Lie theory is a branch of mathematics that studies Lie groups and Lie algebras, which are foundational structures in various areas of mathematics and theoretical physics. Named after the Norwegian mathematician Sophus Lie, the theory originated in the study of continuous symmetries and their applications to differential equations and geometry.

Here's a list of some notable mathematicians who were born in the 19th century: 1. **Carl Friedrich Gauss** (1777–1855) - Often referred to as the "Prince of Mathematicians," he made significant contributions to many fields, including number theory, statistics, and astronomy.

Here’s a list of topics related to the history of mathematics that covers various eras, cultures, and significant developments: 1. **Ancient Mathematics** - Babylonian Mathematics - Egyptian Mathematics - Greek Mathematics (e.g., Euclid, Pythagoras, Archimedes) - Indian Mathematics (e.g., Aryabhata, Brahmagupta) - Chinese Mathematics (e.g., Liu Hui, Zhusha) 2.

Early electron diffraction experiment from 1927 that drastically confirmed the matter wave hypothesis.

The Mathematical Tables Project refers to a historical initiative primarily aimed at compiling, producing, and disseminating mathematical tables to aid in calculations and various scientific computations. One prominent example of such an effort is the "Mathematical Tables" created by mathematicians in the early to mid-20th century, often involving extensive collaborations and labor. These tables typically included values for functions such as logarithms, trigonometric functions, exponential functions, and other mathematical computations that were labor-intensive to calculate by hand.

The Mathematische Arbeitstagung, often abbreviated as MAT, is a mathematical conference that typically brings together mathematicians to discuss recent research, developments, and ideas in various fields of mathematics. The term is German for "Mathematical Working Conference." These gatherings provide a platform for sharing scientific findings, networking among researchers, and fostering collaboration in the mathematical community. Such events often feature presentations, discussions, and workshops focusing on both theoretical and applied mathematics.

The Polish School of Mathematics refers to a group of mathematicians and a specific mathematical movement that emerged in Poland in the early to mid-20th century, particularly after World War I and during the interwar period. This movement is characterized by its contributions to various branches of mathematics, including set theory, topology, functional analysis, and logic.

Pre-intuitionism is a philosophical concept primarily associated with mathematics and the foundations of mathematical logic. It is a viewpoint that emphasizes a certain type of epistemological foundation for mathematics, focused on the nature of mathematical truth and knowledge prior to the development of formal intuitionism as articulated by mathematicians like L.E.J. Brouwer. In general, intuitionism is a philosophy of mathematics that asserts that mathematical objects are constructed by the mind and that mathematical truths are not discovered but instead are created through mental processes.

Quadrature of the parabola refers to the process of finding the area under a parabolic arc. This concept was historically significant in the development of calculus and the understanding of integration. The term "quadrature" is derived from the Latin word "quadratus," meaning "square," and it essentially means finding the area (or squared measure) of a figure. The classic example involves the specific parabola described by the equation \( y = x^2 \).

Ramanujan's "lost notebook" refers to a collection of highly significant and previously unpublished mathematical results that were discovered by mathematician George Andrews in the spring of 1976. The notebook is thought to contain a wealth of results regarding partition theory, mock theta functions, and q-series, among other topics. The contents of the lost notebook include formulas and identities that have profound implications in various areas of mathematics, including number theory and combinatorics.

Raymond Clare Archibald (1875–1955) was a prominent American mathematician known for his contributions to various fields in mathematics, particularly in analysis, number theory, and mathematical education. He was a professor at Harvard University and played a significant role in developing mathematics curricula and promoting mathematical research. Archibald is also well-known for his work on mathematical bibliographies and history, and he was involved in editorial tasks for several mathematical journals.

Nuclear magnetic resonance work:

"Revolutions in Mathematics" can refer to various concepts or contexts depending on the focus. While there isn't a universally recognized book or concept with that exact title, it can generally relate to: 1. **Historical Developments**: The phrase might be used to describe significant shifts or breakthroughs in mathematics throughout history.

The Scottish Book is a concept in set theory, particularly associated with the work of the mathematician Paul Erdős. It refers to a collaborative effort among mathematicians, primarily in the context of the "Scottish Book," where various mathematicians contribute problems that are then solved or discussed by others. The idea is that the book itself is a collection of open problems, often posed in a creative or interesting way, which encourages collaboration and communication in the mathematical community.

The London Hydraulic Power Company (LHPC) was established in 1882 to provide hydraulic power to various types of machinery across London, replacing traditional steam power. The company developed a network of high-pressure water pipes throughout the city, enabling businesses and industries to access hydraulic power for applications such as cranes, lifts, and other machinery. At its peak, the system supplied power to numerous commercial enterprises, including those in construction, shipping, and manufacturing.

Gas chromatography.

Sphuṭacandrāpti is a Sanskrit term used in the context of Indian philosophy and logic, particularly in the study of epistemology and rational inquiry. The term can be broken down into two components: "Sphuṭa," meaning clear or distinct, and "candrāpti," which may refer to the attainment or realization of a quality or truth. The concept is often associated with discussions on the clarity of knowledge or cognition.

The term "Classification Theorem" can refer to various significant results in different fields of mathematics and science, so the meaning can vary depending on the context. Here are a few notable examples: 1. **Classification Theorem for Finite Groups**: In group theory, the classification of finite simple groups is a major result that categorizes all finite simple groups into several families, along with a number of exceptional groups.

Mathematical principles refer to fundamental concepts, theories, and rules that govern the field of mathematics. These principles serve as the foundation for mathematical reasoning and problem-solving. Here are some key aspects of mathematical principles: 1. **Axioms and Postulates**: These are basic statements or assumptions that are accepted without proof. They form the foundation from which other statements are derived.

"Quantity" refers to a measurable property or attribute of an object or phenomenon that can be expressed numerically. It indicates how much of something exists and can apply to a wide range of subjects, including physical objects, time, volume, weight, distance, and more. In mathematics and science, quantities can often be classified as: 1. **Scalar Quantities**: These are quantities that have magnitude only and no direction. Examples include temperature, mass, and speed.