algebra

Richard Dedekind and the Real Numbers

Richard Dedekind and the Real Numbers

On October 6, 1831, German mathematician Julius Wilhelm Richard Dedekind was born. He is known for making important contributions to abstract algebra (particularly ring theory), algebraic number theory and the foundations of the real numbers. “Numbers are the free creation of the human mind.” Richard Dedekind Richard Dedekind – Early Years Richard Dedekind, the son of the Braunschweig lawyer and university teacher Julius Dedekind, attended the Martino-Katharineum Braunschweig and studied mathematics at the Collegium…
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Carl Jacobi and the Elliptic Functions

On December 10, 1804, German mathematician Carl Gustav Jacob Jacobi was born. He made fundamental contributions to elliptic functions, dynamics, differential equations, and number theory. “Any progress in the theory of partial differential equations must also bring about a progress in Mechanics.” – Carl Jacobi, Vorlesungen über Dynamik [Lectures on Dynamics] (1842/3) Carl Jacobi – A Child Prodigy Carl Jacobi was the son of a banker and grew up in a rather…
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Felix Hausdorff and the Basic Principles of Set Theory

Felix Hausdorff and the Basic Principles of Set Theory

On November 8, 1868, German mathematician Felix Hausdorff was born. He is considered a co-founder of general topology and made significant contributions to general and descriptive set theory, measure theory, functional analysis and algebra. In addition to his profession, he also worked as a philosophical writer and literary figure under the pseudonym Paul Mongré. Felix Hausdorff – Early Years Felix Hausdorff was born in Breslau, Kingdom of Prussion, today Wroclaw in Poland. Hausdorff’s…
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William Hamilton and the Invention of Quaterions

William Hamilton and the Invention of Quaterions

On August 4, 1805, Irish physicist, astronomer, and mathematician William Rowan Hamilton was born. He made important contributions to classical mechanics, optics, and algebra, but is perhaps best known as the inventor of quaternions, a number system that extends the complex numbers. ‘This young man, I do not say will be, but is, the first mathematician of his age.’ (Astronomer Bishop Dr. John Brinkley about 18-year-old Hamilton) At Age 13 Hamilton spoke…
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Carl Friedrich Gauss – The Prince of Mathematicians

Carl Friedrich Gauss – The Prince of Mathematicians

On April 30, 1777, German mathematician and physical scientist Carl Friedrich Gauss was born. He contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics. He is often referred to as Princeps mathematicorum (Latin, “the Prince of Mathematicians”) as well as “greatest mathematician since antiquity”. “Mathematics is the Queen of Science, and Arithmetic is the Queen of Mathematics” – handed down in Wolfgang Sartorius…
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Only the Good Die Young – the Very Short Life of Évariste Galois

Only the Good Die Young – the Very Short Life of Évariste Galois

On June 1st, 1832, French mathematician Évariste Galois was killed in a duel. He was only 20 years of age. He left an elaborate manuscript three years earlier, in which he established that an algebraic equation is solvable by radicals, if and only if the group of permutations of its roots has a certain structure, thereby solving a problem standing for 350 years. But why did he have to die so young? Just because…
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Emmy Noether and the Love for Mathematics

Emmy Noether and the Love for Mathematics

On April 23, 1882, German mathematician and physicist Emmy Noether was born, who is best known for her groundbreaking contributions to abstract algebra and theoretical physics. Albert Einstein called her the most important woman in the history of mathematics, as she revolutionized the theories of rings, fields, and algebras. “My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously.” Letter to Helmut Hasse (1931)…
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Lewis Carroll – Mathematician and Creator of the Wonderland

Lewis Carroll – Mathematician and Creator of the Wonderland

On January 27, 1832, British mathematician, photographer, and children’s book author Charles Lutwidge Dodgson, better known under his pen name Lewis Carroll, creator of the stories about ‘Alice in Wonderland‘, was born. With his ability for pun, logic and fantasy he managed to captivate a wide audience. His works, known as nonsense literature, have remained popular to this day and have influenced not only children’s literature, but also writers such as James Joyce, surrealists…
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Arthur Cayley and his Love for Pure Mathematics

Arthur Cayley and his Love for Pure Mathematics

On January 26, 1895, British mathematician Arthur Cayley passed away. He was the first to define the concept of a group in the modern way and helped to found the modern British school of pure mathematics. “As for everything else, so for a mathematical theory: beauty can be perceived but not explained. “ — Arthur Cayley, President’s address (1883) to the British Association for the Advancement of Science, in [13] Arthur Cayley –…
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Sophus Lie and the Theory of Continuous Symmetry

Sophus Lie and the Theory of Continuous Symmetry

On December 17, 1842, Norwegian mathematician Sophus Lie was born. Lie largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. He made significant contributions to the theories of algebraic invariants, continuous groups of transformations and differential equations. Lie groups and Lie algebras are named after him. “In our century the conceptions substitution and substitution group, transformation and transformation group, operation and operation group,…
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