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Stefan Banach and Modern Function Analysis

Stefan Banach and Modern Function Analysis

Harald Sack
On March 30, 1892, Polish mathematician Stefan Banach was born. One of the founders of modern functional analysis, he is generally considered one of the world’s most important and influential 20th-century mathematicians. Some of the notable mathematical concepts that bear Banach‘s name include Banach spaces, Banach algebras, the Banach–Tarski paradox, the Hahn–Banach theorem, the Banach–Steinhaus theorem, the Banach-Mazur game, the Banach–Alaoglu theorem, and the Banach fixed-point theorem. “A mathematician is a person…
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mathematics
Bernard Bolzano and the Theory of Knowledge

Bernard Bolzano and the Theory of Knowledge

Harald Sack
On October 5, 1781, Bohemian mathematician, logician, philosopher, theologian and Catholic priest of Italian extraction Bernard Bolzano was born. Bolzano made significant contributions to both mathematics and the theory of knowledge. He provided a more detailed proof for the binomial theorem and suggested the means of distinguishing between finite and infinite classes. His major work, Wissenschaftslehre (1837), contains various contributions to logic and semantics concerning the relations of compatibility, derivability, and consequence,…
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mathematics
Bernhard Riemann’s innovative approaches to Geometry

Bernhard Riemann’s innovative approaches to Geometry

Harald Sack
On September 17, 1826, influential German mathematician Bernhard Riemann was born. Riemann‘s profound and novel approaches to the study of geometry laid the mathematical foundation for Albert Einstein’s theory of relativity. He also made important contributions to the theory of functions, complex analysis, and number theory. “Nevertheless, it remains conceivable that the measure relations of space in the infinitely small are not in accordance with the assumptions of our geometry [Euclidean geometry],…
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mathematics
Vito Volterra and Functional Analysis

Vito Volterra and Functional Analysis

Harald Sack
On May 3, 1860, Italian mathematician and physicist Vito Volterra was born. He is known for his contributions to mathematical biology and integral equations. Moreover, he is considered as one of the founders of functional analysis. “Empires die, but Euclid’s theorems keep their youth forever” — Vito Volterra Youth and Education Vito Volterra was born in Ancona, then part of the Papal States, as son of Abramo Volterra, a cloth merchant, into…
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mathematics
Augustin-Louis Cauchy and the Rigor of Analysis

Augustin-Louis Cauchy and the Rigor of Analysis

Harald Sack
On August 21, 1789, French mathematician Augustin-Louis Cauchy was born. He is considered one of the greatest mathematicians during the nineteenth century. There are 16 concepts and theorems named for Cauchy, more than for any other mathematician. Cauchy was one of the most prolific mathematicians of all times. Cauchy wrote 789 papers, a quantity exceeded only by Euler and Cayley, which brought precision and rigor to mathematics. Cauchy throughout my Maths Lectures…
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astronomy
Carl Friedrich Gauss – The Prince of Mathematicians

Carl Friedrich Gauss – The Prince of Mathematicians

Harald Sack
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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mathematics
Karl Weierstrass – the Father of Modern Analysis

Karl Weierstrass – the Father of Modern Analysis

Harald Sack
On February 19, 1897, German mathematician Karl Theodor Wilhelm Weierstrass passed away. Weierstrass often is cited as the “father of modern analysis“. He formalized the definition of the continuity of a function, proved the intermediate value theorem and the Bolzano–Weierstrass theorem, and used the latter to study the properties of continuous functions on closed bounded intervals. “… it is true that a mathematician who is not somewhat of a poet, will never be a…
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