Top 10 most inspiring quotes by Georg Cantor
- A false conclusion once arrived at and widely accepted is not easily dislodged and the less it is understood the more tenaciously it is held.
- The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.
- Great innovation only happens when people aren’t afraid to do things differently.
- I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.
- The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.
- Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.
- There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.
- Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.
- This view [of the infinite], which I consider to be the sole correct one, is held by only a few. While possibly I am the very first in history to take this position so explicitly, with all of its logical consequences, I know for sure that I shall not be the last!
- I entertain no doubts as to the truths of the tranfinites, which I recognized with God’s help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science.
Georg Cantor was a renowned German mathematician who lived from 1845 to 1918. He is best known for his groundbreaking work in the field of set theory and the development of the concept of infinite numbers. Cantor’s contributions to mathematics revolutionized the understanding of infinity and laid the foundation for modern mathematical analysis.
Born in Saint Petersburg, Russia, Cantor showed early aptitude in mathematics and pursued his passion by studying at the University of Berlin. He worked extensively on set theory, investigating the properties and cardinality of infinite sets. Cantor introduced the concept of a “set” and developed the notion of different sizes of infinity. He demonstrated that some infinities are larger than others, challenging the prevailing mathematical beliefs of his time.
Cantor’s work faced considerable resistance and criticism from his contemporaries, who were uncomfortable with the idea of multiple infinities. Despite the opposition, Cantor persisted and published several influential papers that solidified his position as a pioneer in the field of mathematics.
His work on set theory had profound implications for various branches of mathematics, including analysis, topology, and logic. Cantor’s discoveries laid the groundwork for further advancements in mathematics, providing a framework for understanding infinite structures and their properties.
Georg Cantor’s contributions continue to shape modern mathematics, and his ideas have influenced numerous mathematicians and philosophers. His legacy stands as a testament to the power of rigorous reasoning and exploration in pushing the boundaries of human knowledge.
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