Father of the Set Theory.
On 3 March 1845, the German mathematician Georg Cantor was born in the Russian city of St. Petersburg. Cantor was a mathematician whose ideas revolutionised mathematics in his time, and who even today has ensured that his mathematical constructs give shape and structure to modern mathematics with such fundamental contributions as set theory and abstract concepts such as infinity, to name just a few of his many scientific contributions, always keeping implications even in philosophy, since the construct of infinity is really something that transcends mathematics and acquires a universalist and philosophical character.
Main Mathematical Contributions.
- Set Theory:
Cantor made an incredible development in set theory, giving us such transcendental and abstract concepts as the cardinality of sets and transfinite sets, just to mention a few of the many foundational ideas that make up set theory.
Regarding the concept of ‘infinity’, Georg Cantor proved mathematically that there are different sizes of infinities, which would prove to be a fact that would change the shape of mathematics to this day and will surely continue to do so in the future of mankind. In addition, in his definition of numerable sets, he managed to make a clear distinction between numerable and non-numerable sets, and he also managed to prove that, for example, the real numbers (|R) are not numerable.
- Transfinite Numbers:
He succeeded in giving a precise definition of transfinite numbers, which perform the task of representing the cardinality (number of elements of a set) of sets of infinite nature, and he also constructed a whole arithmetic for this type of numbers.
- Continuum Hypothesis:
This hypothesis states the non-existence of a set whose cardinality lies exactly between that of integers and real numbers.
Life and Performance.
A remarkable fact of Cantor's prodigious academic life is that he was a student of another famous mathematician, Karl Weierstrass, at the University of Berlin. By 1869 he had already obtained a doctorate in mathematics, and later began to work as a professor and researcher at the University of Halle.
But the path would not be full of roses for Georg Cantor, as he would face numerous criticisms and strong opposition from renowned colleagues of his time, due to the revolutionary nature of his theories and concepts related to infinity and its nature. Furthermore, it is said that the above led him to have problems with his mental health, suffering severe nervous breakdowns and even having to be hospitalized for periods of time in institutions for the treatment of mental health.
He was a man with a strong religious belief, and often expressed that all his work and different conceptions about infinity were a manifestation of God's will.
Key Publications:
Articles published in the Journal 'Mathematische Annalen'.
The following two articles are fundamental for understanding the work presented by Cantor: 'Beiträge zur Begründung der transfiniten Mengenlehre' (Contributions to the foundation of the theory of transfinite sets) (1895-1897) and 'Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen' (On a property of the collection of all real algebraic numbers) (1874).
Finally, we can say with complete confidence that Cantor was a visionary of mathematics and science in general, whose work contributed essential pieces to the advancement of universal knowledge of humanity, giving us concepts as brilliant and useful as infinity and sets and their multiple natures. Despite all the opposition he faced, he never gave up on the task of making known his constructs and theories that ultimately ended up forging the way in which modern mathematics is conceived.
Georg Cantor Passed away a January 06 - 1918, on the city of Halle - Germany.
Some of His Contributions.
Note: All the images related to Georg Cantor Contributions are crafted by me using the text editor based on LaTeX: Beamer. The Structure of this article is by my authorship too.
Regards.
References
Weisstein, Eric W. "Cantor's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CantorsTheorem.html
Yaqub, Aladdin M. (24 October 2014). An Introduction to Metalogic. Broadview Press. ISBN 978-1-4604-0244-3.
Lawrence Paulson (1992). Set Theory as a Computational Logic (PDF). University of Cambridge Computer Laboratory.
Excellent work! Your dedication to creating quality content is evident. Thank you for making Hive a more interesting place.
Exploring blockchain games can be confusing at first. Follow us, delegate voting power, and vote for content. It's the best way to learn and grow without risks.
Hey thanks a lot, mates for the support :)
The rewards earned on this comment will go directly to the people( @paultactico2 ) sharing the post on Reddit as long as they are registered with @poshtoken. Sign up at https://hiveposh.com. Otherwise, rewards go to the author of the blog post.
Thanks for your contribution to the STEMsocial community. Feel free to join us on discord to get to know the rest of us!
Please consider delegating to the @stemsocial account (85% of the curation rewards are returned).
You may also include @stemsocial as a beneficiary of the rewards of this post to get a stronger support.