sucharit Sarkar is a name associated with the field of astrophysics and astronomy, particularly known for contributions in cosmology and theoretical physics. However, the details about his work or background may not be widely recognized in public domains.

The Trisectrix of Maclaurin is a specific mathematical curve that is notable for its property of trisecting angles. In polar coordinates, it can be expressed as a curve defined by the equation: \[ r = a \cdot \theta \] where \( r \) is the distance from the origin, \( \theta \) is the angle in polar coordinates, and \( a \) is a constant.

Hilbert's fifth problem is one of the famous problems posed by the mathematician David Hilbert in his list of 23 unsolved problems presented in 1900. The fifth problem specifically concerns the characterization of continuous transformations and their relation to group theory, particularly the concept of topological groups.

Double-negation translation is a concept primarily associated with the field of logic and philosophy, particularly in relation to the principles of translation between different logical systems or languages. It often comes into play when discussing how to interpret and translate statements, particularly those involving negation, across systems that might have different rules or structures. In simple terms, double-negation translation refers to the process of translating a negation (not P) in a way that uses two negations to clarify or preserve meaning.

Michael Dummett (1925–2011) was a prominent British philosopher known for his work in philosophy of language, philosophy of mathematics, and metaphysics, as well as for his contributions to the study of logic and epistemology. He was particularly influential in the development of anti-realism in the philosophy of language, which argues that the meaning of statements is tied to their language and use rather than to an independent reality.

Stephen Cole Kleene (1909–1994) was an American mathematician and logician who made significant contributions to the fields of mathematical logic, recursion theory, and theoretical computer science. He is renowned for his work in the areas of automata theory and formal languages. Kleene is particularly well-known for developing the concept of regular sets and regular expressions, which are essential in the theory of computation.

Lancelot Hogben (1895–1975) was a British biologist, statistician, and author known for his contributions to science and education in the mid-20th century. He was particularly influential in promoting the use of statistics in biology and the social sciences. Hogben advocated for the importance of scientific literacy and popularized complex scientific concepts through accessible writing.

The concept of "necessity of identity" can be understood in different contexts, particularly in philosophy, psychology, sociology, and other fields. Here are a few interpretations: 1. **Philosophical Context**: In philosophy, particularly in metaphysics, identity refers to the concept of what it means for something to be the same as itself. The necessity of identity involves discussions about the nature of objects, individuals, and their properties.