The Classification of Finite Simple Groups is a monumental result in the field of group theory, specifically in the area of finite groups. It establishes a comprehensive framework for understanding the structure of finite simple groups, which are the building blocks of all finite groups in a manner akin to how prime numbers function in number theory.

The Harish-Chandra isomorphism is a fundamental result in the representation theory of Lie groups and Lie algebras, particularly in the context of semisimple Lie groups. It relates the spaces of invariant differential operators on a symmetric space to the space of functions on the Lie algebra of the group. More specifically, consider a semisimple Lie group \( G \) and a maximal compact subgroup \( K \).

Markov's inequality is a result in probability theory that provides an upper bound on the probability that a non-negative random variable is greater than or equal to a positive constant. The inequality is named after the Russian mathematician Andrey Markov. The statement of Markov's inequality is as follows: Let \(X\) be a non-negative random variable (i.e., \(X \geq 0\)), and let \(a > 0\) be a positive constant.

The Narasimhan-Seshadri theorem is a fundamental result in the theory of vector bundles over complex curves (or Riemann surfaces). It establishes a deep connection between the geometry of vector bundles and the representation theory of groups, particularly in the context of holomorphic vector bundles on Riemann surfaces and unitary representations of the fundamental group.

The Poincaré inequality is a fundamental result in mathematical analysis and partial differential equations. It provides a bound on the integral of a function in terms of the integral of its derivative.

The Denjoy-Wolff theorem is a result in complex analysis, particularly in the field of iterated function systems and the study of holomorphic functions. It characterizes the dynamics of holomorphic self-maps of the unit disk, specifically focusing on the behavior of iterates of such functions.

The Double Limit Theorem, often referred to in the context of limits in calculus, relates to the properties and behavior of limits involving functions of two variables.

The Unique Homomorphic Extension Theorem is a result in the field of algebra, particularly concerning rings and homomorphisms. It typically states that if you have a ring \( R \) and a subring \( S \), along with a homomorphism defined on \( S \), then there exists a unique (in the case of certain conditions) homomorphic extension of this mapping up to the whole ring \( R \).

The Whitney extension theorem is a fundamental result in the field of analysis and differential geometry, concerning the extension of functions defined on a subset of a Euclidean space to the entire space while preserving certain properties.

In computational complexity theory, a theorem typically refers to a proven statement or result about the inherent difficulty of computational problems, particularly concerning the resources required (such as time or space) for their solution.

Example: Figure "caesium-137 decay scheme"

Extensive quantities are properties of a system that depend on the amount of material or the size of the system. In other words, they are additive properties that change when the system is divided into smaller parts. Extensive quantities are proportional to the size or extent of the system. Common examples of extensive quantities include: 1. **Mass** - The total amount of matter in a system. 2. **Volume** - The amount of three-dimensional space occupied by the system.

Lagrange's identity is a mathematical formula that relates the sums of squares of two sets of variables. It is often stated in the context of inner product spaces or in terms of quadratic forms.

Free borrow on the Internet Archive: archive.org/details/inwardboundofmat0000pais/page/88/mode/2up

The book unfortunately does not cover the history of quantum mechanics very, the author specifically says that this will not be covered, the focus is more on particles/forces. But there are still some mentions.

The Nexon Computer Museum is a museum located in Seongnam, South Korea, dedicated to the history and culture of computers and gaming. Opened in 2018, it is a part of Nexon, a well-known video game company, and aims to preserve and showcase the evolution of computer technology and gaming from the 20th century to the present day.