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Sierpiński, A Great Master in Topology

In 1882, on 14 March, one of the great masters of topology of all time was born, the prominent Polish mathematician Wacław Sierpiński, who was born in the Polish capital, Warsaw. Although he was primarily noted for his great contributions to the mathematical branch of topology, Sierpiński was in fact a great contributor to mathematics in general, with his contributions to number theory and set theory being particularly noteworthy.

Beyond his very formal and well-defined mathematical concepts, the polish mathematician provided us with a large number of mathematical objects with unusual properties, among which the famous Sierpiński's triangle and Sierpiński's carpet stand out.

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Main Mathematical Contributions.

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• Set Theory:
  Everyone who has worked in any depth in set theory has come across the famous ‘Axiom of Choice’, a construct for which Sierpiński made an important contribution to its establishment in modern set theory. In addition, he also made contributions to the continuum hypothesis, which is also a fundamental part of set theory as we conceive it today.

  His work is closely related to that of another giant of mathematics, Georg Cantor, as Professor Waclaw also helped to develop the mathematical properties of infinite sets and cardinal numbers.

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• Topology:
  His work was fundamental to the development and establishment of point set topology. He made topological constructions of special sets and mathematical objects called fractals, which often report mathematically unusual properties and behaviour. These objects include, as mentioned above, the Sierpiński's Triangle and Sierpiński's Carpet.

A Sierpiński's Triangle

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• Number Theory:
  He made many contributions to number theory, but really Sierpiński's most outstanding work in number theory concerns the study of the properties of prime numbers and diophantine equations.

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Life and Performance.

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He developed his career as a mathematician at the University of Warsaw, where he graduated in 1904. He also became a professor at the University of Warsaw, where he excelled as a scholar and researcher, and also taught at the University of Lwów, where he also had an outstanding academic career.

He was a very active member of the Polish mathematical community of the time, where he is credited with an important role in the founding of the Warsaw school of mathematics. His mathematical work did not cease even in the times of the first two world wars, which he had to face in his native Poland, and where he had to keep working under very harsh and decadent living conditions as a consequence of both war conflicts.

Key Publications:

• ‘Hypothèse du continu' (Continuum hypothesis) (1934) :
  In this book, Sierpiński presents a fairly detailed monograph on the continuum hypothesis, exploring formulations and consequences of the continuum hypothesis, as well as the related results that follow from its application.

• 'Cardinal and Ordinal Numbers' (1958):
  This work focuses comprehensively on the study of the properties of central concepts of number theory such as cardinal and ordinal numbers, and also presents a rigorous exposition of the possible applications and properties of these types of numbers.

• 'Elementary Theory of Numbers" (1964):'
  This book is celebrated among mathematics students worldwide, as it offers a very accessible introduction to elementary number theory, covering foundational topics such as prime numbers, diophantine equations and modular arithmetic. This academic material can be used by students of formal mathematics as well as by people who approach mathematics out of curiosity or for recreational purposes.

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Finally, one can certainly see how Professor Sierpinski's work is still particularly relevant today, where we can see how these mathematical constructs remain fundamental to the structure of mathematics as we know it today. For example, his contributions to the development of fractal geometry, best known as the aforementioned Sierpiński's triangle, Sierpiński's curve and Sierpiński's carpet, have found applications in fields as diverse as computer science and art.

Note: An important fact to know is that Professor Wacław managed to publish more than 700 scientific articles during his career, which shows his commitment and extensive mathematical work.

Passed away in Warsaw, the capital of Poland, on 21 October 1969.

Your work will never be forgotten, Professor Sierpiński.

Some of His Contributions.

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A Sierpiński's Carpet

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Wacław Sierpiński Portrait Image Source

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Note: All the images related to Sierpiński Contributions are crafted by me using the text editor based on LaTeX: Beamer. Also, the plots about the Triangle and Carpet of Sierpiński shown in this post were created by me using the Wolfram language: 'Mathematica'.

'The Structure of this article is by my authorship too.'

Regards.

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References

Michael Tiefenback (1977) "Topological Genealogy", Mathematics Magazine 50(3): 158–60 doi:10.2307/2689505

Weisstein, Eric W. "Sierpiński Carpet." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SierpinskiCarpet.html

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