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Georg Cantor and the Beauty of Infinity

Georg Cantor and the Beauty of Infinity

Harald Sack
On March 3, 1845, German mathematician Georg Cantor, creator of the set theory was born. Set Theory is considered the fundamental theory of mathematics. He also proved that the real numbers are “more numerous” than the natural numbers, which was quite shocking for his contemporaries that there should be different numbers of infinity. “In mathematics the art of asking questions is more valuable than solving problems.” – Georg Cantor, Doctoral thesis (1867) Youth…
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mathematics
Number Theory, Topology, and Fractals with Wacław Sierpiński

Number Theory, Topology, and Fractals with Wacław Sierpiński

Harald Sack
On March 14, 1882, Polish mathematician Wacław Franciszek Sierpiński was born. Sierpiński is known for contributions to set theory, research on the axiom of choice and the continuum hypothesis, number theory, theory of functions and topology. Three well-known fractals are named after him (the Sierpiński triangle, the Sierpiński carpet and the Sierpiński curve), as are Sierpiński numbers and the associated Sierpiński problem. Wacław Sierpiński – Early Years in Russian occupied Poland Wacław…
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mathematics
Felix Hausdorff and the Basic Principles of Set Theory

Felix Hausdorff and the Basic Principles of Set Theory

Harald Sack
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 Prussia, today Wroclaw in Poland. Hausdorff’s…
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mathematics
Giuseppe Peano and the Axiomatization of Mathematics

Giuseppe Peano and the Axiomatization of Mathematics

Harald Sack
On August 27, 1858, Italian mathematician and philosopher Giuseppe Peano was born. He is the author of over 200 books and papers, and is considered the founder of mathematical logic and set theory. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of consistency and completeness of number…
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mathematics
Every Set can be Well Ordered – Ernst Zermelo

Every Set can be Well Ordered – Ernst Zermelo

Harald Sack
On July 27, 1871, German logician and mathematician Ernst Zermelo was born. Zermelo’s work had major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem. “…self-evidence … must not be confused with … provability.” – Ernst Zermelo The Son of a Grammar School Professor Zermelo was the son of a grammar school professor and attended the…
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