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An algebra of orders

Infinitely More • 17 implied HN points • 04 Feb 24
🔬 Science Mathematics Algebra Operations
  1. There is a rich algebra of orders involving operations like addition and multiplication.
  2. The disjoint sum operation creates a combined order without interactions between the two parts.
  3. The ordered sum operation combines two orders by placing one above the other, creating new orders with distinct properties.

Influential Mathematicians: Sophus Lie

Quantum Formalism • 19 implied HN points • 13 Aug 20
🔬 Science Mathematics Quantum Mechanics Symmetry Geometry Algebra
  1. Sophus Lie was a Norwegian mathematician who made significant contributions to mathematics, developing the theory of continuous transformation groups that later led to Lie groups and Lie algebras.
  2. Lie Groups and Lie Algebras, named after Sophus Lie, are essential in the Hilbert space formalism of quantum mechanics, specifically in understanding symmetry and operators in quantum systems.
  3. Although Sophus Lie did not directly contribute to quantum formalism, his mathematical work has had a profound influence on areas of mathematics that are crucial to understanding quantum mechanics.

Influential Mathematicians: Emmy Amalie Noether

Quantum Formalism • 0 implied HN points • 29 Jun 20
🔬 Science Mathematics Quantum Algebra Abstract Physics
  1. Emmy Noether, despite facing discrimination as a woman in academia, made significant contributions to mathematics and physics.
  2. Noether's work in invariant theory and abstract algebra, along with her collaborations, influenced the development of advanced algebraic tools used in treating quantum formalism.
  3. Noether played a mentorship role in shaping the career of another influential female mathematician, Grete Hermann, who made important contributions to the foundations of quantum mechanics.
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