Carl Sagan (1934–1996) was an American astrophysicist, cosmologist, author, and science communicator renowned for his work in popularizing science and making complex scientific concepts accessible to the general public. He played a pivotal role in the development of planetary science and was involved in numerous space missions, including those to Mars and the Voyager missions.

Grigory Shajn (or Grigoriy Shayn) is not widely recognized in mainstream sources, and there may be some ambiguity regarding the name. Historically, Grigory Shajn is a name associated with sciences, particularly in fields like astronomy or other scientific research.

Jacob ben Machir ibn Tibbon, often referred to simply as Jacob ibn Tibbon, was a medieval Jewish scholar, physician, and translator who lived in the 13th century, around the years 1236-1300. He was part of a prominent family of Jewish translators from Provence, France, and is especially known for his work in translating and interpreting philosophical and scientific texts from Arabic to Hebrew.

"Twilight of the Idols," also known as "Twilight of the Idols, or: How to Philosophize with a Hammer," is a philosophical work by the German philosopher Friedrich Nietzsche, published in 1888. This essay is one of Nietzsche's later works and serves as a critical examination of various philosophical and moral concepts prevalent in Western thought.

Joseph Solomon Delmedigo (1591–1655) was a notable figure in the fields of philosophy, mathematics, and science during the early modern period. He was born in Crete and later moved to Italy, where he became involved in the intellectual circles of the time. Delmedigo was known for his work in mathematics, particularly his interest in the mathematical sciences and astronomy, and he corresponded with several prominent thinkers of his time.

Jigsaw puzzle manufacturers are companies that produce jigsaw puzzles, which are puzzles consisting of oddly shaped interlocking pieces that, when assembled, form a complete picture or design. These manufacturers create puzzles in a variety of themes, difficulties, sizes, and materials to appeal to different audiences, from children to adults. Some well-known jigsaw puzzle manufacturers include: 1. **Ravensburger**: A German company known for high-quality puzzles with unique pieces and a wide range of images.

The 2023 World Jigsaw Puzzle Championship is an annual competitive event where participants from various countries come together to compete in assembling jigsaw puzzles. This championship typically involves teams and individuals racing against the clock to complete puzzles in the shortest time possible. The event may include various categories and types of puzzles, showcasing not only speed but also teamwork and puzzle-solving skills.

"Works by John Dewey" typically refers to the extensive body of writings by John Dewey, an influential American philosopher, psychologist, and educational reformer associated with pragmatism and progressive education. Dewey's work spans a wide array of topics, including philosophy, education, psychology, and social theory.

The ATLAS of Finite Groups is a comprehensive reference work that provides detailed information on the finite simple groups and their characteristics. Published in 1986 by Daniel G. Higman, John Conway, and Robert W. Curtis, the ATLAS is significant in the field of group theory, particularly in the classification of finite groups.

Conway algebra refers to a mathematical framework developed by the British mathematician John Horton Conway. It is closely associated with the structure known as the "Conway group," which is part of a broader study of symmetries in higher-dimensional spaces. One of the most notable aspects of Conway's work is his exploration of algebraic systems that connect to geometrical and combinatorial structures.

The Conway base 13 function is a part of a broader family of base-n functions introduced by mathematician John Horton Conway. The most widely recognized version of the function is often referred to in the context of a notation for representing numbers in sequences or functions. In Conway's system, numbers are represented as tuples, and the behavior of the functions can be somewhat complex because they define values in a non-standard numeral system that allows for certain properties, such as self-similarity and recursive relationships.

The Conway group \( Co_2 \) is one of the sporadic simple groups in group theory, which is a branch of abstract algebra. Specifically, it is one of the 26 sporadic groups that do not fit into any of the infinite families of simple groups.

The Conway puzzle often refers to the game "Conway's Game of Life," which is a cellular automaton devised by mathematician John Horton Conway in 1970. It is not a puzzle in the traditional sense but rather a mathematical simulation involving a grid of cells that can live, die, or multiply based on a set of rules. In the Game of Life, each cell in an infinite grid can be in one of two states: "alive" or "dead.

Von Neumann–Bernays–Gödel (NBG) set theory is a foundational system for mathematics that extends Zermelo-Fraenkel set theory (ZF) by incorporating classes, which are collections of sets that can be too large to be sets themselves. NBG is often considered a more expressive framework than ZF, while still being able to avoid certain paradoxes that can arise in naive set theories.

Monstrous moonshine is a term used in mathematics, specifically in the field of modular forms and algebraic geometry. It refers to a surprising and deep connection between the monster group, which is the largest of the sporadic finite simple groups, and modular functions. The term was introduced by mathematician Richard Borcherds in the context of his work on the representation theory of the monster group.

John Rawls was a prominent American philosopher best known for his contributions to moral and political philosophy. His most influential work is "A Theory of Justice," published in 1971, where he introduces key concepts such as the "original position," "veil of ignorance," and the "difference principle." **Key Works of John Rawls:** 1.

The "original position" is a theoretical construct used in political philosophy, particularly by the American philosopher John Rawls in his work "A Theory of Justice." It is a thought experiment designed to determine the principles of justice that should govern a just society. In the original position, individuals are imagined to be in a hypothetical situation where they are behind a "veil of ignorance.

The Middle-square method is an early algorithm used for generating pseudorandom numbers. It was introduced by the mathematician John von Neumann in the 1940s. The basic idea of the method is to take the square of a number, and then extract the middle digits of the result to form a new number. This new number can then be squared again, and the process can be repeated to generate a sequence of pseudorandom numbers.

Additive K-theory is a branch of algebraic K-theory that focuses on understanding certain additive invariants associated with rings and categories. It can be thought of as a refinement of classical K-theory, emphasizing the structured behavior of additive operations. In general, K-theory studies vector bundles, projective modules, and their relations to the topology of the underlying spaces or algebraic structures.

The Steinberg group, often denoted as \( S_n(R) \), arises in the context of algebraic K-theory and the study of linear algebraic groups, particularly over a commutative ring \( R \). More specifically, the term is typically associated with the special linear group and its associated K-theory.